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Go Math Grade 6 Chapter 4 Model Ratios Answer Key

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Lesson 1: Investigate • Model Ratios

• Model Ratios – Page No. 213
• Model Ratios – Page No. 214
• Model Ratios – Page No. 215
• Model Ratios Lesson Check – Page No. 216

Lesson 2: Ratios and Rates

• Ratios and Rates – Page No. 219
• Ratios and Rates – Page No. 220
• Ratios and Rates – Page No. 221
• Ratios and Rates Lesson Check – Page No. 222

Lesson 3: Equivalent Ratios and Multiplication Tables

• Equivalent Ratios and Multiplication Tables – Page No. 225
• Equivalent Ratios and Multiplication Tables – Page No. 226
• Equivalent Ratios and Multiplication Tables – Page No. 227
• Equivalent Ratios and Multiplication Tables Lesson Check – Page No. 228

Lesson 4: Problem Solving • Use Tables to Compare Ratios

• Use Tables to Compare Ratios – Page No. 231
• Use Tables to Compare Ratios – Page No. 232
• Use Tables to Compare Ratios – Page No. 233
• Use Tables to Compare Ratios Lesson Check – Page No. 234

Lesson 5: Algebra • Use Equivalent Ratios

• Use Equivalent Ratios – Page No. 237
• Use Equivalent Ratios – Page No. 238
• Use Equivalent Ratios – Page No. 239
• Use Equivalent Ratios Lesson Check – Page No. 240

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Page No. 241
• Mid-Chapter Checkpoint – Page No. 242

Lesson 6: Find Unit Rates

• Find Unit Rates – Page No. 245
• Find Unit Rates – Page No. 246
• Find Unit Rates – Page No. 247
• Find Unit Rates Lesson Check – Page No. 248

Lesson 7: Algebra • Use Unit Rates

• Use Unit Rates – Page No. 251
• Use Unit Rates – Page No. 252
• Use Unit Rates – Page No. 253
• Use Unit Rates Lesson Check – Page No. 254

Lesson 8: Algebra • Equivalent Ratios and Graphs

• Equivalent Ratios and Graphs – Page No. 257
• Equivalent Ratios and Graphs – Page No. 258
• Equivalent Ratios and Graphs – Page No. 259
• Equivalent Ratios and Graphs Lesson Check – Page No. 260

Chapter 4 Review/Test

• Review/Test – Page No. 261
• Review/Test – Page No. 262
• Review/Test – Page No. 263
• Review/Test – Page No. 264
• Review/Test – Page No. 265
• Review/Test – Page No. 266

Share and Show – Page No. 213

Write the ratio of yellow counters to red counters.

Question 1.

Type below:
___________

Answer:
1: 2

Explanation:
There are one yellow counter and two red counters.
So, the ratio is 1:2

Question 2.

Type below:
___________

Answer:
5: 3

Explanation:
There are 5 yellow counter and 3 red counters.
So, the ratio is 5:3

Draw a model of the ratio.

Question 3.
3 : 2
Type below:
___________

Answer:

Explanation:
As the ratio is 3:2, we can draw three yellow counters and 2 red counters.

Question 4.
1 : 5
Type below:
___________

Answer:

Explanation:
As the ratio is 1:5, we can draw 1 yellow counter and 5 red counters.

Use the ratio to complete the table.

Question 5.
Wen is arranging flowers in vases. For every 1 rose she uses, she uses 6 tulips. Complete the table to show the ratio of roses to tulips.

Type below:
___________

Answer:

Explanation:
There is 1 box for every 6 Tulips.
The ratio is 1 : 6.
Each time the number of boxes increases by 1, the number of Tulips increases by 6
So, for 2 boxes, 6 + 6 = 12 Tulips
For 3 boxes, 12 + 6 = 18 Tulips
For 4 boxes, 18 + 6 = 24 Tulips

Question 6.
On the sixth-grade field trip, there are 8 students for every 1 adult. Complete the table to show the ratio of students to adults.

Type below:
___________

Answer:

Explanation:
There is 1 adult out of 8 Students.
The ratio is 8:1.
Each time the number of students increases double, the number of adults becomes double.
So, for 8 + 8 = 16 students, 2 Adults available
For 16 + 8 = 24 students, 2 + 1 = 3 Adults available
For 24 + 8 = 32 students, 3 + 1 = 4 Adults available

Question 7.
Zena adds 4 cups of flour for every 3 cups of sugar in her recipe. Draw a model that compares cups of flour to cups of sugar.
Type below:
___________

Answer:

Explanation:
Zena adds 4 cups of flour for every 3 cups of sugar in her recipe.
For every 3 cups of sugar, she adds 4 cups of flour.
For 6 cups of sugar, she adds 8 cups of flour
For 9 cups of sugar, she adds 12 cups of flour
For 12 cups of sugar, she adds 16 cups of flour

Draw Conclusions – Page No. 214

The reading skill draw conclusions can help you analyze and make sense of information.

Hikers take trail mix as a snack on long hikes because it is tasty, nutritious, and easy to carry. There are many different recipes for trail mix, but it is usually made from different combinations of dried fruit, raisins, seeds, and nuts. Tanner and his dad make trail mix that has 1 cup of raisins for every 3 cups of sunflower seeds.

Question 8.
Model Mathematics Explain how you could model the ratio that compares cups of raisins to cups of sunflower seeds when Tanner uses 2 cups of raisins.
Type below:
___________

Answer:

Explanation:
Hikers take trail mix as a snack on long hikes because it is tasty, nutritious, and easy to carry. There are many different recipes for trail mix, but it is usually made from different combinations of dried fruit, raisins, seeds, and nuts. Tanner and his dad make trail mix that has 1 cup of raisins for every 3 cups of sunflower seeds.
For 2 cups of raisins, he needs 3 + 3 = 6 cups of sunflower seeds

The table shows the ratio of cups of raisins to cups of sunflower seeds for different amounts of trail mix. Model each ratio as you complete the table.

Question 9.
Describe the pattern you see in the table.
Type below:
___________

Answer:
Multiply Raisins by 3 to get number of Sunflower Seeds.

Question 10.
Draw Conclusions What conclusion can Tanner draw from this pattern?
Type below:
___________

Answer:
He needs 3 times as many seeds as raisins

Question 11.
What is the ratio of cups of sunflower seeds to cups of trail mix when Tanner uses 4 cups of raisins?
Type below:
___________

Answer:
4:12

Explanation:
If tanner uses 4 cups of raisins, he needs 12 cups of sunflower seeds.

Model Ratios – Page No. 215

Write the ratio of gray counters to white counters.

Question 1.

Type below:
___________

Answer:
3:4

Explanation:
There are 3 gray counter and 4 white counters.
So, the ratio is 3:4

Question 2.

Type below:
___________

Answer:
4:1

Explanation:
There are 4 gray counter and 1 white counter.
So, the ratio is 4:1

Question 3.

Type below:
___________

Answer:
2:3

Explanation:
There are 2 gray counter and 3 white counters.
So, the ratio is 2:3

Draw a model of the ratio.

Question 4.
5 : 1
Type below:
___________

Answer:

Explanation:
As the ratio is 5:1, we can draw 5 yellow counters and 1 red counter.

Question 5.
6 : 3
Type below:
___________

Answer:

Explanation:
As the ratio is 6:3, we can draw 6 yellow counters and 3 red counters.

Use the ratio to complete the table.

Question 6.
Marc is assembling gift bags. For every 2 pencils he places in the bag, he uses 3 stickers. Complete the table to show the ratio of pencils to stickers.

Type below:
___________

Answer:

Explanation:
Marc is assembling gift bags. For every 2 pencils he places in the bag, he uses 3 stickers.
For 4 pencils, he uses 3 + 3 = 6 stickers
For 6 pencils, he uses 6 + 3 = 9 stickers
For 8 pencils, he uses 9 + 3 = 12 stickers

Question 7.
Singh is making a bracelet. She uses 5 blue beads for every 1 silver bead. Complete the table to show the ratio of blue beads to silver beads

Type below:
___________

Answer:

Explanation:
Singh is making a bracelet. She uses 5 blue beads for every 1 silver bead.
For 2 silver bead, she uses 5 + 5 = 10 blue beads.
For 3 silver bead, she uses 10 + 5 = 15 blue beads.
For 4 silver bead, she uses 15 + 5 = 20 blue beads.

Problem Solving

Question 8.
There are 4 quarts in 1 gallon. How many quarts are in 3 gallons?
______ quarts

Answer:
12 quarts

Explanation:
There are 4 quarts in 1 gallon. If there are 3 gallons, he uses 3 × 4 = 12 quarts

Question 9.
Martin mixes 1 cup lemonade with 4 cups cranberry juice to make his favorite drink. How much cranberry juice does he need if he uses 5 cups of lemonade?
______ cups

Answer:
20 cups

Explanation:
Martin mixes 1 cup lemonade with 4 cups cranberry juice to make his favorite drink. If he uses 5 cups of lemonade, 5 × 4 = 20 cups

Question 10.
Suppose there was 1 centerpiece for every 5 tables. Use counters to show the ratio of centerpieces to tables. Then make a table to find the number of tables if there are 3 centerpieces.
Type below:
___________

Answer:

Explanation:
Suppose there was 1 centerpiece for every 5 tables.
If there are 3 centerpieces, 5 × 3 = 15 tables

Lesson Check – Page No. 216

Question 1.
Francine is making a necklace that has 1 blue bead for every 6 white beads. How many white beads will she use if she uses 11 blue beads?
______ white beads

Answer:
66 white beads

Explanation:
Francine is making a necklace that has 1 blue bead for every 6 white beads.
11 × 6 = 66 white beads

Question 2.
A basketball league assigns 8 players to each team. How many players can sign up for the league if there are 24 teams?
______ players

Answer:
192 players

Explanation:
A basketball league assigns 8 players to each team.
If there are 24 teams, 24 × 8 = 192 players to each team

Spiral Review

Question 3.
Louis has 45 pencils and 75 pens to divide into gift bags at the fair. He does not want to mix the pens and pencils. He wants to place an equal amount in each bag. What is the greatest number of pens or pencils he can place in each bag?
______

Answer:
Louis can form at most 15 bags, each of them will contain 3 pencils and 5 pens.

Explanation:
Louis has 45 pencils and 75 pens to divide into gift bags at the fair. He does not want to mix the pens and pencils. He wants to place an equal amount in each bag.
Factor both these numbers:
45 = 3·3·5;
75 = 3·5·5.
The greatest common factor (write all common factors and multiply them) is 3·5=15. Then:
45=15·3;
75=15·5.
Louis can form at most 15 bags, each of them will contain 3 pencils and 5 pens.

Question 4.
Of the 24 students in Greg’s class, \(\frac{3}{8}\) ride the bus to school. How many students ride the bus?
______ students

Answer:
9 students

Explanation:
Of the 24 students in Greg’s class, \(\frac{3}{8}\) ride the bus to school.
3/8 x 24= 9

Question 5.
Elisa made 0.44 of the free throws she attempted. What is that amount written as a fraction in simplest form?
\(\frac{□}{□}\)

Answer:
\(\frac{11}{25}\)

Explanation:
Elisa made 0.44 of the free throws she attempted.
0.44 = 44/100
44/100 = 22/50 = 11/25
11/25

Question 6.
On a coordinate plane, the vertices of a rectangle are (–1, 1), (3, 1), (–1, –4), and (3, –4). What is the perimeter of the rectangle?
______ units

Answer:
18 units

Explanation:
On a coordinate plane, the vertices of a rectangle are (–1, 1), (3, 1), (–1, –4), and (3, –4).
|-1| = 1
The distance from (–1, 1), (3, 1) is 1 + 0 + 0 + 3 = 4
|-4| = 4
The distance from (3, 1), (3, –4) is 1 + 0 + 0 + 4 = 5
perimeter of the rectangle = 4 + 5 + 5 + 4 = 18

Share and Show – Page No. 219

Question 1.
Write the ratio of the number of red bars to blue stars.

\(\frac{□}{□}\)

Answer:
\(\frac{8}{3}\)

Explanation:
There are 8 stars and 3 red boxes.
So, the ratio is 8:3

Write the ratio in two different ways.

Question 2.
8 to 16
Type below:
___________

Answer:
\(\frac{8}{16}\)
8:16

Explanation:
8 to 16 as a fraction 8/16
8 to 16 with a colon 8:16

Question 3.
\(\frac{4}{24}\)
Type below:
___________

Answer:
4 to 24
4:24

Explanation:
\(\frac{4}{24}\) using words 4 to 24
\(\frac{4}{24}\) with a colon 4:24

Question 4.
1 : 3
Type below:
___________

Answer:
1 to 3
\(\frac{1}{3}\)

Explanation:
1 : 3 using words 1 to 3
1 : 3 as a fraction 1/3

Question 5.
7 to 9
Type below:
___________

Answer:
\(\frac{7}{9}\)
7:9

Explanation:
7 to 9 as a fraction 7/9
7 to 9 with a colon 7:9

Question 6.
Marilyn saves $15 per week. Complete the table to find the rate that gives the amount saved in 4 weeks. Write the rate in three different ways.

Type below:
___________

Answer:

Explanation:
Marilyn saves $15 per week.
for 4 weeks, $15 × 4 = $60

On Your Own

Write the ratio in two different ways.

Question 7.
\(\frac{16}{40}\)
Type below:
___________

Answer:
16 to 40
16:40

Explanation:
\(\frac{16}{40}\) using words 16 to 40
\(\frac{16}{40}\) with a colon 16:40

Question 8.
8 : 12
Type below:
___________

Answer:
8 to 12
\(\frac{8}{12}\)

Explanation:
8 : 12 using words 8 to 12
8 : 12 as a fraction \(\frac{8}{12}\)

Question 9.
4 to 11
Type below:
___________

Answer:
\(\frac{4}{11}\)
4:11

Explanation:
4 to 11 as a fraction \(\frac{4}{11}\)
4 to 11 with a colon 4:11

Question 10.
2 : 13
Type below:
___________

Answer:
2 to 13
\(\frac{2}{13}\)

Explanation:
2 : 13 using words 2 to 13
2 : 13 as a fraction \(\frac{2}{13}\)

Question 11.
There are 24 baseball cards in 4 packs. Complete the table to find the rate that gives the number of cards in 2 packs. Write this rate in three different ways.

Type below:
___________

Answer:

Explanation:
There are 24 baseball cards in 4 packs.
For 2 packs, (2 × 24)/4 = 12
For 1 pack, (1× 24)/4 = 6

Question 12.
Make Connections Explain how the statement “There is \(\frac{3}{4}\) cup per serving” represents a rate.
Type below:
___________

Answer:
There is a 3/4 cup of whatever in one serving. If that serving amount changed to 2, then the 3/4 would be multiplied by 2. If there is half a serving, then it would be divided by 2. There is a constant change and not one that is always changing.

Problem Solving + Applications – Page No. 220

Use the diagram of a birdhouse for 13–15.

Question 13.
Write the ratio of AB to BC in three different ways.
Type below:
___________

Answer:
28 : 12, 28 to 12, \(\frac{2}{13}\)

Explanation:
AB = 28 in
BC = 12 in
AB : BC = 28 : 12, 28 to 12, \(\frac{2}{13}\)

Question 14.
Write the ratio of the shortest side length of triangle ABC to the perimeter of the triangle in three different ways.
Type below:
___________

Answer:
12 : 64, 12 to 64, \(\frac{12}{64}\)

Explanation:
the shortest side length of triangle ABC = 12 in
the perimeter of the triangle 12 + 28 + 24 = 64
12 : 64, 12 to 64, \(\frac{12}{64}\)

Question 15.
Represent a Problem Write the ratio of the perimeter of triangle ABC to the longest side length of the triangle in three different ways.
Type below:
___________

Answer:
64 : 28, 64 to 28, \(\frac{64}{28}\)

Explanation:
the ratio of the perimeter of triangle ABC = 12 + 28 + 24 = 64
the longest side length of the triangle = 28 in
64 : 28, 64 to 28, \(\frac{64}{28}\)

Question 16.
Leandra places 6 photos on each page in a photo album. Find the rate that gives the number of photos on 2 pages. Write the rate in three different ways.
Type below:
___________

Answer:
6 : 12, 6 to 12, \(\frac{6}{12}\)

Explanation:
Leandra places 6 photos on each page in a photo album.
For 2 pages, 6 × 2 = 12 in
6 : 12, 6 to 12, \(\frac{6}{12}\)

Question 17.
What’s the Question? The ratio of total students in Ms. Murray’s class to students in the class who have an older brother is 3 to 1. The answer is 1:2. What is the question?
Type below:
___________

Answer:
What is the ratio of students in the class who don’t have an older brother to students in the class with an older brother.

Question 18.
What do all unit rates have in common?
Type below:
___________

Answer:
A rate is a ratio that is used to compare different kinds of quantities. A unit rate describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

Question 19.
Julia has 2 green reusable shopping bags and 5 purple reusable shopping bags. Select the ratios that compare the number of purple reusable shopping bags to the total number of reusable shopping bags. Mark all that apply.

• 5 to 7
• 5 : 7
• 5 : 2
• \(\frac{2}{5}\)
• 2 to 7
• \(\frac{5}{7}\)

Type below:
___________

Answer:
5 to 7, 5 : 7, \(\frac{5}{7}\)

Explanation:
the number of purple reusable shopping bags = 5
the total number of reusable shopping bags = 5 + 2 = 7
5 to 7, 5 : 7, \(\frac{5}{7}\)

Ratios and Rates – Page No. 221

Write the ratio in two different ways.

Question 1.
\(\frac{4}{5}\)
Type below:
___________

Answer:
4 to 5
4 : 5

Explanation:
\(\frac{4}{5}\) using words 4 to 5
\(\frac{4}{5}\) with a colon 4 : 5

Question 2.
16 to 3
Type below:
___________

Answer:
\(\frac{16}{3}\)
16 : 3

Explanation:
16 to 3 as a fraction \(\frac{16}{3}\)
16 to 3 with a colon 16 : 3

Question 3.
9 : 13
Type below:
___________

Answer:
9 to 13
\(\frac{9}{13}\)

Explanation:
9 : 13 using words 9 to 13
9 : 13 as a fraction \(\frac{9}{13}\)

Question 4.
\(\frac{15}{8}\)
Type below:
___________

Answer:
15 to 8
15 : 8

Explanation:
\(\frac{15}{8}\) using words 15 to 8
\(\frac{15}{8}\) with a colon 15 : 8

Question 5.
There are 20 light bulbs in 5 packages. Complete the table to find the rate that gives the number of light bulbs in 3 packages. Write this rate in three different ways.

Type below:
___________

Answer:

Explanation:
There are 20 light bulbs in 5 packages.
For 1 package, 4 light bulbs available
For 2 package, 8 light bulbs available
For 3 package, 12 light bulbs available
For 4 package, 16 light bulbs available

Problem Solving

Question 6.
Gemma spends 4 hours each week playing soccer and 3 hours each week practicing her clarinet. Write the ratio of hours spent practicing clarinet to hours spent playing soccer three different ways.
Type below:
___________

Answer:
\(\frac{3}{4}\), 3 : 4, 3 to 4

Explanation:
Gemma spends 4 hours each week playing soccer and 3 hours each week practicing her clarinet.
3/4, 3 : 4, 3 to 4

Question 7.
Randall bought 2 game controllers at Electronics Plus for $36. What is the unit rate for a game controller at Electronics Plus?
Type below:
___________

Answer:
\(\frac{$18}{1}\)

Explanation:
Randall bought 2 game controllers at Electronics Plus for $36. $36/2 = $18/1 is the unit rate for a game controller at Electronics Plus

Question 8.
Explain how to determine if a given rate is also a unit rate.
Type below:
___________

Answer:
when rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates. If you have a multiple-unit rate such as 120 student for every 3 buses, an want to find the single-unit rate, write a ratio equal to the multiple-unit rate with 1 as the second term

Lesson Check – Page No. 222

Question 1.
At the grocery store, Luis bought 10 bananas and 4 apples. What are three different ways to write the ratio of apples to bananas?
Type below:
___________

Answer:
4 : 10, 4 to 10, \(\frac{4}{10}\)

Explanation:
At the grocery store, Luis bought 10 bananas and 4 apples. 4/10, 4 : 10, 4 to 10

Question 2.
Rita checked out 7 books from the library. She had 2 non-fiction books. The rest were fiction. What are three different ways to write the ratio of non-fiction to fiction?
Type below:
___________

Answer:
2 to 5, 2 : 5, \(\frac{2}{5}\)

Explanation:
Rita checked out 7 books from the library. She had 2 non-fiction books. The rest were fiction.
fiction = 5
2 to 5, 2 : 5, \(\frac{2}{5}\)

Spiral Review

Question 3.
McKenzie bought 1.2 pounds of coffee for $11.82. What was the cost per pound?
$ ______

Answer:
$9.85

Explanation:
McKenzie bought 1.2 pounds of coffee for $11.82. $11.82/1.2 = $9.85

Question 4.
Pedro has a bag of flour that weighs \(\frac{9}{10}\) pound. He uses \(\frac{2}{3}\) of the bag to make gravy. How many pounds of flour does Pedro use to make gravy?
\(\frac{□}{□}\) pound

Answer:
\(\frac{3}{5}\) pound

Explanation:
Pedro has a bag of flour that weighs \(\frac{9}{10}\) pound. He uses \(\frac{2}{3}\) of the bag to make gravy.
\(\frac{9}{10}\) × \(\frac{2}{3}\) = 3/5

Question 5.
Gina draws a map of her town on a coordinate plane. The point that represents the town’s civic center is 1 unit to the right of the origin and 4 units above it. What are the coordinates of the point representing the civic center?
Type below:
___________

Answer:
(-1, 4)

Explanation:
Gina draws a map of her town on a coordinate plane. The point that represents the town’s civic center is 1 unit to the right of the origin and 4 units above it.
(-1, 4)

Question 6.
Stefan draws these shapes. What is the ratio of triangles to stars?

Type below:
___________

Answer:
2 to 5

Explanation:
There are 2 triangles and 5 stars. So, the ratio is 2 : 5

Share and Show – Page No. 225

Write two equivalent ratios.

Question 1.
Use a multiplication table to write two ratios that are equivalent to \(\frac{4}{7}\).
Type below:
___________

Answer:
\(\frac{4}{7}\) = \(\frac{8}{14}\), \(\frac{12}{21}\)

Explanation:
The original ratio is 4/7. Shade the row for 4 and the row for 7 on the multiplication table.
The column for 2 shows there are 2 ∙ 4, when there are 2 ∙ 7. So, 4/7 equal to 8/14
The column for 3 shows there are 3 ∙ 4, when there are 3 ∙ 7. So, 4/7 equal to 12/21

Question 2.

Type below:
___________

Answer:

Explanation:
The original ratio is 3/7. Shade the row for 3 and the row for 7 on the multiplication table.
The column for 2 shows there are 2 ∙ 3, when there are 2 ∙ 7. So, 3/7 equal to 6/14
The column for 3 shows there are 3 ∙ 3, when there are 3 ∙ 7. So, 3/7 equal to 9/21

Question 3.

Type below:
___________

Answer:

Explanation:
The original ratio is 5/2. Shade the row for 5 and the row for 2 on the multiplication table.
The column for 2 shows there are 2 ∙ 5 when there are 2 ∙ 2. So, 5/2 equal to 10/4
The column for 3 shows there are 3 ∙ 5 when there are 3 ∙ 2. So, 5/2 equal to 15/6

Question 4.

Type below:
___________

Answer:

Explanation:
The original ratio is 2/10. Shade the row for 2 and the row for 10 on the multiplication table.
The column for 1 shows there are 1 ∙ 2 when there are 5 ∙ 2. So, 2/10 equal to 1/5
The column for 3 shows there are 1 ∙ 3 when there are 5 ∙ 3. So, 2/10 equal to 3/15

Question 5.
\(\frac{4}{5}\)
Type below:
___________

Answer:
\(\frac{4}{5}\) = \(\frac{8}{10}\), \(\frac{12}{15}\)

Explanation:
The original ratio is 4/5. Shade the row for 4 and the row for 5 on the multiplication table.
The column for 2 shows there are 2 ∙ 4, when there are 2 ∙ 5. So, 4/5 equal to 8/10
The column for 3 shows there are 3 ∙ 4, when there are 3 ∙ 5. So, 4/5 equal to 12/15

Question 6.
\(\frac{12}{30}\)
Type below:
___________

Answer:
\(\frac{12}{30}\) = \(\frac{24}{60}\), \(\frac{36}{90}\)

Explanation:
The original ratio is 12/30. Shade the row for 12 and the row for 30 on the multiplication table.
The column for 2 shows there are 2 ∙ 12 when there are 2 ∙ 30. So, 12/30 equal to 24/60
The column for 3 shows there are 3 ∙ 12 when there are 3 ∙ 30. So, 12/30 equal to 36/90

Question 7.
\(\frac{2}{9}\)
Type below:
___________

Answer:
\(\frac{2}{9}\) = \(\frac{4}{18}\), \(\frac{6}{27}\)

Explanation:
The original ratio is 2/9. Shade the row for 2 and the row for 9 on the multiplication table.
The column for 2 shows there are 2 ∙ 2, when there are 2 ∙ 9. So, 2/9 equal to 4/18
The column for 3 shows there are 3 ∙ 2, when there are 3 ∙ 9. So, 2/9 equal to 6/27

On Your Own

Write two equivalent ratios.

Question 8.

Type below:
___________

Answer:

Explanation:
The original ratio is 9/8. Shade the row for 9 and the row for 8 on the multiplication table.
The column for 2 shows there are 2 ∙ 9 when there are 2 ∙ 8. So, 9/8 equal to 18/16
The column for 3 shows there are 3 ∙ 9 when there are 3 ∙ 8. So, 9/8 equal to 27/24

Question 9.

Type below:
___________

Answer:

Explanation:
The original ratio is 5/4. Shade the row for 5 and the row for 4 on the multiplication table.
The column for 2 shows there are 2 ∙ 5 when there are 2 ∙ 4. So, 5/4 equal to 10/8
The column for 3 shows there are 3 ∙ 5 when there are 3 ∙ 4. So, 5/4 equal to 15/20

Question 10.

Type below:
___________

Answer:

Explanation:
The original ratio is 6/9. Shade the row for 6 and the row for 9 on the multiplication table.
The column for 1 shows there are 1 ∙ 3 when there are 1. 4.5. So, 5/4 equal to 3/4.5
The column for 3 shows there are 3 ∙ 3 when there are 3 ∙ 4.5. So, 5/4 equal to 9/13.5

Question 11.
\(\frac{8}{7}\)
Type below:
___________

Answer:
\(\frac{8}{7}\) = \(\frac{16}{14}\), \(\frac{24}{21}\)

Explanation:
The original ratio is 8/7. Shade the row for 8 and the row for 7 on the multiplication table.
The column for 2 shows there are 2 ∙ 8, when there are 2 ∙ 7. So, 8/7 equal to 16/14
The column for 3 shows there are 3 ∙ 8, when there are 3 ∙ 7. So, 8/7 equal to 24/21

Question 12.
\(\frac{2}{6}\)
Type below:
___________

Answer:
\(\frac{2}{6}\) = \(\frac{4}{12}\), \(\frac{6}{18}\)

Explanation:
The original ratio is 2/6. Shade the row for 2 and the row for 6 on the multiplication table.
The column for 2 shows there are 2 ∙ 2, when there are 2 ∙ 6. So, 2/6 equal to 4/12
The column for 3 shows there are 3 ∙ 2, when there are 3 ∙ 6. So, 2/6 equal to 6/18

Question 13.
\(\frac{4}{11}\)
Type below:
___________

Answer:
\(\frac{4}{11}\) = \(\frac{8}{22}\), \(\frac{12}{33}\)

Explanation:
The original ratio is 4/11. Shade the row for 4 and the row for 11 on the multiplication table.
The column for 2 shows there are 2 ∙ 4, when there are 2 ∙ 11. So, 4/11 equal to 8/22
The column for 3 shows there are 3 ∙ 4, when there are 3 ∙ 11. So, 4/11 equal to 12/33

Determine whether the ratios are equivalent.

Question 14.
\(\frac{2}{3} \text { and } \frac{8}{12}\)
___________

Answer:
Yes

Explanation:
2/3 × 4/4 = 8/12
So, 2/3 is equal to 8/12

Question 15.
\(\frac{8}{10} \text { and } \frac{6}{10}\)
___________

Answer:
No

Explanation:
8/10 ÷ 2/2 = 4/5
8/10 is not equal to 6/10

Question 16.
\(\frac{16}{60} \text { and } \frac{4}{15}\)
___________

Answer:
yes

Explanation:
16/60 ÷ 4/4 = 4/15
16/60 is equal to 4/15

Question 17.
\(\frac{3}{14} \text { and } \frac{8}{28}\)
___________

Answer:
No

Explanation:
3/14 is not equal to 8/28

Problem Solving + Applications – Page No. 226

Use the multiplication table for 18 and 19.

Question 18.
In Keith’s baseball games this year, the ratio of times he has gotten on base to the times he has been at bat is \(\frac{4}{14}\). Write two ratios that are equivalent to \(\frac{4}{14}\).
Type below:
___________

Answer:
\(\frac{4}{14}\) = \(\frac{8}{28}\), \(\frac{2}{7}\)

Explanation:
4/14
multiply both numbers by 2
8/28
divide both numbers by 2
2/7

Question 19.
Pose a Problem Use the multiplication table to write a new problem involving equivalent ratios. Then solve the problem.
Type below:
___________

Answer:
The ratio of times he has gotten on base to the times he has been at bat is \(\frac{6}{9}\). Write two ratios that are equivalent to \(\frac{6}{9}\)
.multiply both numbers by 2 = 12/18
multiply both numbers by 3 = 18/ 27

Question 20.
Describe how to write an equivalent ratio for \(\frac{9}{27}\) without using a multiplication table.
Type below:
___________

Answer:
\(\frac{9}{27}\) = \(\frac{18}{54}\), \(\frac{3}{9}\)

Explanation:
\(\frac{9}{27}\)
multiply both numbers by 2, 18/54
divide both numbers by 3
3/9

Question 21.
Write a ratio that is equivalent to \(\frac{6}{9} \text { and } \frac{16}{24}\).
\(\frac{□}{□}\)

Answer:
\(\frac{2}{3}\)

Explanation:
\(\frac{6}{9} \text { and } \frac{16}{24}\)
\(\frac{2}{3}\) is the equivalent ratio to \(\frac{6}{9} \text { and } \frac{16}{24}\)

Question 22.
Determine whether each ratio is equivalent to \(\frac{1}{3}, \frac{5}{10}, \text { or } \frac{3}{5}\). Write the ratio in the correct box.

Type below:
___________

Answer:
3/9, 7/21, 18/30, 10/30

Explanation:
2/4 = 1/2
3/9 = 1/3
7/21 = 1/3
18/30 = 3/5
10/30 = 1/3
6/10 = 2/5
8/16 = 4/8 = 1/2

Equivalent Ratios and Multiplication Tables – Page No. 227

Write two equivalent ratios.

Question 1.
Use a multiplication table to write two ratios that are equivalent to \(\frac{5}{3}\).
Type below:
___________

Answer:
\(\frac{5}{3}\) = \(\frac{10}{6}\), \(\frac{15}{9}\)

Explanation:
The original ratio is 5/3. Shade the row for 5 and the row for 3 on the multiplication table.
The column for 2 shows there are 2 ∙ 5, when there are 2 ∙ 3. So, 5/3 equal to 10/6
The column for 3 shows there are 3 ∙ 5, when there are 3 ∙ 3. So, 5/3 equal to 15/9

Question 2.

Type below:
___________

Answer:

Explanation:
The original ratio is 6/7. Shade the row for 6 and the row for 7 on the multiplication table.
The column for 2 shows there are 2 ∙ 6 when there are 2 ∙ 7. So, 6/7 equal to 12/14
The column for 3 shows there are 3 ∙ 6 when there are 3 ∙ 7. So, 6/7 equal to 18/21

Question 2.

Type below:
___________

Answer:

Explanation:
The original ratio is 3/2. Shade the row for 3 and the row for 2 on the multiplication table.
The column for 2 shows there are 2 ∙ 3 when there are 2 ∙ 2. So, 3/2 equal to 6/4
Multiply 3/2 with 4/4 = 12/8

Question 4.
\(\frac{6}{8}\)
Type below:
___________

Answer:
\(\frac{6}{8}\) =\(\frac{12}{16}\), \(\frac{18}{24}\)

Explanation:
The original ratio is 6/8. Shade the row for 6 and the row for 8 on the multiplication table.
The column for 2 shows there are 2 ∙ 6, when there are 2 ∙ 8. So, 6/8 equal to 12/16
The column for 3 shows there are 3 ∙ 6, when there are 3 ∙ 8. So, 6/8 equal to 18/24

Question 5.
\(\frac{11}{1}\)
Type below:
___________

Answer:
\(\frac{11}{1}\) = \(\frac{22}{2}\), \(\frac{33}{3}\)

Explanation:
The original ratio is 11/1. Shade the row for 11 and the row for 1 on the multiplication table.
The column for 2 shows there are 2 ∙ 11, when there are 2 ∙ 1. So, 11/1 equal to 22/2
The column for 3 shows there are 3 ∙ 11, when there are 3 ∙ 1. So, 11/1 equal to 33/3

Determine whether the ratios are equivalent.

Question 6.
\(\frac{2}{3} \text { and } \frac{5}{6}\).
___________

Answer:
No

Explanation:
2/3 is not equal to 5/6

Question 7.
\(\frac{5}{10} \text { and } \frac{1}{6}\).
___________

Answer:
No

Explanation:
5/10 is not equal to 1/6

Question 8.
\(\frac{8}{3} \text { and } \frac{32}{12}\).
___________

Answer:
Yes

Explanation:
8/3 × 4/4 = 32/12
8/3 is equal to 32/12

Question 9.
\(\frac{9}{12} \text { and } \frac{3}{4}\).
___________

Answer:
Yes

Explanation:
9/12 ÷ 3/3 = 3/4
9/12 is equal to 3/4

Problem Solving

Question 10.
Tristan uses 7 stars and 9 diamonds to make a design. Write two ratios that are equivalent to \(\frac{7}{9}\).
Type below:
___________

Answer:
\(\frac{7}{9}\)  = \(\frac{14}{18}\) , \(\frac{21}{27}\)

Explanation:
Tristan uses 7 stars and 9 diamonds to make a design.
\(\frac{7}{9}\)
The original ratio is 7/9. Shade the row for 7 and the row for 9 on the multiplication table.
The column for 2 shows there are 2 ∙ 7, when there are 2 ∙ 9. So, 7/9 equal to 14/18
The column for 3 shows there are 3 ∙ 7, when there are 3 ∙ 9. So, 7/9 equal to 21/27

Question 11.
There are 12 girls and 16 boys in Javier’s math class. There are 26 girls and 14 boys in Javier’s choir class. Are the ratios of girls to boys in the two classes equivalent? Explain.
Type below:
___________

Answer:
No, the ratio 26/14 is not equal to the ratio 12/16

Question 12.
Explain how to determine whether two ratios are equivalent.
Type below:
___________

Answer:
If any ratio is multiplied or divided by the same number, then the ratios are equivalent.

Lesson Check – Page No. 228

Question 1.
A pancake recipe calls for 4 cups of flour and 3 cups milk. Does a recipe calling for 2 cups flour and 1.5 cups milk use the same ratio of flour to milk?
___________

Answer:
A muffin recipe that calls for 2 cups flour and 1.5 cups milk

Explanation:
A pancake recipe calls for 4 cups of flour and 3 cups milk. A muffin recipe that calls for 2 cups flour and 1.5 cups milk.

Question 2.
A bracelet is made of 14 red beads and 19 gold beads. A necklace is made of 84 red beads and 133 gold beads. Do the two pieces of jewelry have the same ratio of red beads to gold beads?
___________

Answer:
The bracelet has 14 red and 19 gold, so the ratio between red and gold is 14/19. We cannot simplify this ratio as there are not common factors between 14 and 19, because 19 is a prime number.
As there are 84 red and 133 gold the ratio will be 84/133. For this ratio to be equal to 14/19 it should be that 84 is multiple of 14 and 133 multiple of 19, and both multiples must the same,
84/133 is not equal to 14/19

Spiral Review

Question 3.
Scissors come in packages of 3. Glue sticks come in packages of 10. Martha wants to buy the same number of each. What is the fewest glue sticks Martha can buy?
_____ glue sticks

Answer:
30 glue sticks

Explanation:
Scissors come in packages of 3. Glue sticks come in packages of 10. Martha wants to buy the same number of each.
3 × 10 = 30 glue sticks

Question 4.
Cole had \(\frac{3}{4}\) hour of free time before dinner. He spent \(\frac{2}{3}\) of the time playing the guitar. How long did he play the guitar?
\(\frac{□}{□}\) hour

Answer:
\(\frac{1}{2}\) hour

Explanation:
Cole had \(\frac{3}{4}\) hour of free time before dinner. He spent \(\frac{2}{3}\) of the time playing the guitar.
\(\frac{2}{3}\) × \(\frac{3}{4}\) = 1/2 hour

Question 5.
Delia has 3 \(\frac{5}{8}\) yards of ribbon. About how many \(\frac{1}{4}\)-yard-long pieces can she cut?
About _____ pieces

Answer:
About 14 pieces

Explanation:
Length of yards of ribbon is 3 5/8 = 29/8
Length of yards of ribbon pieces need to be cut is 1/4
Number of yards = 29/8 ÷ 1/4 = 14.5 = 14

Question 6.
Which point is located at –1.1?

Type below:
___________

Answer:
B

Explanation:
-1.1 is in between -1 and -2
-1.1 is close to -1
So, the answer is point B

Share and Show – Page No. 231

Question 1.
In Jawan’s school, 4 out of 10 students chose basketball as a sport they like to watch, and 3 out of 5 students chose football. Is the ratio of students who chose basketball (4 to 10) equivalent to the ratio of students who chose football (3 to 5)?
Type below:
___________

Answer:
the ratio of students who chose basketball (4 to 10) is not equivalent to the ratio of students who chose football (3 to 5)

Explanation:
In Jawan’s school, 4 out of 10 students chose basketball as a sport they like to watch, and 3 out of 5 students chose football.
4/10 = 0.4
3/5 = 0.6
0.4 is not equal to 0.6
The ratio of students who chose basketball (4 to 10) is not equivalent to the ratio of students who chose football (3 to 5)

Question 2.
What if 20 out of 50 students chose baseball as a sport they like to watch? Is this ratio equivalent to the ratio for either basketball or football? Explain.
Type below:
___________

Answer:
The baseball ratio is equal to the basketball ratio

Explanation:
If 20 out of 50 students chose baseball, 20/50 = 2/5
2/5 × 2/2 = 4/10
The baseball ratio is equal to the basketball ratio.

Question 3.
Look for Structure The table shows the results of the quizzes Hannah took in one week. Did Hannah get the same score on her math and science quizzes? Explain.

Type below:
___________

Answer:
Hannah didn’t get the same score on her math and science quizzes

Explanation:
Social Studies = 4/5
Math = 8/10 = 0.8
Science = 3/4 = 0.75
English = 10/12
Math = 8/10
Divide the 8/10 with 2/2 = 8/10 ÷ 2/2 = 4/5
Hannah didn’t get the same score on her math and science quizzes

Question 4.
Did Hannah get the same score on the quizzes in any of her classes? Explain.
Type below:
___________

Answer:
The ratio of Social Studies is equal to the ratio of Math

Explanation:
Social Studies = 4/5 = 0.8
Math = 8/10 = 0.8
Science = 3/4 = 0.75
English = 10/12 = 0.8333
The ratio of Social Studies is equal to the ratio of Math

On Your Own – Page No. 232

Question 5.
For every $10 that Julie makes, she saves $3. For every $15 Liam makes, he saves $6. Is Julie’s ratio of money saved to money earned equivalent to Liam’s ratio of money saved to money earned?
Type below:
___________

Answer:
Julie’s ratio of money saved to money earned is not equivalent to Liam’s ratio of money saved to money earned.

Explanation:
No. Julie’s ratio is 3:10 or 30 percent towards her savings while Lion’s is 6:15 which is 40 percent towards savings.

Question 6.
A florist offers three different bouquets of tulips and irises. The list shows the ratios of tulips to irises in each bouquet. Determine the bouquets that have equivalent ratios.

Type below:
___________

Answer:
The ratio of Spring Mix is equal to the ratio of Splash of Sun

Explanation:
Spring Mix = 4/6 = 0.66
Morning Melody = 9/12 = 0.75
Splash of Sun = 10/15 =0.66
The ratio of Spring Mix is equal to the ratio of Splash of Sun

Question 7.
The ratio of boys to girls in a school’s soccer club is 3 to 5. The ratio of boys to girls in the school’s chess club is 13 to 15. Is the ratio of boys to girls in the soccer club equivalent to the ratio of boys to girls in the chess club? Explain
Type below:
___________

Answer:
No

Explanation:
They are not equivalent because you can not reduce 13 any further because it is a prime number and if you multiply 3 by 3 and 5 by 3 you would get 9:15 as the equivalent ratio.

Question 8.
Analyze Thad, Joey, and Mia ran in a race. The finishing times were 4.56 minutes, 3.33 minutes, and 4.75 minutes. Thad did not finish last. Mia had the fastest time. What was each runner’s time?
Type below:
___________

Answer:
Mia = 3.33 minutes
Joey = 4.75 minutes
Thad = 4.56 minutes

Explanation:
Mia had the fastest time. 3.33 minutes
Thad did not finish last. So, Joey = 4.75 minutes
Thad = 4.56 minutes

Question 9.
Fernando donates $2 to a local charity organization for every $15 he earns. Cleo donates $4 for every $17 she earns. Is Fernando’s ratio of money donated to money earned equivalent to Cleo’s ratio of money donated to money earned? Explain.
Type below:
___________

Answer:
Fernando’s ratio of money donated to money earned is not equivalent to Cleo’s ratio of money donated to money earned

Explanation:
Fernando donates $2 to a local charity organization for every $15 he earns.
$2/$15 = 0.1333
Cleo donates $4 for every $17 she earns. $4/$17 = 0.2359
Fernando’s ratio of money donated to money earned is not equivalent to Cleo’s ratio of money donated to money earned

Problem Solving Use Tables to Compare Ratios – Page No. 233

Read each problem and solve.

Question 1.
Sarah asked some friends about their favorite colors. She found that 4 out of 6 people prefer blue, and 8 out of 12 people prefer green. Is the ratio of friends who chose blue to the total asked equivalent to the ratio of friends who chose green to the total asked?
Type below:
___________

Answer:
Yes, 4/6 is equivalent to 8/12

Explanation:

4/6 = 0.666
8/12 = 0.666

Question 2.
Lisa and Tim make necklaces. Lisa uses 5 red beads for every 3 yellow beads. Tim uses 9 red beads for every 6 yellow beads. Is the ratio of red beads to yellow beads in Lisa’s necklace equivalent to the ratio in Tim’s necklace?
Type below:
___________

Answer:
The ratio of red beads to yellow beads in Lisa’s necklace is not equivalent to the ratio in Tim’s necklace

Explanation:
Lisa and Tim make necklaces. Lisa uses 5 red beads for every 3 yellow beads.
5/3 = 1.666
Tim uses 9 red beads for every 6 yellow beads. 9/6 = 1.5
The ratio of red beads to yellow beads in Lisa’s necklace is not equivalent to the ratio in Tim’s necklace

Question 3.
Mitch scored 4 out of 5 on a quiz. Demetri scored 8 out of 10 on a quiz. Did Mitch and Demetri get equivalent scores?
Type below:
___________

Answer:
Mitch and Demetri get equivalent scores

Explanation:
Mitch scored 4 out of 5 on a quiz. 4/5 = 0.8
Demetri scored 8 out of 10 on a quiz. = 8/10 = 0.8
Mitch and Demetri get equivalent scores

Question 4.
Use tables to show which of these ratios are equivalent : \(\frac{4}{6}\), \(\frac{10}{25}, \text { and } \frac{6}{15}\).
Type below:
___________

Answer:
\(\frac{10}{25}, \text { and } \frac{6}{15}\) are equal

Explanation:
\(\frac{4}{6}\) = 0.6666
\(\frac{10}{25}\) = 0.4
\(\frac{6}{15}\) = 0.4
\(\frac{10}{25}, \text { and } \frac{6}{15}\) are equal

Page No. 234

Question 1.
Mrs. Sahd distributes pencils and paper to students in the ratio of 2 pencils to 10 sheets of paper. Three of these ratios are equivalent to \(\frac{2}{10}\). Which one is NOT equivalent?
\(\frac{1}{5} \frac{7}{15} \frac{4}{20} \frac{8}{40}\)
Type below:
___________

Answer:
\(\frac{7}{15}\) is not equal \(\frac{2}{10}\)

Explanation:
Mrs. Sahd distributes pencils and paper to students in the ratio of 2 pencils to 10 sheets of paper. Three of these ratios are equivalent to \(\frac{2}{10}\) = 0.2
\(\frac{1}{5}\) = 0.2
\(\frac{7}{15}\) = 0.4666
\(\frac{4}{20}\) = 0.2
\(\frac{8}{40}\) = 0.2
\(\frac{7}{15}\) is not equal \(\frac{2}{10}\)

Question 2.
Keith uses 18 cherries and 3 peaches to make a pie filling. Lena uses an equivalent ratio of cherries to peaches when she makes pie filling. Can Lena use a ratio of 21 cherries to 6 peaches? Explain.
Type below:
___________

Answer:
No, she cannot use a ratio of 21 cherries to 6 peaches

Explanation:
Keith uses 18 cherries and 3 peaches to make a pie filling. 18/3 = 6
Lena uses a ratio of 21 cherries to 6 peaches, 21/6 = 3.5
No, she cannot use a ratio of 21 cherries to 6 peaches

Spiral Review

Question 3.
What is the quotient \(\frac{3}{20} \div \frac{7}{10}\)?
Type below:
___________

Answer:
\(\frac{3}{14}\)

Explanation:
\(\frac{3}{20} \div \frac{7}{10}\)
3/20 × 10/7 = 3/14

Question 4.
Which of these numbers is greater than – 2.25 but less than –1?
1 -1.5 0 -2.5
Type below:
___________

Answer:

Explanation:
1 lies between 0 to 1
-1.5 lies between -1 and -2. It is greater than -2.25 and also less than -1
0 lies between -1 to 1
-2.5 lies between -2 and -3. -2.5 is less than -2.25

Question 5.
Alicia plots a point at (0, 5) and (0, –2). What is the distance between the points?
Type below:
___________

Answer:
7 units

Explanation:
Alicia plots a point at (0, 5) and (0, –2).
The given points have the same x-coordinates.
|-2| = 2
5 + 0 = 5
0 + 2 = 2
5 + 2 = 7
The distance is 7 units

Question 6.
Morton sees these stickers at a craft store. What is the ratio of clouds to suns?

Type below:
___________

Answer:
3 : 2

Explanation:
there are 3 clouds and 2 suns. So, the ratio is 3 to 2.

Share and Show – Page No. 237

Use equivalent ratios to find the unknown value.

Question 1.
\(\frac{?}{10}=\frac{4}{5}\)
_____

Answer:
\(\frac{8}{10}\) = \(\frac{4}{5}\)

Explanation:
Use common denominators to write equivalent ratios.
10 is a multiple of 5, so 10 is a common denominator.
Multiply the 4 and denominator by 2 to write the ratios using a common denominator.
4/5 × 2/2 = 8/10
The denominators are the same, so the numerators are equal to each other.
So, the unknown value is 8/10 = 4/5
\(\frac{8}{10}\)

Question 2.
\(\frac{18}{24}=\frac{6}{?}\)
_____

Answer:
\(\frac{6}{8}\) = \(\frac{18}{24}\)

Explanation:
Write an equivalent ratio with 18 in the numerator.
Divide 18 by 6 to get 3
So, divide the denominator by 24 as well.
24/3 = 8
The numerators are the same, so the denominators are equal to each other.
So, the unknown value is 6/8 = 18/24
\(\frac{6}{8}\)

Question 3.
\(\frac{3}{6}=\frac{15}{?}\)
_____

Answer:
\(\frac{15}{30}\)

Explanation:
Write an equivalent ratio with 15 in the numerator.
Multiply 3 with 5 to get 15
So, Multiply 6 with 5 to get the denominator of unknown number.
6 × 5 = 30
The numerators are the same, so the denominators are equal to each other.
So, the unknown value is 3/6 = 15/30
\(\frac{15}{30}\)

Question 4.
\(\frac{?}{5}=\frac{8}{10}\)
_____

Answer:
\(\frac{4}{5}\)

Explanation:
Write an equivalent ratio with 10 in the denominator.
Divide 10 by 2 to get 5
So, divide the numerator 8 as well.
8/2 = 4
The denominators are the same, so the numerators are equal to each other.
So, the unknown value is 8/10 = 4/5
\(\frac{4}{5}\)

Question 5.
\(\frac{7}{4}=\frac{?}{12}\)
_____

Answer:
\(\frac{21}{12}\)

Explanation:
Write an equivalent ratio with 12 in the denominator.
Multiply 4 with 3 to get 12
So, Multiply 7 with 3 to get the numerator of unknown number.
7 × 3 = 21
The denominators are the same, so the numerators are equal to each other.
So, the unknown value is 21/12 = 7/4
\(\frac{21}{12}\)

Question 6.
\(\frac{10}{?}=\frac{40}{12}\)
_____

Answer:
\(\frac{10}{3}\)

Explanation:
Write an equivalent ratio with 40 in the numerator.
Divide 40 by 4 to get 10
So, divide the denominator 12 as well.
12/4 = 3
The numerators are the same, so the denominators are equal to each other.
So, the unknown value is 10/3 = 40/12
\(\frac{10}{3}\)

On Your Own

Use equivalent ratios to find the unknown value.

Question 7.
\(\frac{2}{6}=\frac{?}{30}\)
_____

Answer:
\(\frac{10}{30}\)

Explanation:
Use common denominators to write equivalent ratios.
30 is a multiple of 6, so 30 is a common denominator.
Multiply the 6 and denominator by 5 to write the ratios using a common denominator.
2/6 × 5/5 =10/30
The denominators are the same, so the numerators are equal to each other.
So, the unknown value is 10/30 = 2/6
\(\frac{10}{30}\)

Question 8.
\(\frac{5}{?}=\frac{55}{110}\)
_____

Answer:
\(\frac{5}{10}\)

Explanation:
Write an equivalent ratio with 55 in the numerator.
Divide 55 with 11 to get 5
So, Divide 110 with 11 to get the denominator of unknown number.
110/11 = 10
The numerators are the same, so the denominators are equal to each other.
So, the unknown value is 5/10 = 55/110
\(\frac{5}{10}\)

Question 9.
\(\frac{3}{9}=\frac{9}{?}\)
_____

Answer:
\(\frac{9}{27}\)

Explanation:
Write an equivalent ratio with 9 in the numerator.
Multiply 3 with 3 to get 9
So, Multiply 9 with 3 to get the denominator of unknown number.
9 × 3 = 27
The numerators are the same, so the denominators are equal to each other.
So, the unknown value is 9/27 = 3/9
\(\frac{9}{27}\)

Question 10.
\(\frac{?}{6}=\frac{16}{24}\)
_____

Answer:
\(\frac{4}{6}\)

Explanation:
Use common denominators to write equivalent ratios.
Divide 24 with 4 to get 6.
So, divide 16 with 4 to know the unknown number of numerator
16/4 = 4
The denominators are the same, so the numerators are equal to each other.
So, the unknown value is 4/6 = 16/24
\(\frac{4}{6}\)

Question 11.
Mavis walks 3 miles in 45 minutes. How many minutes will it take Mavis to walk 9 miles?
_____ minutes

Answer:
135 minutes

Explanation:
Mavis walks 3 miles in 45 minutes.
For 9 miles, (9 × 45)/3 = 135 minutes

Question 12.
The ratio of boys to girls in a choir is 3 to 8. There are 32 girls in the choir. How many members are in the choir?
_____ members

Answer:
12 members

Explanation:
The ratio of boys to girls in a choir is 3 to 8.
3/8 × 4/ 4 = 12/32
So, if there are 32 girls in the choir, there will be 12 boys present.

Question 13.
Use Reasoning Is the unknown value in \(\frac{2}{3}=\frac{?}{18}\) the same as the unknown value in \(\frac{3}{2}=\frac{18}{?}\)? Explain.
Type below:
___________

Answer:
12

Explanation:
\(\frac{2}{3}=\frac{?}{18}\)
2/3 × 6/6 = 12/18
the unknown value is 12
\(\frac{3}{2}=\frac{18}{?}\)
3/2 × 6/6 = 18/12
the unknown value is 12

Problem Solving + Applications – Page No. 238

Solve by finding an equivalent ratio.

Question 14.
It takes 8 minutes for Sue to make 2 laps around the go-kart track. How many laps can Sue complete in 24 minutes?
_____ laps

Answer:
6 laps

Explanation:
It takes 8 minutes for Sue to make 2 laps around the go-kart track.
For 24 minutes, (24 × 2)/8 = 48/8 =6

Question 15.
The width of Jay’s original photo is 8 inches. The length of the original photo is 10 inches. He prints a smaller version that has an equivalent ratio of width to length. The width of the smaller version is 4 inches less than the width of the original. What is the length of the smaller version?
_____ inches

Answer:
5 inches

Explanation:
The width of Jay’s original photo is 8 inches. The length of the original photo is 10 inches.
8/10
He prints a smaller version that has an equivalent ratio of width to length. The width of the smaller version is 4 inches less than the width of the original.
4/s
8/10 ÷ 2/2 = 4/5
5 inches

Question 16.
Ariel bought 3 raffle tickets for $5. How many tickets could Ariel buy for $15?
_____ tickets

Answer:
9 tickets

Explanation:
Ariel bought 3 raffle tickets for $5.
For $15, ($15 × 3)/ $5 = 45/5 = 9

Question 17.
What’s the Error? Greg used the steps shown to find the unknown value. Describe his error and give the correct solution.
\(\frac{2}{6}=\frac{?}{12}\)
\(\frac{2+6}{6+6}=\frac{?}{12}\)
\(\frac{8}{12}=\frac{?}{12}\)
The unknown value is 8.
Type below:
___________

Answer:
Greg added 6 to the numerator and denominator which is not correct to find the unknown value.
\(\frac{2}{6}=\frac{?}{12}\)
2/6 × 2/2 = 4/12
4 is the unknown value.

Question 18.
Courtney bought 3 maps for $10. Use the table of equivalent ratios to find how many maps she can buy for $30.

Type below:
___________

Answer:

Explanation:
3/10 × 3/3 = 9/30

Use Equivalent Ratios – Page No. 239

Use equivalent ratios to find the unknown value.

Question 1.
\(\frac{4}{10}=\frac{?}{40}\)
_____

Answer:
\(\frac{16}{40}\)

Explanation:
4/10 × 4/4 = 16/40

Question 2.
\(\frac{3}{24}=\frac{33}{?}\)
_____

Answer:
\(\frac{33}{264}\)

Explanation:
3/24 × 11/11 = 33/264

Question 3.
\(\frac{7}{?}=\frac{21}{27}\)
_____

Answer:
\(\frac{7}{9}\)

Explanation:
21/27 ÷ 3/3 = 7/9

Question 4.
\(\frac{?}{9}=\frac{12}{54}\)
_____

Answer:
\(\frac{2}{9}\)

Explanation:
12/54 ÷ 6/6 = 2/9

Question 5.
\(\frac{3}{2}=\frac{12}{?}\)
_____

Answer:
\(\frac{12}{8}\)

Explanation:
3/2 × 4/4 = 12/8

Question 6.
\(\frac{4}{5}=\frac{?}{40}\)
_____

Answer:
\(\frac{32}{40}\)

Explanation:
4/5 × 8/8 = 32/40

Question 7.
\(\frac{?}{2}=\frac{45}{30}\)
_____

Answer:
\(\frac{3}{2}\)

Explanation:
45/30 ÷ 15/15 = 3/2

Question 8.
\(\frac{45}{?}=\frac{5}{6}\)
_____

Answer:
\(\frac{45}{54}\)

Explanation:
5/6 × 9/9 = 45/54

Problem Solving

Question 9.
Honeybees produce 7 pounds of honey for every 1 pound of beeswax they produce. Use equivalent ratios to find how many pounds of honey are produced when 25 pounds of beeswax are produced.
_____ pounds

Answer:
175 pounds

Explanation:
Honeybees produce 7 pounds of honey for every 1 pound of beeswax they produce.
7/1
25 pounds of beeswax, 25 × 7 = 175 pounds

Question 10.
A 3-ounce serving of tuna provides 21 grams of protein. Use equivalent ratios to find how many grams of protein are in 9 ounces of tuna.
_____ grams of protein

Answer:
63 grams of protein

Explanation:
A 3-ounce serving of tuna provides 21 grams of protein.
For 9 ounces of tuna, (21 × 9)/3 = 63

Question 11.
Explain how using equivalent ratios is like adding fractions with unlike denominators.
Type below:
___________

Answer:
Equivalent ratios have different numbers but represent the same relationship. In this tutorial, you’ll see how to find equivalent ratios by first writing the given ratio as a fraction. And it cannot be the same by adding tow fraction with different ratio

Lesson Check – Page No. 240

Question 1.
Jaron paid $2.70 for 6 juice boxes. How much should Jaron expect to pay for 18 juice boxes?
$ _____

Answer:
$8.1

Explanation:
Jaron paid $2.70 for 6 juice boxes. For 6 boxes he paid $2.70.
For 18 juice boxes, (18 × $2.70)/6 = $8.1

Question 2.
A certain shade of orange paint is made by mixing 3 quarts of red paint with 2 quarts of yellow paint. To make more paint of the same shade, how many quarts of yellow paint should be mixed with 6 quarts of red paint?
_____ quarts

Answer:
4 quarts

Explanation:
A certain shade of orange paint is made by mixing 3 quarts of red paint with 2 quarts of yellow paint.
3 quarts of red paint is mixed with 2 quarts of yellow paint
So, 6 quarts of red paint is mixed with 6/3 × 2 = 4 quarts of yellow paint

Spiral Review

Question 3.
What is the quotient \(2 \frac{4}{5} \div 1 \frac{1}{3}\)?
______ \(\frac{□}{□}\)

Answer:
2\(\frac{1}{10}\)

Explanation:
2 4/5 = 14/5 = 2.8
1 1/3 = 4/3 = 1.333
2.8/1.333 = 2 1/10

Question 4.
What is the quotient \(-2 \frac{2}{3}\)?
______ \(\frac{□}{□}\)

Answer:
1\(\frac{11}{16}\)

Explanation:
−4 1/2 ÷ -2 2/3
1 11/16

Question 5.
On a map, a clothing store is located at (–2, –3). A seafood restaurant is located 6 units to the right of the clothing store. What are the coordinates of the restaurant?
Type below:
___________

.Answer:
(4, -3)

Explanation:
On a map, a clothing store is located at (–2, –3). A seafood restaurant is located 6 units to the right of the clothing store.
|-2| = 2
2 + 0 = 2
0+4 = 4
2 + 4 = 6 units

Question 6.
Marisol plans to make 9 mini-sandwiches for every 2 people attending her party. Write a ratio that is equivalent to Marisol’s ratio.
Type below:
___________

Answer:
27/6 and 45/10

Explanation:
Marisol plans to make 9 mini-sandwiches for every 2 people attending her party. 9/2 × 3/3 = 27/6
9/2 × 5/5 = 45/10

Mid-Chapter Checkpoint – Vocabulary – Page No. 241

Choose the best term from the box to complete the sentence.

Question 1.
A _____ is a rate that makes a comparison to 1 unit.
Type below:
___________

Answer:
rate

Question 2.
Two ratios that name the same comparison are _____ .
Type below:
___________

Answer:
Equivalent Ratios

Concepts and Skills

Question 3.
Write the ratio of red circles to blue squares.
Type below:
___________

Answer:
3 : 5

Explanation:
There are 3 red counter and 5 square boxes.
So, the ratio is 3 : 5

Write the ratio in two different ways.

Question 4.
8 to 12
Type below:
___________

Answer:
\(\frac{8}{12}\)
8 : 12

Explanation:
8 to 12 as a fraction  \(\frac{8}{12}\)
8 to 12 with a colon 8 : 12

Question 5.
7 : 2
Type below:
___________

Answer:
\(\frac{7}{2}\)
7 to 2

Explanation:
7 : 2 as a fraction  \(\frac{7}{2}\)
7 : 2 using words 7 to 2

Question 6.
\(\frac{5}{9}\)
Type below:
___________

Answer:
5 to 9
5 : 9

Explanation:
\(\frac{5}{9}\) using words 5 to 9
\(\frac{5}{9}\) with a colon 5 : 9

Question 7.
11 to 3
Type below:
___________

Answer:
\(\frac{11}{3}\)
11 : 3

Explanation:
11 to 3 as a fraction \(\frac{11}{3}\)
11 to 3 with a colon 11 : 3

Write two equivalent ratios.

Question 8.
\(\frac{2}{7}\)
Type below:
___________

Answer:
\(\frac{2}{7}\) = \(\frac{4}{14}\), \(\frac{6}{21}\)

Explanation:
The original ratio is 2/7. Shade the row for 2 and the row for 7 on the multiplication table.
The column for 2 shows there are 2 ∙ 2, when there are 2 ∙ 7. So, 2/7 equal to 4/14
The column for 3 shows there are 3 ∙ 2, when there are 3 ∙ 7. So, 2/7 equal to 6/21

Question 9.
\(\frac{6}{5}\)
Type below:
___________

Answer:
\(\frac{6}{5}\) = \(\frac{12}{10}\), \(\frac{18}{15}\)

Explanation:
The original ratio is 6/5. Shade the row for 6 and the row for 5 on the multiplication table.
The column for 2 shows there are 2 ∙ 6, when there are 2 ∙ 5. So, 6/5 equal to 12/10
The column for 3 shows there are 3 ∙ 6, when there are 3 ∙ 5. So, 6/5 equal to 18/15

Question 10.
\(\frac{9}{12}\)
Type below:
___________

Answer:
\(\frac{9}{12}\) = \(\frac{18}{24}\), \(\frac{27}{36}\)

Explanation:
The original ratio is 9/12. Shade the row for 9 and the row for 12 on the multiplication table.
The column for 2 shows there are 2 ∙ 9, when there are 2 ∙ 12. So, 9/12 equal to 18/24
The column for 3 shows there are 3 ∙ 9, when there are 3 ∙ 12. So, 9/12 equal to 27/36

Question 11.
\(\frac{18}{6}\)
Type below:
___________

Answer:
\(\frac{18}{6}\) = \(\frac{36}{12}\), \(\frac{54}{18}\)

Explanation:
The original ratio is 18/6. Shade the row for 18 and the row for 6 on the multiplication table.
The column for 2 shows there are 2 ∙ 18, when there are 2 ∙ 6. So, 18/6 equal to 36/12
The column for 3 shows there are 3 ∙ 18, when there are 3 ∙ 6. So, 18/6 equal to 54/18

Find the unknown value.

Question 12.
\(\frac{15}{?}=\frac{5}{10}\)
Type below:
___________

Answer:
30

Explanation:
5/10 × 3/3 = 15/30
So, the unknown number is 30

Question 13.
\(\frac{?}{9}=\frac{12}{3}\)
Type below:
___________

Answer:
36

Explanation:
12/3 × 3/3 = 36/9
So, the unknown number is 36

Question 14.
\(\frac{48}{16}=\frac{?}{8}\)
Type below:
___________

Answer:
24

Explanation:
48/16 ÷ 2/2 = 24/8
So, the unknown number is 24

Question 15.
\(\frac{9}{36}=\frac{3}{?}\)
Type below:
___________

Answer:
12

Explanation:
9/36 ÷ 3/3 = 3/12
So, the unknown number is 12

Page No. 242

Question 16.
There are 36 students in the chess club, 40 students in the drama club, and 24 students in the film club. What is the ratio of students in the drama club to students in the film club?
Type below:
___________

Answer:
40 to 24

Explanation:
There are 36 students in the chess club, 40 students in the drama club, and 24 students in the film club.
The ratio of students in the drama club to students in the film club 40 to 24

Question 17.
A trail mix has 4 cups of raisins, 3 cups of dates, 6 cups of peanuts, and 2 cups of cashews. Which ingredients are in the same ratio as cashews to raisins?
Type below:
___________

Answer:
dates to peanuts

Explanation:
A trail mix has 4 cups of raisins, 3 cups of dates, 6 cups of peanuts, and 2 cups of cashews.
cashews to raisins = 2/4 = 1/2
dates to peanuts = 3/6 = 1/2

Question 18.
There are 32 adults and 20 children at a school play. What is the ratio of children to people at the school play?
Type below:
___________

Answer:
5 to 13

Explanation:
There are 32 adults and 20 children at a school play.
people = 32 + 20 = 52
the ratio of children to people at the school play = 20/52 = 5/13

Question 19.
Sonya got 8 out of 10 questions right on a quiz. She got the same score on a quiz that had 20 questions. How many questions did Sonya get right on the second quiz? How many questions did she get wrong on the second quiz?
Type below:
___________

Answer:
4 wrong

Explanation:
8/10 = x/20
So, 10 × 2 = 20, so 8 × 2=16
so she got 16 out of 20 right and 20 – 16 = 4
She got 4 wrong.

Share and Show – Page No. 245

Write the rate as a fraction. Then find the unit rate.

Question 1.
Sara drove 72 miles on 4 gallons of gas.
_____ miles/gallon

Answer:
18 miles/gallon

Explanation:
Sara drove 72 miles on 4 gallons of gas.
72/4
Divide 72/4 with 4/4
72/4 ÷ 4/4 = 18

Question 2.
Dean paid $27.00 for 4 movie tickets.
$ _____ per ticket

Answer:
$6.75 per ticket

Explanation:
Dean paid $27.00 for 4 movie tickets.
$27.00/4
Divide $27.00/4 with 4/4
$27.00/4 ÷ 4/4 = $6.75

Question 3.
Amy and Mai have to read Bud, Not Buddy for a class. Amy reads 20 pages in 2 days. Mai reads 35 pages in 3 days. Who reads at a faster rate?
___________

Answer:
Mai reads at a faster rate

Explanation:
Amy and Mai have to read Bud, Not Buddy for a class.
Amy reads 20 pages in 2 days. 20/2 = 10 pages for each day
Mai reads 35 pages in 3 days. 35/3 = 11.66 pages for each day
Mai reads at a faster rate

Question 4.
An online music store offers 5 downloads for $6.25. Another online music store offers 12 downloads for $17.40. Which store offers the better deal?
___________

Answer:
An online music store offers 5 downloads for $6.25 offers the better deal

Explanation:
An online music store offers 5 downloads for $6.25.
$6.25/5 = $1.25
Another online music store offers 12 downloads for $17.40.
$17.40/12 = $1.45
An online music store offers 5 downloads for $6.25 offers the better deal

On Your Own

Write the rate as a fraction. Then find the unit rate.

Question 5.
A company packed 108 items in 12 boxes.
Type below:
___________

Answer:
9

Explanation:
A company packed 108 items in 12 boxes.
108/12
Divide 108/12 with 12/12
108/12 ÷ 12/12 = 9

Question 6.
There are 112 students for 14 teachers.
Type below:
___________

Answer:
8

Explanation:
There are 112 students for 14 teachers.
112/14
Divide 112/14 with 14/14
112/14 ÷ 14/14 = 8

Question 7.
Geoff charges $27 for 3 hours of swimming lessons. Anne charges $31 for 4 hours. How much more does Geoff charge per hour than Anne?
$ _____

Answer:
$1.25

Explanation:
Geoff charges $27 for 3 hours of swimming lessons.
$27/3 = $9 for an hour
Anne charges $31 for 4 hours.
$31/4 = $7.75
$9 – $7.75 = $1.25
Geoff charge $1.25 per hour more than Anne

Question 8.
Compare One florist made 16 bouquets in 5 hours. A second florist made 40 bouquets in 12 hours. Which florist makes bouquets at a faster rate?
Type below:
___________

Answer:
A second florist made 40 bouquets in 12 hours at a faster rate

Explanation:
Compare One florist made 16 bouquets in 5 hours.
16/5 = 3.2
A second florist made 40 bouquets in 12 hours.
40/12 = 3.333
A second florist made 40 bouquets in 12 hours at a faster rate

Tell which rate is faster by comparing unit rates.

Question 9.
\(\frac{160 \mathrm{mi}}{2 \mathrm{hr}} \text { and } \frac{210 \mathrm{mi}}{3 \mathrm{hr}}\)
Type below:
___________

Answer:
160mi/2hr

Explanation:
160mi/2hr ÷ 2/2 = 80mi/hr
210mi/3hr = 70mi/hr
80mi/hr > 70mi/hr

Question 10.
\(\frac{270 \mathrm{ft}}{9 \mathrm{min}} \text { and } \frac{180 \mathrm{ft}}{9 \mathrm{min}}\)
Type below:
___________

Answer:
270ft/9min

Explanation:
270ft/9min = 30ft/min
180ft/9min = 20ft/min
30ft/min > 20ft/min

Question 11.
\(\frac{250 \mathrm{m}}{10 \mathrm{s}} \text { and } \frac{120 \mathrm{m}}{4 \mathrm{s}}\)
Type below:
___________

Answer:
250m/10s

Explanation:
250m/10s = 25m/s
120m/4s = 20m/s
25m/s > 20m/s

Unlock the Problem – Page No. 246

Question 12.
Ryan wants to buy treats for his puppy. If Ryan wants to buy the treats that cost the least per pack, which treat should he buy? Explain.

a. What do you need to find?
Type below:
___________

Answer:
We need to find that cost the least per pack

Question 12.
b. Find the price per pack for each treat.
Type below:
___________

Answer:
Pup bites = $5.76/4 ÷ 4/4 = $1.44
Doggie Treats = $7.38/6 ÷ 6/6 = $1.23
Pupster snacks = $7.86/6 ÷ 6/6 = $1.31
Nutri-Biscuits = $9.44/8 ÷ 8/8 = $1.18

Question 12.
c. Complete the sentences
The treat with the highest price per pack is _____.
The treat with the lowest price per pack is _____.
Ryan should buy _____ because _____.
Type below:
___________

Answer:
The treat with the highest price per pack is Pup bites.
The treat with the lowest price per pack is Nutri-Biscuits.
Ryan should buy Nutri-Biscuits because it has the least cost.

Question 13.
Reason Abstractly What information do you need to consider in order to decide whether one product is a better deal than another? When might the lower unit rate not be the best choice? Explain.
Type below:
___________

Answer:
We will consider the low cost in order to decide whether one product is a better deal than another.
The lower unit rate is not the best choice. Because it will show the highest cost.

Question 14.
Select the cars that get a higher mileage per gallon of gas than a car that gets 25 miles per gallon. Mark all that apply.
Options:
a. Car A 22 miles per 1 gallon
b. Car B 56 miles per 2 gallons
c. Car C 81 miles per 3 gallons
d. Car D 51 miles per 3 gallons

Answer:
b. Car B 56 miles per 2 gallons
c. Car C 81 miles per 3 gallons

Explanation:
22/1 = 22
56/2 = 28
81/3 = 27
51/3 = 17

Find Unit Rates – Page No. 247

Write the rate as a fraction. Then find the unit rate.

Question 1.
A wheel rotates through 1,800º in 5 revolutions.
Type below:
___________

Answer:

Explanation:
A wheel rotates through 1,800º in 5 revolutions.
1,800º/5 revolutions
1,800º/5 revolutions ÷ 5/5 = 360º/1revolution

Question 2.
There are 312 cards in 6 decks of playing cards.
Type below:
___________

Answer:
52 cards/1 deck of playing cards

Explanation:
There are 312 cards in 6 decks of playing cards.
312/6 ÷ 6/6 = 52 cards/1 deck of playing cards

Question 3.
Bana ran 18.6 miles of a marathon in 3 hours.
Type below:
___________

Answer:
6.2 miles/hour

Explanation:
Bana ran 18.6 miles of a marathon in 3 hours.
18.6 miles/ 3 hours ÷ 3/3 = 6.2 miles/hour

Question 4.
Cameron paid $30.16 for 8 pounds of almonds.
Type below:
___________

Answer:
$3.77/1 pound

Explanation:
Cameron paid $30.16 for 8 pounds of almonds.
$30.16/8 pounds ÷ 8/8 = $3.77/1 pound

Compare unit rates.

Question 5.
An online game company offers a package that includes 2 games for $11.98. They also offer a package that includes 5 games for $24.95. Which package is a better deal?
_____ package

Answer:
5 game package

Explanation:
An online game company offers a package that includes 2 games for $11.98.
$11.98/2 = $5.99
They also offer a package that includes 5 games for $24.95.
$24.95/5 = $4.99

Question 6.
At a track meet, Samma finished the 200-meter race in 25.98 seconds. Tom finished the 100-meter race in 12.54 seconds. Which runner ran at a faster average rate?
___________

Answer:
Tom

Explanation:
At a track meet, Samma finished the 200-meter race in 25.98 seconds.
200/25.98 seconds = 7.698 – meter/1 sec
Tom finished the 100-meter race in 12.54 seconds.
100 – meter/12.54 seconds = 7.974 – meter/1 sec

Problem Solving

Question 7.
Sylvio’s flight is scheduled to travel 1,792 miles in 3.5 hours. At what average rate will the plane have to travel to complete the trip on time?
Type below:
___________

Answer:
512 miles per hour

Explanation:
Sylvio’s flight is scheduled to travel 1,792 miles in 3.5 hours.
1,792 miles/3.5 hours ÷ 3.5/3.5 = 512 miles per hour

Question 8.
Rachel bought 2 pounds of apples and 3 pounds of peaches for a total of $10.45. The apples and peaches cost the same amount per pound. What was the unit rate?
Type below:
___________

Answer:
$2.09 per pound

Explanation:
Rachel bought 2 pounds of apples and 3 pounds of peaches for a total of $10.45.
The apples and peaches cost the same amount per pound.
2 + 3 = 5
$10.45/5 = $2.09 per pound

Question 9.
Write a word problem that involves comparing unit rates.
Type below:
___________

Answer:
At a track meet, Samma finished the 200-meter race in 25.98 seconds. Tom finished the 100-meter race in 12.54 seconds. Which runner ran at a faster average rate?
At a track meet, Samma finished the 200-meter race in 25.98 seconds.
200/25.98 seconds = 7.698 – meter/1 sec
Tom finished the 100-meter race in 12.54 seconds.
100 – meter/12.54 seconds = 7.974 – meter/1 sec
Tom

Lesson Check – Page No. 248

Question 1.
Cran–Soy trail mix costs $2.99 for 5 ounces, Raisin–Nuts mix costs $3.41 for 7 ounces, Lots of Cashews mix costs $7.04 for 8 ounces, and Nuts for You mix costs $2.40 for 6 ounces. List the trail mix brands in order from the least expensive to the most expensive.
Type below:
___________

Answer:
Nuts for You, Raisin–Nuts, Cran–Soy trail mix, Lots of Cashews mix

Explanation:
Cran–Soy trail mix costs $2.99 for 5 ounces,
$2.99/5 = $0.598
Raisin–Nuts mix costs $3.41 for 7 ounces,
$3.41/7 = $0.487
Lots of Cashews mix costs $7.04 for 8 ounces,
$7.04/8 = $0.88
and Nuts for You mix costs $2.40 for 6 ounces.
$2.40/6 = $0.4

Question 2.
Aaron’s heart beats 166 times in 120 seconds. Callie’s heart beats 88 times in 60 seconds. Emma’s heart beats 48 times in 30 seconds. Galen’s heart beats 22 times in 15 seconds. Which two students’ heart rates are equivalent?
Type below:
___________

Answer:
Callie and Galen

Explanation:
Aaron’s heart beats 166 times in 120 seconds.
166/120 = 1.3833
Callie’s heart beats 88 times in 60 seconds.
88/60 = 1.4666
Emma’s heart beats 48 times in 30 seconds.
48/30 = 1.6
Galen’s heart beats 22 times in 15 seconds.
22/15 = 1.4666

Spiral Review

Question 3.
Courtlynn combines \(\frac{7}{8}\) cup sour cream with \(\frac{1}{2}\) cup cream cheese. She then divides the mixture between 2 bowls. How much mixture does Courtlynn put in each bowl?
\(\frac{□}{□}\) cup

Answer:
\(\frac{11}{16}\) cup

Explanation:
Courtlynn combines \(\frac{7}{8}\) cup sour cream with \(\frac{1}{2}\) cup cream cheese.
7/8 + 1/2 = 11/8
11/8 ÷ 2 = 11/8 × 1/2 = 11/16 cup

Question 4.
Write a comparison using < or > to show the relationship between |-\(\frac{2}{3}\)| and – \(\frac{5}{6}\).
Type below:
___________

Answer:
>

Explanation:
|-\(\frac{2}{3}\)| = 2/3 = 0.666
– \(\frac{5}{6}\) = -0.8333
|-\(\frac{2}{3}\)| > – \(\frac{5}{6}\)

Question 5.
There are 18 tires on one truck. How many tires are on 3 trucks of the same type?
_____ tires

Answer:
54 tires

Explanation:
There are 18 tires on one truck.
For 3 trucks, (3 × 18)/1 = 54 tires

Question 6.
Write two ratios that are equivalent to \(\frac{5}{6}\).
Type below:
___________

Answer:
\(\frac{5}{6}\) = \(\frac{10}{12}\), \(\frac{15}{18}\)

Explanation:
5/6 × 2/2 = 10/12
5/6 × 3/3 = 15/18

Share and Show – Page No. 251

Use a unit rate to find the unknown value.

Question 1.
\(\frac{10}{?}=\frac{6}{3}\)
_____

Answer:
5

Explanation:
6/3 ÷ 3/3 = 2/1
2/1 × 5/5 = 10/1
The unknown value is 5

Question 2.
\(\frac{6}{8}=\frac{?}{20}\)
_____

Answer:
15

Explanation:
6/8 ÷ 8/8 = 0.75/1
0.75/1 × 20/20 = 15/20
The unknown value is 15

On Your Own

Use a unit rate to find the unknown value.

Question 3.
\(\frac{40}{8}=\frac{45}{?}\)
_____

Answer:
9

Explanation:
40/8 ÷ 8/8 = 5/1
5/1 × 9/9 = 45/9
The unknown value is 9

Question 4.
\(\frac{42}{14}=\frac{?}{5}\)
_____

Answer:
15

Explanation:
42/14 ÷ 14/14 = 3/1
3/1 × 5/5 = 15/5
The unknown value is 15

Question 5.
\(\frac{?}{2}=\frac{56}{8}\)
_____

Answer:
14

Explanation:
56/8 ÷ 8/8 = 7/1
7/1 × 2/2 = 14/2
The unknown value is 14

Question 6.
\(\frac{?}{4}=\frac{26}{13}\)
_____

Answer:
8

Explanation:
26/13 ÷ 13/13 = 2/1
2/1 × 4/4 = 8/4
The unknown value is 8

Practice: Copy and Solve Draw a bar model to find the unknown value.

Question 7.
\(\frac{4}{32}=\frac{9}{?}\)
_____

Answer:

Explanation:
4/32 ÷ 32/32 = 0.125/1
0.125/1 × 72/72 = 9/72
The unknown value is 72

Question 8.
\(\frac{9}{3}=\frac{?}{4}\)
_____

Answer:

12

Explanation:
9/3 ÷ 3/3 = 3/1
3/1 × 4/4 = 12/4
The unknown value is 12

Question 9.
\(\frac{?}{14}=\frac{9}{7}\)
_____

Answer:

Explanation:
9/7 ÷ 7/7 = 1.2857/1
1.2857/1 × 14/14 = 18/14
The unknown value is 18

Question 10.
\(\frac{3}{?}=\frac{2}{1.25}\)
_____

Answer:
1.875

Explanation:
2/1.25 ÷ 1.25/1.25 = 1.6/1
1.6/1 × 1.875/1.875 = 3/1.875
The unknown value is 1.875

Question 11.
Communicate Explain how to find an unknown value in a ratio by using a unit rate.
Type below:
___________

Answer:
Firstly, Identify the known ratio, where both values are known. Then, Identify the ratio with one known value and one unknown value. Next, Use the two ratios to create a proportion. Finally, Cross-multiply to solve the problem.

Question 12.
Savannah is tiling her kitchen floor. She bought 8 cases of tile for $192. She realizes she bought too much tile and returns 2 unopened cases to the store. What was her final cost for tile?
$ _____

Answer:
$144

Explanation:
Savannah is tiling her kitchen floor. She bought 8 cases of tile for $192.
$192/8 ÷ 8/8 = $24 per each case of tile
She realizes she bought too much tile and returns 2 unopened cases to the store.
So, she bought 8 – 2 = 6 cases of tiles.
6 × $24 = $144

Problem Solving + Applications – Page No. 251

Pose a Problem

Question 13.
Josie runs a T-shirt printing company. The table shows the length and width of four sizes of T-shirts. The measurements of each size T-shirt form equivalent ratios.

What is the length of an extra-large T-shirt?
Write two equivalent ratios and find the unknown value:

The length of an extra-large T-shirt is 36 inches.
Write a problem that can be solved by using the information in the table and could be solved by using equivalent ratios
Type below:
___________

Answer:
Small = 27/18 ÷ 18/18 = 1.5
Medium = 30/20 = 3/2 = 1.5
Large = 1.5/1 × 22/22 = 33/22
the length of an extra-large T-shirt = 1.5/1 × 24/24 = 36/24
What is the length of an large T-shirt?
Write two equivalent ratios and find the unknown value?
Large = 1.5/1 × 22/22 = 33/22
33/22 × 2/2 = 66/44
33/22 × 3/3 = 99/66

Question 14.
Peri earned $27 for walking her neighbor’s dog 3 times. If Peri earned $36, how many times did she walk her neighbor’s dog? Use a unit rate to find the unknown value.
_____ times

Answer:
4 times

Explanation:
Peri earned $27 for walking her neighbor’s dog 3 times.
If Peri earned $36, ($36 × 3)/$27 = 4

Use Unit Rates – Page No. 253

Use a unit rate to find the unknown value.

Question 1.
\(\frac{34}{7}=\frac{?}{7}\)
_____

Answer:
34

Explanation:
34/7 ÷ 7/7 = 4.8571/1
4.8571/1 × 7/7 = 34
The unknown value is 34

Question 2.
\(\frac{16}{32}=\frac{?}{14}\)
_____

Answer:
7

Explanation:
16/32 ÷ 32/32 = 0.5/1
0.5/1 × 14/14 = 7/1
The unknown value is 7

Question 3.
\(\frac{18}{?}=\frac{21}{7}\)
_____

Answer:
6

Explanation:
21/7 ÷ 7/7 = 3/1
3/1 × 6/6 = 18/6
The unknown value is 6

Question 4.
\(\frac{?}{16}=\frac{3}{12}\)
_____

Answer:
4

Explanation:
3/12 ÷ 12/12 = 0.25/1
0.25/1 × 16/16 = 4
The unknown value is 4

Draw a bar model to find the unknown value.

Question 5.
\(\frac{15}{45}=\frac{6}{?}\)
_____

Answer:

18

Explanation:
15/45 ÷ 45/45 = 1/3
1/3 × 6/6 = 6/18
The unknown value is 18

Question 6.
\(\frac{3}{6}=\frac{?}{7}\)
_____

Answer:

3.5

Explanation:
3/6 ÷ 6/6 = 1/2
1/2 × 3.5/3.5 = 3.5/7
The unknown value is 3.5

Problem Solving

Question 7.
To stay properly hydrated, a person should drink 32 fluid ounces of water for every 60 minutes of exercise. How much water should Damon drink if he rides his bike for 135 minutes?
_____ fluid ounces

Answer:
72 fluid ounces

Explanation:
To stay properly hydrated, a person should drink 32 fluid ounces of water for every 60 minutes of exercise.
If he rides his bike for 135 minutes, (135 × 32)/60 = 72

Question 8.
Lillianne made 6 out of every 10 baskets she attempted during basketball practice. If she attempted to make 25 baskets, how many did she make?
_____ baskets

Answer:
15 baskets

Explanation:
Lillianne made 6 out of every 10 baskets she attempted during basketball practice. If she attempted to make 25 baskets,
(25 × 6)/10 = 15 baskets

Question 9.
Give some examples of real-life situations in which you could use unit rates to solve an equivalent ratio problem.
Type below:
___________

Answer:
1) If a 10-ounce box of cereal costs $3 and a 20-ounce box of cereal costs $5, the 20 ounce box is the better value because each ounce of cereal is cheaper.
2) Yoda Soda is the intergalactic party drink that will have all your friends saying, “Mmmmmm, good this is!”
You are throwing a party, and you need 555 liters of Yoda Soda for every 121212 guests.
If you have 363636 guests, how many liters of Yoda Soda do you need?

Lesson Check – Page No. 254

Question 1.
Randi’s school requires that there are 2 adult chaperones for every 18 students when the students go on a field trip to the museum. If there are 99 students going to the museum, how many adult chaperones are needed?
_____ chaperones

Answer:
11 chaperones

Explanation:
Randi’s school requires that there are 2 adult chaperones for every 18 students when the students go on a field trip to the museum.
If there are 99 students going to the museum, (99 × 2)/18 = 11 chaperones

Question 2.
Landry’s neighbor pledged $5.00 for every 2 miles he swims in a charity swim-a-thon. If Landry swims 3 miles, how much money will his neighbor donate?
$ _____

Answer:
$7.5

Explanation:
Landry’s neighbor pledged $5.00 for every 2 miles he swims in a charity swim-a-thon. If Landry swims 3 miles, 15/2 = $7.5

Spiral Review

Question 3.
Describe a situation that could be represented by –8.
Type below:
___________

Answer:
In Alaska the normal temperature in December was 3 degrees. Scientist predicted that by February the temperature would drop 11 degrees. What is the predicted temperature for February? The answer is -8.

Question 4.
What are the coordinates of point G?

Type below:
___________

Answer:
(-2, 0.5)

Explanation:
The x-coordinate is -2
The y-coordinate is 0.5

Question 5.
Gina bought 6 containers of yogurt for $4. How many containers of yogurt could Gina buy for $12?
_____ containers

Answer:
18 containers

Explanation:
Gina bought 6 containers of yogurt for $4.
For $12, ($12 × 6)/$4 = 18

Question 6.
A bottle containing 64 fluid ounces of juice costs $3.84. What is the unit rate?
$ _____

Answer:
$0.06

Explanation:
A bottle containing 64 fluid ounces of juice costs $3.84.
$3.84/64 = $0.06

Share and Show – Page No. 257

A redwood tree grew at a rate of 4 feet per year. Use this information for 1–3.

Question 1.
Complete the table of equivalent ratios for the first 5 years.

Type below:
___________

Answer:

Explanation:
A redwood tree grew at a rate of 4 feet per year.
For 2 years, 2 × 4 = 8ft
For 3 years, 3 × 4 = 12ft
For 4 years, 4 × 4 = 16ft
For 5 years, 5 × 4 = 20ft

Question 2.
Write ordered pairs, letting the x-coordinate represent time in years and the y-coordinate represent height in feet.
Type below:
___________

Answer:
(1, 4), (2, 8), (3, 12), (4, 16), (5, 20)

Question 3.
Use the ordered pairs to graph the tree’s growth over time.
Type below:
___________

Answer:

On Your Own

The graph shows the rate at which Luis’s car uses gas, in miles per gallon. Use the graph for 4–8.

Question 4.
Complete the table of equivalent ratios.
Type below:
___________

Answer:
30/1, 60/2, 90/3, 120/4, 150/5

Question 5.
Find the car’s unit rate of gas usage.
Type below:
___________

Answer:
30mi/gal

Question 6.
How far can the car go on 5 gallons of gas?
_____ miles

Answer:
150 miles

Explanation:
the car go on 5 gallons of gas, 150/5

Question 7.
Estimate the amount of gas needed to travel 50 miles.
Type below:
___________

Answer:
5/3

Explanation:
30/1,
50/30 = 5/3

Question 8.
Ellen’s car averages 35 miles per gallon of gas. If you used equivalent ratios to graph her car’s gas usage, how would the graph differ from the graph of Luis’s car’s gas usage?
Type below:
___________

Answer:

The distance is high for Ellen’s car’s gas usage compared to Luis’s car’s gas usage per one gal

Explanation:
35/1 × 2/2 = 70/2
35/1 × 3/3 = 105/3
35/1 × 4/4 = 140/4
35/1 × 5/5 = 175/5

Problem Solving + Applications – Page No. 258

Question 9.
Look for Structure The graph shows the depth of a submarine over time. Use equivalent ratios to find the number of minutes it will take the submarine to descend 1,600 feet.

_____ minutes

Answer:
8 minutes

Explanation:
200/1 × 8/8 = 1600/8

Question 10.
The graph shows the distance that a plane flying at a steady rate travels over time. Use equivalent ratios to find how far the plane travels in 13 minutes.

_____ miles

Answer:
91 miles

Explanation:
7/1 × 13/13 = 91/13

Question 11.
Sense or Nonsense? Emilio types at a rate of 84 words per minute. He claims that he can type a 500-word essay in 5 minutes. Is Emilio’s claim sense or nonsense? Use a graph to help explain your answer.
Type below:
___________

Answer:
He said that he can write 84 in 60sec ,500 words will be written in 500×60/84=357 it’s a nonsense

Question 12.
The Tuckers drive at a rate of 20 miles per hour through the mountains. Use the ordered pairs to graph the distance traveled over time.

Type below:
___________

Answer:

Equivalent Ratios and Graphs – Page No. 259

Christie makes bracelets. She uses 8 charms for each bracelet. Use this information for 1–3.

Question 1.
Complete the table of equivalent ratios for the first 5 bracelets.
Type below:
___________

Answer:

Explanation:

Question 2.
Write ordered pairs, letting the x-coordinate represent the number of bracelets and the y-coordinate represent the number of charms.
Type below:
___________

Answer:
(1, 8), (2, 16), (3, 24), (4, 32), (5, 40)

Question 3.
Use the ordered pairs to graph the charms and bracelets.
Type below:
___________

Answer:

The graph shows the number of granola bars that are in various numbers of boxes of Crunch N Go. Use the graph for 4–5.

Question 4.
Complete the table of equivalent ratios.

Type below:
___________

Answer:

Question 5.
Find the unit rate of granola bars per box.
Type below:
___________

Answer:
10 bars/1 box

Problem Solving

Question 6.
Look at the graph for Christie’s Bracelets. How many charms are needed for 7 bracelets?
_____ charms

Answer:
56 charms

Question 7.
Look at the graph for Crunch N Go Granola Bars. Stefan needs to buy 90 granola bars. How many boxes must he buy?
_____ boxes

Answer:
9 boxes

Question 8.
Choose a real-life example of a unit rate. Draw a graph of the unit rate. Then explain how another person could use the graph to find the unit rate.
Type below:
___________

Answer:
Sam prepares 4 bracelets per month. How many bracelets does she prepare in a span of 6 months?
For 1 month, 1 × 4 = 4 bracelets
For 2 months, 2 × 4 = 8 bracelets
For 3 months, 3 × 4 = 12 bracelets
For 4 months, 4 × 4 = 16 bracelets
For 5 months, 5 × 4 = 20 bracelets

Lesson Check – Page No. 260

Question 1.
A graph shows the distance a car traveled over time. The x-axis represents time in hours, and the y-axis represents distance in miles. The graph contains the point (3, 165). What does this point represent?
Type below:
___________

Answer:

Explanation:
In 3 hours the car traveled 165 miles.
(3,165) is (x,y) so 3 = x and 165 = y, and
3=x=time in hours
165=y= miles…. soooo
In 3 hours the car traveled 165 miles

Question 2.
Maura charges $11 per hour to babysit. She makes a graph comparing the amount she charges (the y-coordinate) to the time she babysits (the x-coordinate). Which ordered pair shown is NOT on the graph?
(4, 44) (11, 1) (1, 11) (11, 12)
Type below:
___________

Answer:
(11, 1)

Explanation:
It is not 11,1 because she charges 11 hours per hour (y coordinate) and x would be time to babysit. so it can’t be 11,1

Spiral Review

Question 3.
List 0, –4, and 3 from least to greatest.
Type below:
___________

Answer:
-4, 0, 3

Question 4.
What two numbers can be used in place of the ? to make the statement true?
|?| = \(\frac{8}{9}\)
Type below:
___________

Answer:
–\(\frac{8}{9}\), \(\frac{8}{9}\)

Explanation:
|-\(\frac{8}{9}\)| = \(\frac{8}{9}\)
|\(\frac{8}{9}\)| = \(\frac{8}{9}\)

Question 5.
Morgan plots the point (4, –7) on a coordinate plane. If she reflects the point across the y-axis, what are the coordinates of the reflected point?
Type below:
___________

Answer:
(-4, -7)

Explanation:
Morgan plots the point (4, –7) on a coordinate plane. If she reflects the point across the y-axis, it will be (-4, -7)

Question 6.
Jonathan drove 220 miles in 4 hours. Assuming he drives at the same rate, how far will he travel in 7 hours?
_____ miles

Answer:
385 miles

Explanation:
Jonathan drove 220 miles in 4 hours.
If he travel in 7 hours, (7 × 220)/4 = 385 miles

Chapter 4 Review/Test – Page No. 261

Question 1.
Kendra has 4 necklaces, 7 bracelets, and 5 rings. Draw a model to show the ratio that compares rings to bracelets
Type below:___________

Answer:

Question 2.
There are 3 girls and 2 boys taking swimming lessons. Write the ratio that compares the girls taking swimming lessons to the total number of students taking swimming lessons.
Type below:
___________

Answer:
3 : 5

Explanation:
There are 3 girls and 2 boys taking swimming lessons.
the total number of students taking swimming lessons = 5
3 : 5

Question 3.
Luis adds 3 strawberries for every 2 blueberries in his fruit smoothie. Draw a model to show the ratio that compares strawberries to blueberries.
Type below:
___________

Answer:

Question 4.
Write the ratio 3 to 10 in two different ways.
Type below:
___________

Answer:
3/10, 3 : 10

Question 5.
Alex takes 3 steps every 5 feet he walks. As Alex continues walking, he takes more steps and walks a longer distance. Complete the table by writing two equivalent ratios.

Type below:
___________

Answer:

Explanation:
Alex takes 3 steps every 5 feet he walks. As Alex continues walking, he takes more steps and walks a longer distance.
3/5 × 2/2 = 6/10
3/5 × 3/3 = 9/15

Page No. 262

Question 6.
Sam has 3 green apples and 4 red apples. Select the ratios that compare the number of red apples to the total number of apples. Mark all that apply.
Options:
a. 4 to 7
b. 3 to 7
c. 4 : 7
d. 4 : 3
e. \(\frac{3}{7}\)
f. \(\frac{4}{7}\)

Answer:
a. 4 to 7
c. 4 : 7
f. \(\frac{4}{7}\)

Explanation:
Sam has 3 green apples and 4 red apples.
the total number of apples = 3 + 4 = 7
4 : 7

Question 7.
Jeff ran 2 miles in 12 minutes. Ju Chan ran 3 miles in 18 minutes. Did Jeff and Ju Chan run the same number of miles per minute? Complete the tables of equivalent ratios to support your answer.

Type below:
___________

Answer:

Explanation:
2/12 × 2/2 = 4/24
2/12 × 3/3 = 6/39
2/12 × 4/4 = 8/48
3/18 × 2/2 = 6/36
3/18 × 3/3 = 9/24
3/18 × 4/4 = 12/72

Question 8.
Jen bought 2 notebooks for $10. Write the rate as a fraction. Then find the unit rate.
Type below:
___________

Answer:
$10/2
unit rate = $5

Explanation:
Jen bought 2 notebooks for $10.
$10/2 ÷ 2/2 = $5

Page No. 263

Question 9.
Determine whether each ratio is equivalent to \(\frac{1}{2}, \frac{2}{3}, \text { or } \frac{4}{7}\). Write the ratio in the correct box.

Type below:
___________

Answer:

Explanation:
1/2 × 2/2 = 4/8
7/14 ÷ 2/2 = 1/2
20/35 ÷ 5/5 = 4/7
40/80 ÷ 40/40 = 1/2
8/14 ÷ 2/2 = 4/7
4/6 ÷ 2/2 = 2/3
8/12 ÷ 4/4 = 2/3

Question 10.
Amos bought 5 cantaloupes for $8. How many cantaloupes can he buy for $24? Show your work.
_____ cantaloupes

Answer:
15 cantaloupes

Explanation:
Amos bought 5 cantaloupes for $8.
For $24, ($24 × 5)/$8 = 15

Question 11.
Camille said \(\frac{4}{5}\) is equivalent to \(\frac{24}{30}\). Check her work by making a table of equivalent ratios.
Type below:
___________

Answer:

Question 12.
A box of oat cereal costs $3.90 for 15 ounces. A box of rice cereal costs $3.30 for 11 ounces. Which box of cereal costs less per ounce? Use numbers and words to explain your answer.
Type below:
___________

Answer:
A box of oat cereal costs $3.90 for 15 ounces.
$3.90/15 = $0.26
A box of rice cereal costs $3.30 for 11 ounces.
$3.30/11 = $0.3
$0.26 < $0.3

Page No. 264

Question 13.
Scotty earns $35 for babysitting for 5 hours. If Scotty charges the same rate, how many hours will it take him to earn $42?
_____ hours

Answer:
6 hours

Explanation:
Scotty earns $35 for babysitting for 5 hours
For $42, (42 × 5)/35 = 6

Question 14.
Use a unit rate to find the unknown value.

Type below:
___________

Answer:

Explanation:
(9 × 42)/14 = 3

Question 15.
Jenna saves $3 for every $13 she earns. Vanessa saves $6 for every $16 she earns. Is Jenna’s ratio of money saved to money earned equivalent to Vanessa’s ratio of money saved to money earned?
Type below:
___________

Answer:
No, 3/13 = 6/26. Vanessa ratio is 6/16

Question 16.
The Hendersons are on their way to a national park. They are traveling at a rate of 40 miles per hour. Use the ordered pairs to graph the distance traveled over time

Type below:
___________

Answer:

Page No. 265

Question 17.
Abby goes to the pool to swim laps. The graph shows how far Abby swam over time. Use equivalent ratios to find how far Abby swam in 7 minutes

_____ meters

Answer:
350 meters

Explanation:
50/1 × 7/7 = 350/7

Question 18.
Caleb bought 6 packs of pencils for $12.
Part A
How much will he pay for 9 packs of pencils? Use numbers and words to explain your answer
$ _____

Answer:
$18

Explanation:
Caleb bought 6 packs of pencils for $12.
6/12 = 1/2 × 9/9 = 9/18
So, $18 is the answer

Question 18.
Part B
Describe how to use a bar model to solve the problem.
Type below:
___________

Answer:
Take the known ratio and identify the unknown value using known ratio.

Page No. 266

Question 19.
A rabbit runs 35 miles per hour. Select the animals who run at a faster unit rate per hour than the rabbit. Mark all that apply.
Options:
a. Reindeer: 100 miles in 2 hours
b. Ostrich: 80 miles in 2 hours
c. Zebra: 90 miles in 3 hours
d. Squirrel: 36 miles in 3 hours

Answer:
a. Reindeer: 100 miles in 2 hours
b. Ostrich: 80 miles in 2 hours

Explanation:
A rabbit runs 35 miles per hour.
35/1
100/2 = 50/1
80/2 = 40/1
90/3 = 30/1
36/3 = 12/1

Question 20.
Water is filling a bathtub at a rate of 3 gallons per minute.
Part A
Complete the table of equivalent ratios for the first five minutes of the bathtub filling up.

Type below:
___________

Answer:

Question 20.
Part B
Emily said there will be 36 gallons of water in the bathtub after 12 minutes. Explain how Emily could have found her answer
Type below:
___________

Answer:
Emily said there will be 36 gallons of water in the bathtub after 12 minutes.
36/12 ÷ 12/12 = 3/1
She can find the answer using the unit rate.

Conclusion:

Hope the solutions provided in Go Math Grade 6 Answer Key Chapter 4 Model Ratios helped you to enhance your math skills. Also, this Go Math Answer Key helps you to score the highest marks in the exam. Share this pdf link with your friends so that they can overcome the difficulties in maths. All the Best!!!

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Go Math Grade 8 Chapter 7 Solving Linear Equations Answer Key

Improve your performance in exams with the help of Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations. You can find the review questions at the end of the chapter to test your knowledge. The topics covered in this Solving Linear Equations chapter are equations with the variable on both sides, equations with rational numbers, equations with the distributive property, equations with many solutions or no solution, etc. Just go through the online pdf and start practicing now. By looking into the questions and answers available on Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations.

Lesson 1: Equations with the Variable on Both Sides

• · Equations with the Variable on Both Sides – Page No. 200
• · Equations with the Variable on Both Sides – Page No. 201
• · Equations with the Variable on Both Sides Lesson Check – Page No. 202

Lesson 2: Equations with Rational Numbers

• · Equations with Rational Numbers – Page No. 206
• · Equations with Rational Numbers – Page No. 207
• · Equations with Rational Numbers Lesson Check – Page No. 208

Lesson 3: Equations with the Distributive Property

• · Equations with the Distributive Property – Page No. 212
• · Equations with the Distributive Property – Page No. 213
• · Equations with the Distributive Property Lesson Check – Page No. 214

Lesson 4: Equations with Many Solutions or No Solution

• · Equations with Many Solutions or No Solution – Page No. 218
• · Equations with Many Solutions or No Solution – Page No. 219
• · Equations with Many Solutions or No Solution Lesson Check – Page No. 220

Lesson 5: Equations with the Variable on Both Sides

• · Equations with the Variable on Both Sides – Model Quiz – Page No. 221

Reviews

• • Mixed Review – Page No. 222

Guided Practice – Equations with the Variable on Both Sides – Page No. 200

Use algebra tiles to model and solve each equation.

Question 1.
x + 4 = -x – 4
x = ________

Answer:
x = -4

Explanation:
Model x + 4 on the left side of the mat and -x -4 on the right side.

Add one c-tile to both sides. This represents adding x to both sides of the equation. Remove zero pairs.

Place four -1-tiles on both sides. This represents subtracting -4 from both sides of the equation. Remove zero pairs.

Separate each side into 2 equal groups. One x-tile is equivalent to four -1-tiles.

x = -4

Question 2.
2 – 3x = -x – 8
x = ________

Answer:

Explanation:
Given 2 – 3x = -x – 8
Model 2-3x on the left side of the mat and -x-8 on the right side.

Place one x tile to both sides. This represents subtracting from both sides of the equation.

Remove 2 1 tiles from sides. This represents subtracting from both sides of the equation.

Separate each side into 2 equal groups. One -x tile is equivalent to 5 – 1 tile.

The solution is -x = -5 or x = 5

Question 3.
At Silver Gym, membership is $25 per month, and personal training sessions are $30 each. At Fit Factor, membership is $65 per month, and personal training sessions are $20 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
________ sessions

Answer:
4 sessions

Explanation:
At Silver Gym, membership is $25 per month, and personal training sessions are $30 each.
Membership + Personal training session = 25 + 30x
At Fit Factor, membership is $65 per month, and personal training sessions are $20 each.
Membership + Personal training session = 65 + 20x
Membership at Silver Gym = Membership at Fit Factor
25 + 30x = 65 + 20x
30x – 20x = 65 – 25
10x = 40
x = 4
Sarah would have to buy 4 sessions for the total cost at the two gyms to be equal.

Question 4.
Write a real-world situation that could be modeled by the equation 120 + 25x = 45x.
Type below:
_______________

Answer:
120 + 25x = 45x
Sarah offers a plan to tutor a student at $25 per her plus a one-time registration fee of $ 120.
Surah offers an alternative plan to tutor a student at $45 per hour and no registration fee.
120 + 25x = 45x

Question 5.
Write a real-world situation that could be modeled by the equation 100 – 6x = 160 – 10x.
Type below:
_______________

Answer:
100 – 6x = 160 – 10x
The initial water in Tank A is 100 gallons and leaks at 6 gallons per week.
The initial water in Tank B is 160 gallon and leaks at 10 gallons per week
100 – 6x = 160 – 10x

Essential Question Check-In

Question 6.
How can you solve an equation with the variable on both sides?
Type below:
_______________

Answer:
Isolate the variable on one side. Add/subtract the variable with a lower coefficient from both sides. Add/subtract the constant (with the variable) from both sides. Divide both sides by coefficient of isolated variable.

Independent Practice – Equations with the Variable on Both Sides – Page No. 201

Question 7.
Derrick’s Dog Sitting and Darlene’s Dog Sitting are competing for new business. The companies ran the ads shown.

a. Write and solve an equation to find the number of hours for which the total cost will be the same for the two services.
________ hours

Answer:
3 hours

Explanation:
Hourly rate + One time fee = 5x + 12
Hourly rate + One time fee = 3x + 18
5x + 12 = 3x + 18
5x – 3x = 18 – 12
2x = 6
x = 3
the cost of the two dog sitting would be same for 3 hrs.

Question 7.
b. Analyze Relationships
Which dog sitting service is more economical to use if you need 5 hours of service? Explain.
____________

Answer:
Darlene’s Dog Sitting would be cheaper

Explanation:
Let y be the cost of dog sitting after x hours for both companies
y = 5x +12
y = 3x +18
Substitute x = 5
y = 5(5) + 12 = 37
y = 3 (5) + 18 = 33
compare the cost for both companies for x = 5hr.
$37 > $33
Darlene’s Dog Sitting would be cheaper

Question 8.
Country Carpets charges $22 per square yard for carpeting, and an additional installation fee of $100. City Carpets charges $25 per square yard for the same carpeting, and an additional installation fee of $70.
a. Write and solve an equation to find the number of square yards of carpeting for which the total cost charged by the two companies will be the same.
_______ square yards

Answer:
10 square yards

Explanation:
Unit square rate + One time installation fee = 22x + 100
Unit square rate + One time installation fee = 25x + 70
22x + 100 = 25x + 70
25x – 22x = 100 – 70
3x = 30
x = 10
the total cost charged by the two companies will be the same for 10 square yards of carpeting.

Question 8.
b. Justify Reasoning
Mr. Shu wants to hire one of the two carpet companies to install carpeting in his basement. Is he more likely to hire Country Carpets or City Carpets? Explain your reasoning.
___________

Answer:
City Carpets are cheaper when x < 10
y = 25(9) + 70 = 295
y = 22(9) + 100 = 298
Country Carpets are cheaper when x > 10
y = 25(11) + 70 = 345
y = 25(11) + 100 = 342
If Mr.Shu needs the carpenting done for less than 10square yards, he will hire City Carpets and if he needs carpenting for more than 10 square yard, he will hire Country Carpets.

Write an equation to represent each relationship. Then solve the equation.

Question 9.
Two less than 3 times a number is the same as the number plus 10.
________

Answer:
3x – 2 = x + 10
x = 6

Explanation:
Two less than 3 times a number is the same as the number plus 10.
Two less than 3 times x is the same as the x plus 10.
Two less than 3x is the same as the x + 10
3x – 2 is the same as x + 10
3x – 2 = x + 10
3x – x = 10 + 2
2x = 12
x = 6

Question 10.
A number increased by 4 is the same as 19 minus 2 times the number.
______

Answer:
x + 4 = 19 – 2x
x = 5

Explanation:
A number increased by 4 is the same as 19 minus 2 times the number.
x increased by 4 is the same as 19 minus 2x.
x + 4 is the same as 19 – 2x
x + 4 = 19 – 2x
x + 2x = 19 – 4
3x = 15
x = 15/3
x = 5

Question 11.
Twenty less than 8 times a number is the same as 15 more than the number.
Type below:
____________

Answer:
8x – 20 = x + 15
x = 5

Explanation:
Twenty less than 8 times a number is the same as 15 more than the number.
Twenty less than 8 times x is the same as 15 more than the x.
Twenty less than 8x is the same as 15 more than the x
8x – 20 is the same as x + 15
8x – 20 = x + 15
8x – x = 15 + 20
7x = 35
x = 35/7 = 5
x = 5

Equations with the Variable on Both Sides – Page No. 202

Question 12.
The charges for an international call made using the calling card for two phone companies are shown in the table.

a. What is the length of a phone call that would cost the same no matter which company is used?
_______ minutes

Answer:
10 minutes

Explanation:
Cost of minutes + One time fee = 3x + 35
Cost of minutes + One time fee = 2x + 45
3x + 35 = 2x + 45
3x – 2x = 45 – 35
x = 10
The cost would be same for 10 minutes.

Question 12.
b. Analyze Relationships
When is it better to use the card from Company B?
Type below:
____________

Answer:
y = 3x + 35
y = 3(11) + 35 = $68
y = 2x + 45
y = 2(11) + 45 = $67
Since when x > 10, Company B is cheaper so it should be better to use when the length of the call is greater than 10 minutes.

H.O.T.

Focus on Higher Order Thinking

Question 13.
Draw Conclusions
Liam is setting up folding chairs for a meeting. If he arranges the chairs in 9 rows of the same length, he has 3 chairs left over. If he arranges the chairs in 7 rows of that same length, he has 19 left over. How many chairs does Liam have?
______ chairs

Answer:
75 chairs

Explanation:
Number of chairs in 9 row + left over chairs = 9x + 3
Number of chairs in 7 row + left over chairs = 7x + 19
9x + 3 = 7x + 19
9x – 7x = 19 – 3
2x = 16
x = 16/2
x = 8
Total number of chairs = 9(8) + 3 = 75

Question 14.
Explain the Error
Rent-A-Tent rents party tents for a flat fee of $365 plus $125 a day. Capital Rentals rents party tents for a flat fee of $250 plus $175 a day. Delia wrote the following equation to find the number of days for which the total cost charged by the two companies would be the same:
365x + 125 = 250x + 175
Find and explain the error in Delia’s work. Then write the correct equation.
Type below:
____________

Answer:
Delia’s equation
365x + 125 = 250x + 175
The error is that she attached the variable with the flat fee (which is constant) and put the daily rent as a constant (which is variable).
Correct equation
125x + 365 = 175x + 250

Question 15.
Persevere in Problem Solving
Lilliana is training for a marathon. She runs the same distance every day for a week. On Monday, Wednesday, and Friday, she runs 3 laps on a running trail and then runs 6 more miles.On Tuesday and Sunday, she runs 5 laps on the trail and then runs 2 more miles. On Saturday, she just runs laps. How many laps does Lilliana run on Saturday?
________ laps

Answer:
2 laps

Explanation:
Miles covered by lap + Addition number of miles = 3x + 6
Miles covered by lap + Addition number of miles = 5x + 2
3x + 6 = 5x + 2
5x – 3x = 6 – 2
2x = 4
x = 4/2
x = 2

Guided Practice – Equations with Rational Numbers – Page No. 206

Question 1.
Sandy is upgrading her Internet service. Fast Internet charges $60 for installation and $50.45 per month. Quick Internet has free installation but charges $57.95 per month.
a. Write an equation that can be used to find the number of months at which the Internet service would cost the same.
Type below:
____________

Answer:
50.45x + 60 = 57.95x

Explanation:
Write an equation for Fast Internet, where x is the number of months.
Charge per Month × Number of Month + Installation Fee
50.45x + 60
Write an equation for Quick Internet, where x is the number of months.
Charge per Month × Number of Month + Installation Fee
57.95x
50.45x + 60 = 57.95x

Question 1.
b. Solve the equation.
_______ hours

Answer:
8

Explanation:
50.45x + 60 = 57.95x
57.95x – 50.45x = 60
7.5x = 60
x = 60/7.5
x = 8
The total cost will be the same for 8 months.

Solve.

Question 2.
\(\frac{3}{4}\) n – 18 = \(\frac{1}{4}\) n – 4
______

Answer:
n = 28

Explanation:
3/4 . n – 18 = 1/4 . n – 4
Determine the least common multiple of the denominators
LCM is 4
Multiply both sides of the equation by the LCM
4(3/4 . n – 18) = 4(1/4 . n – 4)
3n – 72 = n – 16
3n – n = -16 + 72
2n = 56
n = 56/2
n = 28

Question 3.
6 + \(\frac{4}{5}\) b = \(\frac{9}{10}\) b
_______

Answer:
b = 60

Explanation:
6 + \(\frac{4}{5}\) b = \(\frac{9}{10}\) b
LCM is 10
10(6 + \(\frac{4}{5}\) b) = 10(\(\frac{9}{10}\) b)
60 + 8b = 9b
9b – 8b = 60
b = 60

Question 4.
\(\frac{2}{11}\) m + 16 = 4 + \(\frac{6}{11}\) m
_______

Answer:
m = 33

Explanation:
\(\frac{2}{11}\) m + 16 = 4 + \(\frac{6}{11}\) m
The LCM is 11
11(\(\frac{2}{11}\) m + 16) = 11(4 + \(\frac{6}{11}\) m)
2m + 176 = 44 + 6m
6m – 2m = 176 – 44
4m = 132
m = 132/4
m = 33

Question 5.
2.25t + 5 = 13.5t + 14
_______

Answer:
t = -0.8

Explanation:
2.25t + 5 = 13.5t + 14
13.5t – 2.25t = 5 – 14
11.25t = -9
t = -9/11.25
t = -0.8

Question 6.
3.6w = 1.6w + 24
_______

Answer:
w = 12

Explanation:
3.6w = 1.6w + 24
3.6w – 1.6w = 24
2w = 24
w = 24/2
w = 12

Question 7.
-0.75p – 2 = 0.25p
_______

Answer:
p = -2

Explanation:
-0.75p – 2 = 0.25p
-2 = 0.25p + 0.75p
-2 = p
p = -2

Question 8.
Write a real-world problem that can be modeled by the equation 1.25x = 0.75x + 50.
Type below:
______________

Answer:
1.25x = 0.75x + 50.
Cell offer Plan A for no base fee and $1.25 per minute.
Cell offer Plan B for a $50 base fee and $0.75 per minute.
The equation shows when the total cost of the plan would be equal.

Essential Question Check-In

Question 9.
How does the method for solving equations with fractional or decimal coefficients and constants compare with the method for solving equations with integer coefficients and constants?
Type below:
______________

Answer:
When solving equations with fractional or decimal coefficients, the equations need to be multiplied by the multiple of denominator such that the equations have integer coefficients and constants.

Independent Practice – Equations with Rational Numbers – Page No. 207

Question 10.
Members of the Wide Waters Club pay $105 per summer season, plus $9.50 each time they rent a boat. Nonmembers must pay $14.75 each time they rent a boat. How many times would a member and a non-member have to rent a boat in order to pay the same amount?
_______ times

Answer:
20 times

Explanation:
Members of the Wide Waters Club pay $105 per summer season, plus $9.50 each time they rent a boat.
9.5x + $105
Nonmembers must pay $14.75 each time they rent a boat.
9.5x + $105 = 14.75x
9.5x – 14.75x = $105
5.25x = 105
x = 105/5.25
x = 20
The cost for members and non-members will be the same for 8 visits.

Question 11.
Margo can purchase tile at a store for $0.79 per tile and rent a tile saw for $24. At another store she can borrow the tile saw for free if she buys tiles there for $1.19 per tile. How many tiles must she buy for the cost to be the same at both stores?
_______ tiles

Answer:
60 tiles

Explanation:
Margo can purchase tile at a store for $0.79 per tile and rent a tile saw for $24.
0.79x + 24
At another store she can borrow the tile saw for free if she buys tiles there for $1.19 per tile.
1.19x
0.79x + 24 = 1.19x
1.19x – 0.79x = 24
0.4x = 24
x = 24/0.4
x = 60
Margo should buy 60 tiles for the cost to be the same at both stores.

Question 12.
The charges for two shuttle services are shown in the table. Find the number of miles for which the cost of both shuttles is the same.

_______ miles

Answer:
40 miles

Explanation:
0.1x + 10
0.35x
0.1x + 10 = 0.35x
0.35x – 0.1x = 10
0.25x = 10
x = 10/0.25
x = 40
The cost of shuttles would be the same for 40 miles.

Question 13.
Multistep
Rapid Rental Car charges a $40 rental fee, $15 for gas, and $0.25 per mile driven. For the same car, Capital Cars charges $45 for rental and gas and $0.35 per mile.
a. For how many miles is the rental cost at both companies the same?
_______ miles

Answer:
100 miles

Explanation:
0.25x + 40 + 15 = 0.35x + 45
0.35x – 0.25x = 55 – 45
0.1x = 10
x = 10/0.1
x = 100
The cost of car rentals would be the same for 100 miles.

Question 13.
b. What is that cost?
$ _______

Answer:
$80

Explanation:
Let y be the total cost. Substitute 100 miles in any one of the two equations
y = 0.35x + 45
y = 0.35(100) + 45 = $80
Total cost would be $80.

Question 14.
Write an equation with the solution x = 20. The equation should have the variable on both sides, a fractional coefficient on the left side, and a fraction anywhere on the right side.
Type below:
______________

Answer:
4/3x + 10 = 50/3 + x

Explanation:
Write an equation with the solution x = 20. The equation should have the variable on both sides, a fractional coefficient on the left side, and a fraction anywhere on the right side.
1/3 . x = 1/3 . 20
1/3 . x + x = 1/3 . 20 + x
4/3x = 20/3 + x
4/3x + 10 = 20/3 + x + 10
4/3x + 10 = 50/3 + x

Question 15.
Write an equation with the solution x = 25. The equation should have the variable on both sides, a decimal coefficient on the left side, and a decimal anywhere on the right side. One of the decimals should be written in tenths, the other in hundredths.
Type below:
______________

Answer:
x=25
divide both sides by 25
x/25 = 1
convert 1/25 to decimal form 0.04
0.04x = 1
add x on both sides
1.04x = 1 + x
add 0.1 on both sides
1.04x + 0.1 = x + 1.1

Question 16.
Geometry
The perimeters of the rectangles shown are equal. What is the perimeter of each rectangle?

Perimeter = _______

Answer:
Perimeter = 3.2

Explanation:
Perimeter of the first rectangle
P = 2(n + n + 0.6) = 2(2n + 0.6) = 4n + 1.2
Perimeter of the second rectangle
P = 2(n + 0.1 + 2n) = 2(3n + 0.1) = 6n + 0.2
the perimeter is equal
4n + 1.2 = 6n + 0.2
6n – 4n = 1.2 – 0.2
2n = 1
n = 1/2
n = 0.5
P = 4n + 1.2 = 4(0.5) + 1.2 = 3.2

Question 17.
Analyze Relationships
The formula F = 1.8C + 32 gives the temperature in degrees Fahrenheit (F) for a given temperature in degrees Celsius (C). There is one temperature for which the number of degrees Fahrenheit is equal to the number of degrees Celsius. Write an equation you can solve to find that temperature and then use it to find the temperature
Type below:
______________

Answer:
x = 1.8x + 32

Explanation:
F = 1.8C +32
let x be the temperature such that it is same in both celsius and in fahrenheit
Then the required equation is
x = 1.8x + 32
subtract 1.8x from both sides
-0.8x = 32
divide by -0.8 on both sides
x = -40
So -40 degree celsius

Equations with Rational Numbers – Page No. 208

Question 18.
Explain the Error
Agustin solved an equation as shown. What error did Agustin make? What is the correct answer?

x = _______

Answer:
x = -12

Explanation:
Agustin did not multiply by 12 on both sides in step 2. He only partially multiplied the variable and left the constants as such, which doesn’t make any sense.
The correct solution is
12(x/3 – 4) = 12(3x/4 + 1)
4x – 48 = 9x + 12
subtract 12 on both sides
4x – 60 = 9x
subtract 4x on both sides
-60 = 5x
x = -12

H.O.T.

Focus on Higher Order Thinking

Question 19.
Draw Conclusions
Solve the equation \(\frac{1}{2} x-5+\frac{2}{3} x=\frac{7}{6} x+4\). Explain your results.
Type below:
_____________

Answer:
\(\frac{1}{2} x-5+\frac{2}{3} x=\frac{7}{6} x+4\)
The least common multiple of the denominators: LCM(2, 3, 6) = 6
6(\(\frac{1}{2} x-5+\frac{2}{3} x=\frac{7}{6} x+4\))
6.1/2x – 6.5 + 6.2/3x = 6.7/6x +6.4
3x – 30 + 4x = 7x + 24
7x – 30 = 7x + 24
-30 = 24
This is not true. The equation has no solution.

Question 20.
Look for a Pattern
Describe the pattern in the equation. Then solve the equation.
0.3x + 0.03x + 0.003x + 0.0003x + .. = 3
x = ______

Answer:
x = 9

Explanation:
0.3x + 0.03x + 0.003x + 0.0003x + .. = 3
0.3x = 3
0.9x = 9
x = 9

Question 21.
Critique Reasoning
Jared wanted to find three consecutive even integers whose sum was 4 times the first of those integers. He let k represent the first integer, then wrote and solved this equation : k + (k + 1) + (k + 2) = 4k. Did he get the correct answer? Explain.
__________

Answer:
No, it is wrong on two accounts.
First, he has not specified if k is even or not. An easy way of doing so would assume x to be any integer and k=2a
This ensures that k is an even integer.
Nest the question asks for 3 consecutive even integers, Jared just took 3 consecutive integers, and thus at least 1 of them is odd.
So correct representation would be
k + (k+2) + (k + 4) = 4k
which upon solving yields k=6

Guided Practice – Equations with the Distributive Property – Page No. 212

Solve each equation.

Question 1.
4(x + 8) – 4 = 34 – 2x
________

Answer:
x = 1

Explanation:
4(x + 8) – 4 = 34 – 2x
4x + 32 – 4 = 34 – 2x
4x + 2x = 34 – 28
6x = 6
x = 6/6
x = 1

Question 2.
\(\frac{2}{3}\)(9 + x) = -5(4 – x)
________

Answer:
x = 6

Explanation:
\(\frac{2}{3}\)(9 + x) = -5(4 – x)
2/3(9 + x) = -5(4 – x)
3 (2/3(9 + x)) = 3(-5(4 – x))
2(9 + x ) = -15 (4 – x)
18 + 2x = -60 + 15x
15x – 2x = 18 + 60
13x = 78
x = 78/13
x = 6

Question 3.
-3(x + 4) + 15 = 6 – 4x
________

Answer:
x = 3

Explanation:
-3(x + 4) + 15 = 6 – 4x
-3x – 12 + 15 = 6 – 4x
-3x + 3 = 6 – 4x
-3x + 4x = 6 – 3
x = 3

Question 4.
10 + 4x = 5(x – 6) + 33
________

Answer:
x = 7

Explanation:
10 + 4x = 5(x – 6) + 33
10 + 4x = 5x – 30 + 33
10 + 4x = 5x + 3
5x – 4x = 10 – 3
x = 7

Question 5.
x – 9 = 8(2x + 3) – 18
________

Answer:
x = -1

Explanation:
x – 9 = 8(2x + 3) – 18
x – 9 = 16x + 24 – 18
x – 9 = 16x + 6
16x – x = -9 – 6
15x = – 15
x = -15/15
x = -1

Question 6.
-6(x – 1) – 7 = -7x + 2
________

Answer:
x = 3

Explanation:
-6(x – 1) – 7 = -7x + 2
-6x + 6 – 7 = -7x + 2
-6x – 1 = -7x + 2
-7x + 6x = -1 -2
-x = -3
x = 3

Question 7.
\(\frac{1}{10}\)(x + 11) = -2(8 – x)
________

Answer:
x = 9

Explanation:
\(\frac{1}{10}\)(x + 11) = -2(8 – x)
10(\(\frac{1}{10}\)(x + 11)) = 10 (-2(8 – x))
x + 11 = -20(8 – x)
x + 11 = -160 + 20x
20x – x = 11 + 160
19x = 171
x = 171/19 = 9

Question 8.
-(4 – x) = \(\frac{3}{4}\)(x – 6)
________

Answer:
x = -2

Explanation:
-(4 – x) = \(\frac{3}{4}\)(x – 6)
4(-(4 – x)) = 4 (3/4(x – 6))
-16 + 4x = 3x – 18
4x – 3x = -18 + 16
x = -2

Question 9.
-8(8 – x) = \(\frac{4}{5}\)(x + 10)
________

Answer:
x = 10

Explanation:
-8(8 – x) = \(\frac{4}{5}\)(x + 10)
5(-8(8 – x)) = 5(\(\frac{4}{5}\)(x + 10))
-40(8 – x) = 4(x + 10)
-320 + 40x = 4x + 40
40x – 4x = 40 + 320
36x = 360
x = 360/36
x = 10

Question 10.
\(\frac{1}{2}\)(16 – x) = -12(x + 7)
________

Answer:
x = 8

Explanation:
\(\frac{1}{2}\)(16 – x) = -12(x + 7)
2 (\(\frac{1}{2}\)(16 – x)) = 2 (-12(x + 7))
16 – x = -24 (x + 7)
16 – x = -24x – 168
24x – x = -168 – 16
23x = 184
x = 184/23
x = 8

Question 11.
Sandra saves 12% of her salary for retirement. This year her salary was $3,000 more than in the previous year, and she saved $4,200.What was her salary in the previous year?
Write an equation _____
Sandra’s salary in the previous year was _____
Salary = $ _____

Answer:
Write an equation 0.12x + 360 = 4200
Sandra’s salary in the previous year was $32000
Salary = $3000

Explanation:
0.12(x + 3000) = 4200
0.12x + 360 = 4200
0.12x = 4200 – 360
0.12x = 3840
x = 3840/0.12
x = 32000
Sandra’s salary in the previous year was $32000

Essential Question Check-In

Question 12.
When solving an equation using the Distributive Property, if the numbers being distributed are fractions, what is your first step? Why?
Type below:
___________

Answer:
Multiply both sides by the denominator of the fraction

Independent Practice – Equations with the Distributive Property – Page No. 213

Question 13.
Multistep
Martina is currently 14 years older than her cousin Joey. In 5 years she will be 3 times as old as Joey. Use this information to answer the following questions.
a. If you let x represent Joey’s current age, what expression can you use to represent Martina’s current age?
Type below:
___________

Answer:
y = x + 14

Explanation:
y = x + 14
where x is Joey’s current age and t is Martna’s current age.

Question 13.
b. Based on your answer to part a, what expression represents Joey’s age in 5 years? What expression represents Martina’s age in 5 years?
Type below:
___________

Answer:
Ages in 5 years
Joey’s age = x + 5
Martina’s age = x + 14 + 5 = x + 19

Question 13.
c. What equation can you write based on the information given?
Type below:
___________

Answer:
3(x + 5) = x + 19

Explanation:
In 5 years, Martina will be three times as old as Joey
3(x + 5) = x + 19

Question 13.
d. What is Joey’s current age? What is Martina’s current age?
Joey’s current age ___________
Martina’s current age ___________

Answer:
Joey’s current age 2
Martina’s current age 16

Explanation:
3(x + 5) = x + 19
3x + 15 = x + 19
3x – x = 19 – 15
2x = 4
x = 2

Question 14.
As part of a school contest, Sarah and Luis are playing a math game. Sarah must pick a number between 1 and 50 and give Luis clues so he can write an equation to find her number. Sarah says, “If I subtract 5 from my number, multiply that quantity by 4, and then add 7 to the result, I get 35.” What equation can Luis write based on Sarah’s clues and what is Sarah’s number?
Type below:
___________

Answer:
x = 12

Explanation:
As part of a school contest, Sarah and Luis are playing a math game. Sarah must pick a number between 1 and 50 and give Luis clues so he can write an equation to find her number. Sarah says, “If I subtract 5 from my number, multiply that quantity by 4, and then add 7 to the result, I get 35.”
4 (x – 5) + 7 = 35
4x – 20 + 7 = 35
4x – 13 = 35
4x = 35 + 13
4x = 48
x = 48/4
x = 12

Question 15.
Critical Thinking
When solving an equation using the Distributive Property that involves distributing fractions, usually the first step is to multiply by the LCD to eliminate the fractions in order to simplify computation. Is it necessary to do this to solve \(\frac{1}{2}\)(4x + 6) = 13(9x – 24)? Why or why not?
___________

Answer:
It is not necessary. In this case, distributing the fractions directly results in whole-number coefficients and constants, however, if the results are not in whole-number coefficients and constants it is harder to solve fractions.

Question 16.
Solve the equation given in Exercise 15 with and without using the LCD of the fractions. Are your answers the same?
___________

Answer:
x = 11

Explanation:
\(\frac{1}{2}\)(4x + 6) = 13(9x – 24)
6(\(\frac{1}{2}\)(4x + 6)) = 6(13(9x – 24))
3(4x + 6) = 2(9x – 24)
12x + 18 = 18x – 48
18x – 12x = 18 + 48
6x = 66
x = 66/6
x = 11

Equations with the Distributive Property – Page No. 214

Question 17.
Represent Real-World Problems
A chemist mixed x milliliters of 25% acid solution with some 15% acid solution to produce 100 milliliters of a 19% acid solution. Use this information to fill in the missing information in the table and answer the questions that follow.

a. What is the relationship between the milliliters of acid in the 25% solution, the milliliters of acid in the 15% solution, and the milliliters of acid in the mixture?
Type below:
_____________

Answer:
The milliliters of acid in the 25% solution plus the milliliters of acid in the 15% solution equals the milliliters of acid in the mixture

Explanation:

Question 17.
b. What equation can you use to solve for x based on your answer to part a?
Type below:
_____________

Answer:
0.25x + 0.15(100 – x) = 19

Question 17.
c. How many milliliters of the 25% solution and the 15% solution did the chemist use in the mixture?

Type below:
_____________

Answer:
0.25x + 0.15(100 – x) = 19
0.25x + 15 – 0.15x = 19
0.1x + 15 = 19
0.1x = 4
x = 4/0.1
x = 40
The chemist used 40ml of the 25% solution and 100 – 40 = 60ml of the 15% solution.

H.O.T.

Focus on Higher Order Thinking

Question 18.
Explain the Error
Anne solved 5(2x) – 3 = 20x + 15 for x by first distributing 5 on the left side of the equation. She got the answer x = -3. However, when she substituted -3 into the original equation for x, she saw that her answer was wrong. What did Anne do wrong, and what is the correct answer?
x = ________

Answer:
x = -1.8

Explanation:
Dado que 5 solo se multiplica por 2x, no tiene sentido usar la distribución aquí. Básicamente, distribuir 5 fue el problema
Solución correcta:
5 (2x) – 3 = 20x + 15
10x -3 = 20x + 15
restar 15 en ambos lados
10x – 18 = 20x
restar 10x de ambos lados
-18 = 10x
x = -1.8

Question 19.
Communicate Mathematical Ideas
Explain a procedure that can be used to solve 5[3(x + 4) – 2(1 – x)] – x – 15 = 14x + 45. Then solve the equation.
x = ________

Answer:
x = 1

Explanation:
5[3(x + 4) – 2(1 – x)] – x – 15 = 14x + 45
5[3x + 12 – 2 + 2x] – x – 15 = 14x + 45
5[5x + 10] – x – 15 = 14x + 45
25x + 50 – x – 15 = 14x + 45
24x + 35 = 14x + 45
24x – 14x = 45 – 35
10x = 10
x = 1

Guided Practice – Equations with Many Solutions or No Solution – Page No. 218

Use the properties of equality to simplify each equation. Tell whether the final equation is a true statement.

Question 1.

The statement is: _______

Answer:
The statement is: true

Explanation:
3x – 2 = 25 – 6x
3x + 6x -2 = 25 -6x + 6x
9x – 2 = 25
9x -2 + 2 = 25 + 2
9x = 27
x = 27/9
x = 3
The statement is true.

Question 2.

____________

Answer:
The statement is false.

Explanation:
2x – 4 = 2(x – 1) + 3
2x – 4 = 2x – 2 + 3
2x – 4 = 2x + 1
2x – 4 – 2x = 2x + 1 – 2x
-4 not equal to 1
The statement is false.

Question 3.
How many solutions are there to the equation in Exercise 2?
____________

Answer:
There is no solution to exercise 2.

Question 4.
After simplifying an equation, Juana gets 6 = 6. Explain what this means.
____________

Answer:
When 6 = 6, there are infinite solutions.

Write a linear equation in one variable that has infinitely many solutions.

Question 5.
Start with a _____ statement.
Add the _____ to both sides.
Add the _____ to both sides.
Combine _____ terms.

Type below:
____________

Answer:
Start with a “true” statement
Add the “same variable” to both sides
Add the “same constant” to both sides
Combine “like” terms

Explanation:
Start with a “true” statement
10 = 10
Add the “same variable” to both sides
10 + x = 10 + x
Add the “same constant” to both sides
10 + x + 5 = 10 + x + 5
Combine “like” terms
15 + x = 15 + x

Essential Question Check-In

Question 6.
Give an example of an equation with an infinite number of solutions. Then make one change to the equation so that it has no solution.
Type below:
____________

Answer:
An equation with infinitely many solutions
x – 2x + 3 = 3 – x
-x + 3 = 3 – x
+x/3 = +x/3
An equation for no solution
x – 2x + 3 = 3 – x + 4
-x + 3 = 7 – x
-x/3 = -x/7

Independent Practice – Equations with Many Solutions or No Solution – Page No. 219

Tell whether each equation has one, zero, or infinitely many solutions.

Question 7.
-(2x + 2) – 1 = -x – (x + 3)
____________

Answer:
The statement is true

Explanation:
-(2x + 2) – 1 = -x – (x + 3)
-2x – 2 – 1 = -x – x + 3
-2x – 3 = -2x + 3
-3 = -3
The statement is true

Question 8.
-2(z + 3) – z = -z – 4(z + 2)
____________

Answer:
The statement is false.

Explanation:
-2(z + 3) – z = -z – 4(z + 2)
-3z – 6 = -3z -8
-3z -6 + 3z = -3z – 8 + 3z
-6 not equal to -8
The statement is false.

Create an equation with the indicated number of solutions.

Question 9.
No solution:
3(x – \(\frac{4}{3}\)) = 3x + _____
Type below:
______________

Answer:
3(x – \(\frac{4}{3}\)) = 3x + ?
3x – 4 = 3x + ?
3x – 4 = 3x + 2
When there is no solution, the statement should be false. Any number except -4 would make the equation have no solutions.

Question 10.
Infinitely many solutions:
2(x – 1) + 6x = 4( _____ – 1) + 2
Type below:
______________

Answer:
2(x – 1) + 6x = 4( _____ – 1) + 2
2(x – 1) + 6x = 4( ? – 1) + 2
2x – 2 + 6x = 4(? – 1) + 2
8x – 2 = 4(? – 1) + 2
8x – 2 = 4(2x – 1) + 2
8x – 2 = 8x – 4 + 2
8x – 2 = 8x – 2
When there are infinitely many solutions, the statement should be true

Question 11.
One solution of x = -1:
5x – (x – 2) = 2x – ( _____ )
Type below:
______________

Answer:
Put x = -1 in the equation
-5 – (-1 – 2) = -2 – blank
simplifying
-2 = -2 – blank
add 2 on both sides
0 = blank

Question 12.
Infinitely many solutions:
-(x – 8) + 4x = 2( _____ ) + x
Type below:
______________

Answer:
-(x – 8) + 4x = 2( ?) + x
-x + 8 + 4x = 2(?) + x
3x + 8 = 2(?) + x
3x + 8 = 2 (x + 4) + x
3x + 8 = 2x + 8x + x
3x + 8 = 3x + 8
When there are infinitely many solutions, the statement should be true.

Question 13.
Persevere in Problem Solving
The Dig It Project is designing two gardens that have the same perimeter. One garden is a trapezoid whose nonparallel sides are equal. The other is a quadrilateral. Two possible designs are shown at the right.

a. Based on these designs, is there more than one value for x? Explain how you know this.
______________

Answer:
There are more than one value of x

Explanation:
Perimeter of the trapezoid
P = 2x – 2 + x + 1 + x + x + 1 = 5x
Perimeter of the quadrilateral
P = 2x – 9 + x + x + 8 + x + 1 = 5x
5x = 5x
There are more than one value of x

Question 13.
b. Why does your answer to part a make sense in this context?
Type below:
______________

Answer:
The condition was that the two perimeters are to be equal. However, a specific number was not given, so there are an infinite number of possible perimeters

Explanation:
Interpretation of part a in this context
The condition was that the two perimeters are to be equal. However, a specific number was not given, so there are an infinite number of possible perimeters

Question 13.
c. Suppose the Dig It Project wants the perimeter of each garden to be 60 meters. What is the value of x in this case? How did you find this?
______ meters

Answer:
12 meters

Explanation:
2x – 2 + x + 1 + x + x + 1 = 60
5x = 60
x = 60/5
x = 12

Equations with Many Solutions or No Solution – Page No. 220

Question 14.
Critique Reasoning
Lisa says that the indicated angles cannot have the same measure. Marita disagrees and says she can prove that they can have the same measure. Who do you agree with? Justify your answer.

I agree with: ______________

Answer:
I agree with: Marita

Explanation:
9x – 25 + x = x + 50 + 2x – 12
10x – 25 = 3x + 38
10x – 3x = 38 + 25
7x = 63
x = 63/7
x = 9
When x = 9 the angles will be same and for any other value of x, the angles will not be the same.

Question 15.
Represent Real-World Problems
Adele opens an account with $100 and deposits $35 a month. Kent opens an account with $50 and also deposits $35 a month. Will they have the same amount in their accounts at any point? If so, in how many months and how much will be in each account? Explain.
______________

Answer:
Adele’s amount after x months
A = 100 + 35x
Kent’s amount after x months
A = 50 + 35x
100 + 35x = 50 + 35x
100 is not equal to 50
The statement is false, the amounts in two accounts would never be equal.

H.O.T.

Focus on Higher Order Thinking

Question 16.
Communicate Mathematical Ideas
Frank solved an equation and got the result x = x. Sarah solved the same equation and got 12 = 12. Frank says that one of them is incorrect because you cannot get different results for the same equation. What would you say to Frank? If both results are indeed correct, explain how this happened.
Frank is: ____________

Answer:
Both of them can be correct as both equations give the same result i.e. there are infinitely many solutions. Frank eliminated the constant from both sides while Sarah eliminated the variable from both sides.

Question 17.
Critique Reasoning
Matt said 2x – 7 = 2(x – 7) has infinitely many solutions. Is he correct? Justify Matt’s answer or show how he is incorrect.
Matt is: ____________

Answer:

Explanation:
2x – 7 = 2(x – 7)
2x – 7 = 2x – 14
-7 not equal to -14
The statement is false, there is no solution. Matt is incorrect.

7.1 Equations with the Variable on Both Sides – Model Quiz – Page No. 221

Solve.

Question 1.
4a – 4 = 8 + a
_______

Answer:
a = 4

Explanation:
4a – 4 = 8 + a
4a – a = 8 + 4
3a = 12
a = 12/3
a = 4

Question 2.
4x + 5 = x + 8
_______

Answer:
x = 1

Explanation:
4x + 5 = x + 8
4x – x = 8 – 5
3x = 3
x = 3/3
x = 1

Question 3.
Hue is arranging chairs. She can form 6 rows of a given length with 3 chairs left over, or 8 rows of that same length if she gets 11 more chairs. Write and solve an equation to find how many chairs are in that row length.
_______ chairs

Answer:
7 chairs

Explanation:
Hue is arranging chairs. She can form 6 rows of a given length with 3 chairs left over, or 8 rows of that same length if she gets 11 more chairs.
6x + 3 = 8x – 11
8x – 6x = 3 + 11
2x = 14
x = 14/2
x = 7
There are 7 chairs in each row.

7.2 Equations with Rational Numbers

Solve.

Question 4.
\(\frac{2}{3} n-\frac{2}{3}=\frac{n}{6}+\frac{4}{3}\)
_______

Answer:
n = 4

Explanation:
\(\frac{2}{3} n-\frac{2}{3}=\frac{n}{6}+\frac{4}{3}\)
The LCM is 6.
6(2/3n – 2/3) = 6(n/6 + 4/3)
6(2/3n) -6(2/3) = 6(n/6) + 6(4/3)
4n – 4 = n + 8
4n – n = 8 + 4
3n = 12
n = 12/3
n = 4

Question 5.
1.5d + 3.25 = 1 + 2.25d
_______

Answer:
d = 3

Explanation:
1.5d + 3.25 = 1 + 2.25d
2.25d – 1.5d = 3.25 – 1
0.75d = 2.25
d = 2.25/0.75
d = 3

Question 6.
Happy Paws charges $19.00 plus $1.50 per hour to keep a dog during the day. Woof Watchers charges $14.00 plus $2.75 per hour. Write and solve an equation to find for how many hours the total cost of the services is equal.
_______ hours

Answer:
3.2 hours

Explanation:
Happy Paws charges $19.00 plus $1.50 per hour to keep a dog during the day.
1.5x + 19
Woof Watchers charges $14.00 plus $2.75 per hour.
2.75x + 15
1.5x + 19 = 2.75x + 15
2.75x – 1.5x = 19 – 15
1.25x = 4
x = 4/1.25
x = 3.2
The total cost of the services is equal after 3.2 hrs.

7.3 Equations with the Distributive Property

Solve.

Question 7.
14 + 5x = 3(-x + 3) – 11
_______

Answer:
x = -2

Explanation:
14 + 5x = 3(-x + 3) – 11
14 + 5x = -3x + 9 – 11
14 + 5x = -3x – 2
5x + 3x = -2 –  14
8x = – 16
x = -16/8
x = -2

Question 8.
\(\frac{1}{4}\)(x – 7) = 1 + 3x
_______

Answer:
x = -1

Explanation:
\(\frac{1}{4}\)(x – 7) = 1 + 3x
4(\(\frac{1}{4}\)(x – 7)) = 4(1 + 3x)
(x – 7) = 4 + 12x
12x – x = -7 – 4
11x = -11
x = -11/11
x = -1

Question 9.
-5(2x – 9) = 2(x – 8) – 11
_______

Answer:
x = 6

Explanation:
-5(2x – 9) = 2(x – 8) – 11
-10x + 45 = 2x – 16 – 11
-10x + 45 = 2x – 27
2x + 10x = 45 + 27
12x = 72
x = 72/12
x = 6

Question 10.
3(x + 5) = 2(3x + 12)
_______

Answer:
x = -3

Explanation:
3(x + 5) = 2(3x + 12)
3x + 15 = 6x + 24
6x – 3x = 15 – 24
3x = -9
x = -9/3
x = -3

7.4 Equations with Many Solutions or No Solution

Tell whether each equation has one, zero, or infinitely many solutions.

Question 11.
5(x – 3) + 6 = 5x – 9
____________

Answer:
There are infinitely many solutions

Explanation:
5(x – 3) + 6 = 5x – 9
5x – 15 + 6 = 5x – 9
5x – 9 = 5x – 9
The statement is true. There are infinitely many solutions.

Question 12.
5(x – 3) + 6 = 5x – 10
____________

Answer:
There are no solutions

Explanation:
5(x – 3) + 6 = 5x – 10
5x – 15 + 6 = 5x – 10
5x – 9 = 5x – 10
-9 not equal to -10
The statement is false. There are no solutions.

Question 13.
5(x – 3) + 6 = 4x + 3
____________

Answer:
There is one solution

Explanation:
5(x – 3) + 6 = 4x + 3
5x – 15 + 6 = 4x + 3
5x – 9 = 4x + 3
5x – 4x = 3 + 9
x = 12
There is one solution

Selected Response – Mixed Review – Page No. 222

Question 1.
Two cars are traveling in the same direction. The first car is going 40 mi/h, and the second car is going 55 mi/h. The first car left 3 hours before the second car. Which equation could you solve to find how many hours it will take for the second car to catch up to the first car?
Options:
a. 55t + 3 = 40t
b. 55t + 165 = 40t
c. 40t + 3 = 55t
d. 40t + 120 = 55t

Answer:
d. 40t + 120 = 55t

Explanation:
Two cars are traveling in the same direction. The first car is going 40 mi/h, and the second car is going 55 mi/h. The first car left 3 hours before the second car.
3 × 40 + 40t = 120 + 40t
55t
40t + 120 = 55t

Question 2.
Which linear equation is represented by the table?

Options:
a. y = -x + 5
b. y = 2x – 1
c. y = x + 3
d. y = -3x + 11

Answer:
a. y = -x + 5

Explanation:
Find the slope using
m = (y2 – y1)/(x2 – x1)
where (x1, y1) = (3, 2), (x2, y2) = (1, 4)
Slope = (4 – 2)/(1 – 3) = -2/2 = -1

Question 3.
Shawn’s Rentals charges $27.50 per hour to rent a surfboard and a wetsuit. Darla’s Surf Shop charges $23.25 per hour to rent a surfboard plus $17 extra for a wetsuit. For what total number of hours are the charges for Shawn’s Rentals the same as the charges for Darla’s Surf Shop?
Options:
a. 3
b. 4
c. 5
d. 6

Answer:
b. 4

Explanation:
Shawn’s Rentals charges $27.50 per hour to rent a surfboard and a wetsuit.
27.5x
Darla’s Surf Shop charges $23.25 per hour to rent a surfboard plus $17 extra for a wetsuit.
23.25x + 17
23.25x + 17 = 27.5x
27.5x – 23.25x = 17
4.25x = 17
x = 17/4.25
x = 4
The charge would be equal after 4 hrs

Question 4.
Which of the following is irrational?
Options:
a. -8
b. 4.63
c. \(\sqrt { x } \)
d. \(\frac{1}{3}\)

Answer:
c. \(\sqrt { x } \)

Explanation:
\(\sqrt { x } \) is irrational

Question 5.
Greg and Jane left a 15% tip after dinner. The amount of the tip was $9. Greg’s dinner cost $24. Which equation can you use to find x, the cost of Jane’s dinner?
Options:
a. 0.15x + 24 = 9
b. 0.15(x + 24) = 9
c. 15(x + 24) = 9
d. 0.15x = 24 + 9

Answer:
b. 0.15(x + 24) = 9

Explanation:
Let x be the cost of Jane’s dinner. The amount of tip is the 15% of the total cost of dinner.
0.15(x + 24) = 9

Question 6.
For the equation 3(2x − 5) = 6x + k, which value of k will create an equation with infinitely many solutions?
Options:
a. 15
b. -5
c. 5
d. -15

Answer:
d. -15

Explanation:
3(2x – 5) = 6x + k
6x – 15 = 6x + k
6x – 15 = 6x – 15
The statement is true. k = -15

Question 7.
Which of the following is equivalent to 2⁻⁴?
Options:
a. \(\frac{1}{16}\)
b. \(\frac{1}{8}\)
c. -2
d. -16

Answer:
a. \(\frac{1}{16}\)

Explanation:
2⁻⁴
1/2⁴
1/16

Mini-Task

Question 8.
Use the figures below for parts a and b.

a. Both figures have the same perimeter. Solve for x.
_______

Answer:
x=12

Explanation:
4x+10=3x+22
4x – 3x = 22 – 10
x = 12
Answer: x=12

Question 8.
b. What is the perimeter of each figure?
_______

Answer:
Both are 58

Explanation:
x + x + 5 + x + x + 5
12 + 12 + 5 + 12 + 12 + 5
58
x + 7 + x + 4 + x + 11
12 + 7 + 12 + 4 + 12 + 11
58

Conclusion:

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Lesson 1: Relate Tenths and Decimals

• Relate Tenths and Decimals – Page No. 499
• Relate Tenths and Decimals Lesson Check – Page No. 500

Lesson 2: Relate Hundredths and Decimals

• Relate Hundredths and Decimals – Page No. 503
• Relate Hundredths and Decimals Lesson Check – Page No. 504
• Relate Hundredths and Decimals Lesson Check 1 – Page No. 505
• Relate Hundredths and Decimals Lesson Check 2 – Page No. 506

Lesson 3: Equivalent Fractions and Decimals

• Equivalent Fractions and Decimals – Page No. 509
• Equivalent Fractions and Decimals Lesson Check – Page No. 510
• Equivalent Fractions and Decimals Lesson Check 1 – Page No. 511
• Equivalent Fractions and Decimals Lesson Check 2 – Page No. 512

Lesson 4: Relate Fractions, Decimals, and Money

• Relate Fractions, Decimals, and Money – Page No. 515
• Relate Fractions, Decimals, and Money Lesson Check – Page No. 516
• Relate Fractions, Decimals, and Money Lesson Check 1 – Page No. 517
• Relate Fractions, Decimals, and Money Lesson Check 2 – Page No. 518

Lesson 5: Problem Solving • Money

• Money – Page No. 521
• Money Lesson Check – Page No. 522
• Money Lesson Check 1 – Page No. 523
• Money Lesson Check 2 – Page No. 524

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Page No. 525
• Mid-Chapter Checkpoint Lesson Check – Page No. 526

Lesson 6: Add Fraction Parts of 10 and 100

• Add Fraction Parts of 10 and 100 – Page No. 529
• Add Fraction Parts of 10 and 100 Lesson Check – Page No. 530
• Add Fraction Parts of 10 and 100 Lesson Check 1 – Page No. 531
• Add Fraction Parts of 10 and 100 Lesson Check 2 – Page No. 532

Lesson 7: Compare Decimals

• Compare Decimals – Page No. 535
• Compare Decimals Lesson Check – Page No. 536
• Compare Decimals Lesson Check 1 – Page No. 537
• Compare Decimals Lesson Check 2 – Page No. 538

Review/Test

• Review/Test – Page No. 539
• Review/Test – Page No. 540
• Review/Test – Page No. 541
• Review/Test – Page No. 542
• Review/Test – Page No. 543
• Review/Test – Page No. 544
• Review/Test – Page No. 551
• Review/Test – Page No. 552

Common Core – New – Page No. 499

Relate Tenths and Decimals

Write the fraction or mixed number and the decimal shown by the model.

Question 1

Answer:

Question 2.

Type below:
________

Answer:
1\(\frac{2}{10}\)

Explanation:
The model is divided into 10 equal parts. Each part represents one-tenth.
1 2/10 is 1 whole and 2 tenths.

Question 3.

Type below:
________

Answer:
2\(\frac{3}{10}\) = 2.3

Explanation:

Question 4.

Type below:
________

Answer:
4\(\frac{8}{10}\) = 4.8

Explanation:

Write the fraction or mixed number as a decimal.

Question 5.
\(\frac{4}{10}\)
_____

Answer:
0.4

Explanation:
Write down 4 with the decimal point 1 space from the right (because 10 has 1 zero)
0.4

Question 6.
3 \(\frac{1}{10}\)
_____

Answer:
3.1

Explanation:
Multiply 3 x 10 = 30.
Add 30 + 1 = 31.
So, 31/10.
Write down 31 with the decimal point 1 space from the right (because 10 has 1 zero)
3.1

Question 7.
\(\frac{7}{10}\)
_____

Answer:
0.7

Explanation:
Write down 7 with the decimal point 1 space from the right (because 10 has 1 zero)
0.7

Question 8.
6 \(\frac{5}{10}\)
_____

Answer:
6.5

Explanation:
Multiply 6 x 10 = 60.
Add 60 + 5 = 65.
So, 65/10.
Write down 35 with the decimal point 1 space from the right (because 10 has 1 zero)
6.5

Question 9.
\(\frac{9}{10}\)
_____

Answer:
0.9

Explanation:
Write down 9 with the decimal point 1 space from the right (because 10 has 1 zero)
0.9

Problem Solving

Question 10.
There are 10 sports balls in the equipment closet. Three are kickballs. Write the portion of the balls that are kickballs as a fraction, as a decimal, and in word form.
Type below:
_________

Answer:
\(\frac{3}{10}\) = 0.3 = three tenths

Explanation:
There are 10 sports balls in the equipment closet. Three are kickballs. So, 3/10 kickballs are available.

Question 11.
Peyton has 2 pizzas. Each pizza is cut into 10 equal slices. She and her friends eat 14 slices. What part of the pizzas did they eat? Write your answer as a decimal.
_________

Answer:
1.4 pizzas

Explanation:
Peyton has 2 pizzas. Each pizza is cut into 10 equal slices.
So, total number of slices = 2 x 10 = 20.
She and her friends eat 14 slices.
So, they ate 1 whole pizza and 4 parts out of 10 slices in the second pizza.
1 4/10 = 14/10 = 1.4 pizzas

Common Core – New – Page No. 500

Lesson Check

Question 1.
Valerie has 10 CDs in her music case. Seven of the CDs are pop music CDs. What is this amount written as a decimal?
Options:
a. 70.0
b. 7.0
c. 0.7
d. 0.07

Answer:
c. 0.7

Explanation:
Valerie has 10 CDs in her music case. Seven of the CDs are pop music CDs.
Seven CDs out of 10 CDs = 7/10 =0.7

Question 2.
Which decimal amount is modeled below?

Options:
a. 140.0
b. 14.0
c. 1.4
d. 0.14

Answer:
c. 1.4

Explanation:
1\(\frac{4}{10}\)
Multiply 10 x 1 = 10.
Add 10 + 4 = 14.
So, 14/10 = 1.4.

Spiral Review

Question 3.
Which number is a factor of 13?
Options:
a. 1
b. 3
c. 4
d. 7

Answer:
a. 1

Explanation:
13 has 1 and 13 as its factors.

Question 4.
An art gallery has 18 paintings and 4 photographs displayed in equal rows on a wall, with the same number of each type of art in each row. Which of the following could be the number of rows?
Options:
a. 2 rows
b. 3 rows
c. 4 rows
d. 6 rows

Answer:
a. 2 rows

Explanation:
An art gallery has 18 paintings and 4 photographs displayed in equal rows on a wall, with the same number of each type of art in each row. So, 18 paintings and 4 photographs need to be divided into equal parts.
18/2 = 9; 4/2 = 2.
2 rows can be possible with 9 pictures and 2 pictures in each row.

Question 5.
How do you write the mixed number shown as a fraction greater than 1?

Options:
a. \(\frac{32}{5}\)
b. \(\frac{14}{4}\)
c. \(\frac{6}{4}\)
d. \(\frac{4}{4}\)

Answer:
b. \(\frac{14}{4}\)

Explanation:
3\(\frac{2}{4}\) = 14/4. 14 divided by 4 is equal to 3 with a remainder of 2. The 3 is greater than 1. So, 14/4 > 1.

Question 6.
Which of the following models has an amount shaded that is equivalent to the fraction \(\frac{1}{5}\)?
a.
b.
c.
d.

Answer:
c.

Explanation:
a. \(\frac{2}{3}\)
b. \(\frac{5}{10}\) = \(\frac{1}{2}\)
c. \(\frac{2}{10}\) = \(\frac{1}{5}\)
d. \(\frac{1}{10}\)

Page No. 503

Question 1.
Shade the model to show \(\frac{31}{100}\).
Write the amount as a decimal.

_____

Answer:

Write the fraction or mixed number and the decimal shown by the model.

Question 2.

Type below:
_________

Answer:
\(\frac{68}{100}\) = 0.68

Explanation:
68 boxes are shaded out of 100 boxes.

Question 3.

Type below:
_________

Answer:
\(\frac{8}{100}\) = 0.08

Explanation:
8 boxes are shaded out of 100 boxes.

Question 4.

Type below:
_________

Answer:
6\(\frac{19}{100}\) = 6.19

Explanation:
0.5 is 5 tenths and 0.50 is 5 tenths 0 hundredths. Since both 0.5 and 0.50 have 5 tenths and no hundredths, they are equivalent

Write the fraction or mixed number and the decimal shown by the model.

Question 5.

Type below:
_________

Answer:
1\(\frac{83}{100}\) = 1.83

Explanation:
1 whole number(all the square boxes are shaded) and 83 squares boxes shaded out from 100 boxes.

Question 6.

Type below:
_________

Answer:
\(\frac{75}{100}\)

Explanation:
75 boxes are shaded out of 100 boxes.

Question 7.

Type below:
_________

Answer:
\(\frac{47}{100}\) = 0.47

Explanation:
The point lies between \(\frac{40}{100}\) and \(\frac{50}{100}\). The number of lines in between \(\frac{40}{100}\) and \(\frac{50}{100}\) are 10. The point is placed at 7th line. So, 40 + 7 = 47. Answer = \(\frac{47}{100}\)

Practice: Copy and Solve Write the fraction or mixed number as a decimal.

Question 8.
\(\frac{9}{100}\) = _____

Answer:
0.09

Explanation:
Write down 9 with the decimal point 2 spaces from the right (because 100 has 2 zeros)

Question 9.
4 \(\frac{55}{100}\) = _____

Answer:
4.55

Explanation:
4 \(\frac{55}{100}\) = \(\frac{455}{100}\)
Write down 455 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 4.55 is the answer

Question 10.
\(\frac{10}{100}\) = _____

Answer:
0.10 = 0.1

Explanation:
Write down 10 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 0.10 =0.1 is the answer

Question 11.
9 \(\frac{33}{100}\) = _____

Answer:
9.33

Explanation:
9 \(\frac{33}{100}\) = \(\frac{933}{100}\)
Write down 933 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 9.33 is the answer.

Question 12.
\(\frac{92}{100}\) = _____

Answer:
0.92

Explanation:
Write down 92 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 0.92 is the answer

Question 13.
14 \(\frac{16}{100}\) = _____

Answer:
14.16

Explanation:
14 \(\frac{16}{100}\) = \(\frac{1416}{100}\)
Write down 1416 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 14.16 is the answer.

Page No. 504

Question 14.
Shade the grids to show three different ways to represent \(\frac{16}{100}\) using models.

Type below:
_________

Answer:

Question 15.
Describe Relationships Describe how one whole, one tenth, and one hundredth are related.
Type below:
_________

Answer:
One whole = 1.00
One tenth: 0.1
One hundredth: 0.01
One whole is 10 times the one-tenth, and one-tenth is 10 times the one hundredth.

Question 16.
Shade the model to show 1 \(\frac{24}{100}\). Then write the mixed number in decimal form.

_____

Answer:

1\(\frac{24}{100}\) = \(\frac{124}{100}\) = 1.24

Question 17.
The Memorial Library is 0.3 mile from school. Whose statement makes sense? Whose statement is nonsense? Explain your reasoning.

Type below:
_________

Answer:
The boy’s statement makes sense. Because The Memorial Library is 0.3 miles from the school. Digit 3 in the tenths place after the first place of decimal.
The girl’s statement makes non-sense. Because there she said 3 miles that is not equal to 0.3 miles.

Common Core – New – Page No. 505

Relate Hundredths and Decimals

Write the fraction or mixed number and the decimal shown by the model.

Question 1.

Answer:

Question 2.

Type below:
_________

Answer:
\(\frac{29}{100}\) = 0.29

Explanation:
0.20 names the same amount as 20/100. So, the given point is at 29/100 = 0.29

Question 3.

Type below:
_________

Answer:
1\(\frac{54}{100}\) = 1.54

Explanation:
From the given image, one model is one whole and another model 54 boxes shaded out of 100. So, the answer is 1\(\frac{54}{100}\) = 1.54

Question 4.

Type below:
_________

Answer:
4\(\frac{62}{100}\) = 4.62

Explanation:
4.60 names the same amount as 4\(\frac{60}{100}\). So, the given point is at 4\(\frac{62}{100}\) = 4.62

Write the fraction or mixed number as a decimal.

Question 5.
\(\frac{37}{100}\)
_____

Answer:
0.37

Explanation:
Write down 37 with the decimal point 2 spaces from the right (because 100 has 2 zeros). 0.37

Question 6.
8 \(\frac{11}{100}\)
_____

Answer:
8.11

Explanation:
8\(\frac{11}{100}\) = \(\frac{811}{100}\)
Write down 811 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 8.11 is the answer.

Question 7.
\(\frac{98}{100}\)
_____

Answer:
0.98

Explanation:
Write down 98 with the decimal point 2 spaces from the right (because 100 has 2 zeros). 0.98

Question 8.
25 \(\frac{50}{100}\)
_____

Answer:
25.50

Explanation:
25\(\frac{50}{100}\) = \(\frac{2550}{100}\)
Write down 2550 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 25.50 is the answer.

Question 9.
\(\frac{6}{100}\)
_____

Answer:
0.06

Explanation:
Write down 6 with the decimal point 2 spaces from the right (because 100 has 2 zeros). 0.06

Problem Solving

Question 10.
There are 100 pennies in a dollar. What fraction of a dollar is 61 pennies? Write it as a fraction, as a decimal, and in word form.
Type below:
_________

Answer:
\(\frac{61}{100}\) pennies = 0.61 = sixty-one hundredths

Explanation:
There are 100 pennies in a dollar. So, for 61 pennies, there are \(\frac{61}{100}\) pennies = 0.61 = sixty-one hundredths.

Question 11.
Kylee has collected 100 souvenir thimbles from different places she has visited with her family. Twenty of the thimbles are carved from wood. Write the fraction of thimbles that are wooden as a decimal.
_________

Answer:
It is easier to work with decimals then fractions because it is like adding whole numbers in a normal way.

Common Core – New – Page No. 506

Lesson Check

Question 1.
Which decimal represents the shaded section of the model below?

Options:
a. 830.0
b. 83.0
c. 8.30
d. 0.83

Answer:
d. 0.83

Explanation:
The model is divided into 100 equal parts. Each part represents one hundredth. 83 boxes are shaded out of 100. So, the answer is \(\frac{83}{100}\) = 0.83

Question 2.
There were 100 questions on the unit test. Alondra answered 97 of the questions correctly. What decimal represents the fraction of questions Alondra answered correctly?
Options:
a. 0.97
b. 9.70
c. 90.70
d. 970.0

Answer:
a. 0.97

Explanation:
There were 100 questions on the unit test. Alondra answered 97 of the questions correctly. So, \(\frac{97}{100}\) questions answered correctly. = 0.97

Spiral Review

Question 3.
Which is equivalent to \(\frac{7}{8}\)?
Options:
a. \(\frac{5}{8}+\frac{3}{8}\)
b. \(\frac{4}{8}+\frac{1}{8}+\frac{1}{8}\)
c. \(\frac{3}{8}+\frac{2}{8}+\frac{2}{8}\)
d. \(\frac{2}{8}+\frac{2}{8}+\frac{1}{8}+\frac{1}{8}\)

Answer:
c. \(\frac{3}{8}+\frac{2}{8}+\frac{2}{8}\)

Explanation:
c. \(\frac{3}{8}+\frac{2}{8}+\frac{2}{8}\) = \(\frac{7}{8}\)

Question 4.
What is \(\frac{9}{10}-\frac{6}{10}\)?

Options:
a. \(\frac{1}{10}\)
b. \(\frac{3}{10}\)
c. \(\frac{4}{10}\)
d. \(\frac{6}{10}\)

Answer:
b. \(\frac{3}{10}\)

Explanation:
\(\frac{9}{10}-\frac{6}{10}\). From 9 parts, 6 parts are removed. So, remaining parts are 3.

Question 5.
Misha used \(\frac{1}{4}\) of a carton of 12 eggs to make an omelet. How many eggs did she use?
Options:
a. 2
b. 3
c. 4
d. 6

Answer:
b. 3

Explanation:
Misha used \(\frac{1}{4}\) of a carton of 12 eggs to make an omelet. \(\frac{1}{4}\) x 12 = 3 eggs.

Question 6.
Kurt used the rule add 4, subtract 1 to generate a pattern. The first term in his pattern is 5. Which number could be in Kurt’s pattern?
Options:
a. 4
b. 6
c. 10
d. 14

Answer:
d. 14

Explanation:
Kurt used the rule add 4, subtract 1 to generate a pattern. The first term in his pattern is 5. The pattern numbers are 5, 8, 11, 14, 17, 20, etc. So, the answer is 14.

Page No. 509

Question 1.
Write \(\frac{4}{10}\) as hundredths.
Write \(\frac{4}{10}\) as an equivalent fraction.
\(\frac{4}{10}\) =\(\frac{4 × ■}{10× ■}\)
Write \(\frac{4}{10}\) as a decimal.

Type below:
_________

Answer:
\(\frac{40}{100}\)

0.40

Explanation:
Write \(\frac{4}{10}\) as an equivalent fraction.
\(\frac{4}{10}\) =\(\frac{4 × 10}{10× 10}\) = \(\frac{40}{100}\)
6 tenths is the same as 6 tenths 0 hundredths. So the decimal form = 0.40

Write the number as hundredths in fraction form and decimal form.

Question 2.
\(\frac{7}{10}\)
Type below:
_________

Answer:
\(\frac{70}{100}\)

0.70

Explanation:
Write \(\frac{7}{10}\) as an equivalent fraction.
\(\frac{7}{10}\) =\(\frac{7 × 10}{10× 10}\) = \(\frac{70}{100}\)
7 tenths is the same as 7 tenths 0 hundredths. So the decimal form = 0.70

Question 3.
0.5
Type below:
_________

Answer:
\(\frac{50}{100}\)

0.50

Explanation:
Write 0.5 = \(\frac{5}{10}\) as an equivalent fraction.
\(\frac{5}{10}\) =\(\frac{5 × 10}{10× 10}\) = \(\frac{50}{100}\)
5 tenths is the same as 5 tenths 0 hundredths and also 0.5

Question 4.
\(\frac{3}{10}\)
Type below:
_________

Answer:
\(\frac{30}{100}\)

0.30

Explanation:
Write \(\frac{3}{10}\) as an equivalent fraction.
\(\frac{3}{10}\) =\(\frac{3 × 10}{10× 10}\) = \(\frac{30}{100}\)
3 tenths is the same as 3 tenths 0 hundredths. So the decimal form = 0.30

Write the number as tenths in fraction form and decimal form.

Question 5.
0.40
Type below:
_________

Answer:
\(\frac{4}{10}\) = 0.4

Explanation:

There are no hundredths.
0.40 is equivalent to 4 tenths.
Write 0.40 as 4 tenths = 0.4 = \(\frac{4}{10}\)

Question 6.
\(\frac{80}{100}\)
Type below:
_________

Answer:
\(\frac{8}{10}\)

0.8

Explanation:
10 is a common factor of the numerator and the denominator.
\(\frac{80}{100}\) = \(\frac{80 ÷ 10}{100 ÷ 10}\) = \(\frac{8}{10}\)
0.8

Question 7.
\(\frac{20}{100}\)
Type below:
_________

Answer:
\(\frac{2}{10}\)

0.2

Explanation:
10 is a common factor of the numerator and the denominator.
\(\frac{20}{100}\) = \(\frac{20 ÷ 10}{100 ÷ 10}\) = \(\frac{2}{10}\)
0.2

Practice: Copy and Solve Write the number as hundredths in fraction form and decimal form.

Question 8.
\(\frac{8}{10}\)
Type below:
_________

Answer:
\(\frac{80}{100}\)

0.8

Explanation:
Write \(\frac{8}{10}\) as an equivalent fraction.
\(\frac{8}{10}\) =\(\frac{8 × 10}{10× 10}\) = \(\frac{80}{100}\)
8 tenths is the same as 8 tenths 0 hundredths. So the decimal form = 0.8

Question 9.
\(\frac{2}{10}\)
Type below:
_________

Answer:
\(\frac{20}{100}\)

0.2

Explanation:
Write \(\frac{2}{10}\) as an equivalent fraction.
\(\frac{2}{10}\) =\(\frac{2 × 10}{10× 10}\) = \(\frac{20}{100}\)
2 tenths is the same as 2 tenths 0 hundredths. So the decimal form = 0.2

Question 10.
0.1
Type below:
_________

Answer:
\(\frac{50}{100}\)

0.50

Explanation:
Write 0.1 = \(\frac{1}{10}\) as an equivalent fraction.
\(\frac{1}{10}\) =\(\frac{1 × 10}{10× 10}\) = \(\frac{10}{100}\)
1 tenth is the same as 1 tenth 0 hundredths and also 0.1

Practice: Copy and Solve Write the number as tenths in fraction form and decimal form.

Question 11.
\(\frac{60}{100}\)
Type below:
_________

Answer:
\(\frac{6}{10}\)

0.6

Explanation:
10 is a common factor of the numerator and the denominator.
\(\frac{60}{100}\) = \(\frac{60 ÷ 10}{100 ÷ 10}\) = \(\frac{6}{10}\)
0.6

Question 12.
\(\frac{90}{100}\)
Type below:
_________

Answer:
\(\frac{9}{10}\)

0.9

Explanation:
10 is a common factor of the numerator and the denominator.
\(\frac{90}{100}\) = \(\frac{90 ÷ 10}{100 ÷ 10}\) = \(\frac{9}{10}\)
= 0.9

Question 13.
0.70
Type below:
_________

Answer:
\(\frac{7}{10}\)

0.7

Explanation:

There are no hundredths.
0.70 is equivalent to 7 tenths.
Write 0.70 as 7 tenths = 0.7 = \(\frac{7}{10}\)

Write the number as an equivalent mixed number with hundredths.

Question 14.
1 \(\frac{4}{10}\) = _____

Answer:
1 \(\frac{40}{100}\)

Explanation:
1 \(\frac{4 x 10}{10 x 10}\) = 1 \(\frac{40}{100}\)

Question 15.
3 \(\frac{5}{10}\) = _____

Answer:
3 \(\frac{50}{100}\)

Explanation:
3 \(\frac{5}{10}\) = 3 \(\frac{5 x 10}{10 x 10}\) = 3 \(\frac{50}{100}\)

Question 16.
2 \(\frac{9}{10}\) = _____

Answer:
2 \(\frac{90}{100}\)

Explanation:
2 \(\frac{9}{10}\) = 2 \(\frac{9 x 10}{10 x 10}\) = 2 \(\frac{90}{100}\)

Page No. 510

Question 17.
Carter says that 0.08 is equivalent to \(\frac{8}{10}\). Describe and correct Carter’s error.
Type below:
_________

Answer:

8 hundredths = \(\frac{8}{100}\)
The decimal point is before the 2 numbers. So, the denominator should be 100.

Question 18.
For numbers 18a–18e, choose True or False for the statement.
a. 0.6 is equivalent to \(\frac{6}{100}\).
i. True
ii. False

Answer:
ii. False

Explanation:

0.60 = 6 tenths.
6 tenths = \(\frac{6}{10}\)

Question 18.
b. \(\frac{3}{10}\) is equivalent to 0.30.
i. True
ii. False

Answer:
i. True

Explanation:

0.30 = 3 tenths.
3 tenths = \(\frac{3}{10}\)

Question 18.
c. \(\frac{40}{100}\) is equivalent to \(\frac{4}{10}\).
i. True
ii. False

Answer:
i. True

Explanation:
10 is a common factor of the numerator and the denominator.
\(\frac{40}{100}\) = \(\frac{40 ÷ 10}{100 ÷ 10}\) = \(\frac{4}{10}\)

Question 18.
d. 0.40 is equivalent to \(\frac{4}{100}\).
i. True
ii. False

Answer:
ii. False

Explanation:

4 tenths and 0 hundreds = \(\frac{4}{10}\)

Question 18.
e. 0.5 is equivalent to 0.50.
i. True
ii. False

Answer:
i. True

Explanation:
If you add any zeros after the 5 it will be equal to 0.5. So, 0.5 is equivalent to 0.50

Inland Water
How many lakes and rivers does your state have? The U.S. Geological Survey defines inland water as water that is surrounded by land. The Atlantic Ocean, the Pacific Ocean, and the Great Lakes are not considered inland water.

Question 19.
Just over \(\frac{2}{100}\) of the entire United States is inland water. Write \(\frac{2}{100}\) as a decimal.
_____

Answer:
0.02

Explanation:
Write down 2 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, \(\frac{2}{100}\) = 0.02 is the answer

Question 20.
Can you write 0.02 as tenths? Explain.
_____ tenth

Answer:
0.2 tenth

Explanation:
0.02 = \(\frac{2}{100}\) = \(\frac{2 ÷ 10}{100 ÷ 10}\) = \(\frac{0.2}{10}\)

Question 21.
About 0.17 of the area of Rhode Island is inland water. Write 0.17 as a fraction.
\(\frac{□}{□}\)

Answer:
\(\frac{17}{100}\)

Explanation:

1 tenth and 7 hundred.
So, write 0.17 as \(\frac{17}{100}\)

Question 22.
Louisiana’s lakes and rivers cover about \(\frac{1}{10}\) of the state. Write \(\frac{1}{10}\) as hundredths in words, fraction form, and decimal form.
Type below:
_________

Answer:
Ten hundredths = \(\frac{10}{100}\) = 0.10

Explanation:
1 tenth is the same as the 1 tenth and 0 hundred

0.1 = 0.10 = \(\frac{10}{100}\)

Common Core – New – Page No. 511

Equivalent Fractions and Decimals

Write the number as hundredths in fraction form and decimal form.

Question 1.
\(\frac{5}{10}\) \(\frac{5}{10}\) = \(\frac{5 \times 10}{10 \times 10}\) = \(\frac{50}{100}\)

Think: 5 tenths is the same as 5 tenths and 0 hundredths. Write 0.50.

Question 2.
\(\frac{9}{10}\)
Type below:
_________

Answer:
\(\frac{90}{100}\); 0.90

Explanation:
\(\frac{9}{10}\) = \(\frac{9 \times 10}{10 \times 10}\) = \(\frac{90}{100}\)
9 tenths is the same as 9 tenths and 0 hundredths. Write 0.90

Question 3.
0.2
Type below:
_________

Answer:
\(\frac{20}{100}\)
0.20

Explanation:
2 tenths is the same as 2 tenths and 0 hundredths. Write 0.20.

\(\frac{2}{10}\) = \(\frac{2 x 10}{10 x 10}\) = \(\frac{20}{100}\)

Question 4.
0.8
Type below:
_________

Answer:
\(\frac{80}{100}\) = 0.80

Explanation:
8 tenths is the same as 8 tenths and 0 hundredths. Write 0.80.

\(\frac{8}{10}\) = \(\frac{8 x 10}{10 x 10}\) = \(\frac{80}{100}\)

Write the number as tenths in fraction form and decimal form.

Question 5.
\(\frac{40}{100}\)
Type below:
_________

Answer:
\(\frac{4}{10}\) = 0.4

Explanation:
10 is a common factor of the numerator and the denominator.
\(\frac{40}{100}\) = \(\frac{40 ÷ 10}{100 ÷ 10}\) = \(\frac{4}{10}\)
= 0.4

Question 6.
\(\frac{10}{100}\)
Type below:
_________

Answer:
\(\frac{1}{10}\) = 0.1

Explanation:
10 is a common factor of the numerator and the denominator.
\(\frac{10}{100}\) = \(\frac{10 ÷ 10}{100 ÷ 10}\) = \(\frac{1}{10}\)
= 0.1

Question 7.
0.60
Type below:
_________

Answer:
\(\frac{6}{10}\) = 0.6

Explanation:
0.60 is 60 hundredths.
\(\frac{60}{100}\).
10 is a common factor of the numerator and the denominator.
\(\frac{60}{100}\) = \(\frac{60 ÷ 10}{100 ÷ 10}\) = \(\frac{6}{10}\)
= 0.6

Problem Solving

Question 8.
Billy walks \(\frac{6}{10}\) mile to school each day. Write \(\frac{6}{10}\) as hundredths in fraction form and in decimal form.
Type below:
________

Answer:
\(\frac{60}{100}\)
0.60

Explanation:
Billy walks \(\frac{6}{10}\) mile to school each day.
\(\frac{6}{10}\) = \(\frac{6 x 10}{10 x 10}\) = \(\frac{60}{100}\)

0.60

Question 9.
Four states have names that begin with the letter A. This represents 0.08 of all the states. Write 0.08 as a fraction.
\(\frac{□}{□}\)

Answer:
\(\frac{8}{100}\)

Explanation:
0.08 is 8 hundredths. So, the fraction is \(\frac{8}{100}\)

Common Core – New – Page No. 512

Lesson Check

Question 1.
The fourth-grade students at Harvest School make up 0.3 of all students at the school. Which fraction is equivalent to 0.3?
Options:
a. \(\frac{3}{10}\)
b. \(\frac{30}{10}\)
c. \(\frac{3}{100}\)
d. \(\frac{33}{100}\)

Answer:
a. \(\frac{3}{10}\)

Explanation:
0.3 is same as the 3 tenths. So, the answer is \(\frac{3}{10}\)

Question 2.
Kyle and his brother have a marble set. Of the marbles, 12 are blue. This represents \(\frac{50}{100}\) of all the marbles. Which decimal is equivalent to \(\frac{50}{100}\)?
Options:
a. 50
b. 5.0
c. 0.50
d. 5,000

Answer:
c. 0.50

Explanation:

Write down 50 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 0.50 is the answer

Spiral Review

Question 3.
Jesse won his race by 3 \(\frac{45}{100}\) seconds. What is this number written as a decimal?
Options:
a. 0.345
b. 3.45
c. 34.5
d. 345

Answer:
b. 3.45

Explanation:
3 \(\frac{45}{100}\) = \(\frac{345}{100}\). Write down 345 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 3.45 is the answer

Question 4.
Marge cut 16 pieces of tape for mounting pictures on poster board. Each piece of tape was \(\frac{3}{8}\) inch long. How much tape did Marge use?
Options:
a. 2 inches
b. 4 inches
c. 5 inches
d. 6 inches

Answer:
d. 6 inches

Explanation:
\(\frac{3}{8}\) x 16 = 6 inches

Question 5.
Of Katie’s pattern blocks, \(\frac{9}{12}\) are triangles. What is \(\frac{9}{12}\) in simplest form?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{2}{3}\)
c. \(\frac{3}{4}\)
d. \(\frac{9}{12}\)

Answer:
c. \(\frac{3}{4}\)

Explanation:
\(\frac{9}{12}\) is divided by 3. So, \(\frac{3}{4}\) is the answer.

Question 6.
A number pattern has 75 as its first term. The rule for the pattern is subtract 6. What is the sixth term?
Options:
a. 39
b. 45
c. 51
d. 69

Answer:
b. 45

Explanation:
75 is the first term.
75 – 6 =69
69 – 6 = 63
63 – 6 = 57
57 – 6 = 51
51 – 6 = 45.
The sixth term is 45.

Page No. 515

Question 1.
Write the amount of money as a decimal in terms of dollars.

5 pennies = \(\frac{5}{100}\) of a dollar = _____ of a dollar.
_____ of a dollar

Answer:
5 pennies = \(\frac{5}{100}\) of a dollar = 0.05 of a dollar.
0.05 of a dollar

Explanation:
Write down 5 with the decimal point 2 spaces from the right (because 100 has 2 zeros). 0.05

Write the total money amount. Then write the amount as a fraction or a mixed number and as a decimal in terms of dollars.

Question 2.

Type below:
_________

Answer:
\(\frac{109}{100}\) = 1.09

Explanation:
1 dollar = 1/10 dimes
1 dollar = 1/100 pennies
1 dollar = 25/100 quarters
(3 x 1/10) + (4 x 1/100) + (3 x 25/100)
3/10 + 4/100 + 75/100
30/100 + 4/100 + 75/100 = 109/100 = 1.09

Question 3.

Type below:
_________

Answer:
\(\frac{60}{100}\) = 0.60

Explanation:
Given that 1 quarter, 2 dimes, and 3 cents.
10 dimes = 1 dollars
100 pennies = 1 dollar
4 quarters = 1 dollar
2 cents = 1 dollar
(25/100) + (2 x 1/10) + (3 x 5/100) = 25/100 + 20/100 + 15/100 = 60/100 = 0.60

Write as a money amount and as a decimal in terms of dollars.

Question 4.
\(\frac{92}{100}\)
amount: _____ decimal: _____of a dollar

Answer:
amount: $0.92 decimal: 0.92 of a dollar

Explanation:
\(\frac{92}{100}\) = 0.92

Question 5.
\(\frac{7}{100}\)
money amount: $ _____ decimal: _____ of a dollar

Answer:
money amount: $0.07 decimal: 0.07 of a dollar

Explanation:
\(\frac{7}{100}\) = 0.07

Question 6.
\(\frac{16}{100}\)
money amount: $ _____ decimal: _____ of a dollar

Answer:
money amount: $0.16 decimal: 0.16 of a dollar

Explanation:
\(\frac{16}{100}\) = 0.16

Question 7.
\(\frac{53}{100}\)
money amount: $ _____ decimal: _____ of a dollar

Answer:
money amount: $0.53 decimal: 0.53 of a dollar

Explanation:
\(\frac{53}{100}\) = 0.53

Write the total money amount. Then write the amount as a fraction or a mixed number and as a decimal in terms of dollars.

Question 8.

Type below:
_________

Answer:
\(\frac{46}{100}\) = 0.46

Explanation:
Given that 3 dimes, 3 nickels, 1 pennies
(3 x 10/100) + (3 x 5/100) + 1/100 = 30/100 + 15/100 + 1/100 = 46/100 = 0.46

Question 9.

Type below:
_________

Answer:
\(\frac{136}{100}\) = 1.36

Explanation:
Given that 1 dollar, 1 quarter, 1 pennies, 2 nickels
1 + 25/100 + 1/100 + (2 x 5/100)
1 + 25/100 + 1/100 + 10/100
1 + 36/100
136/100 = 1.36

Write as a money amount and as a decimal in terms of dollars.

Question 10.
\(\frac{27}{100}\)
money amount: $ _____ decimal: _____ of a dollar

Answer:
amount: $0.27 decimal: 0.27 of a dollar

Explanation:
\(\frac{27}{100}\) = 0.27

Question 11.
\(\frac{4}{100}\)
money amount: $ _____ decimal: _____ of a dollar

Answer:
amount: $0.04 decimal: 0.04 of a dollar

Explanation:
\(\frac{4}{100}\) = 0.04

Question 12.
\(\frac{75}{100}\)
money amount: $ _____ decimal: _____ of a dollar

Answer:
amount: $0.75 decimal: 0.75 of a dollar

Explanation:
\(\frac{75}{100}\) = 0.75

Question 13.
\(\frac{100}{100}\)
money amount: $ _____ decimal:_____ of a dollar

Answer:
money amount: $1 decimal: 1 of a dollar

Explanation:
\(\frac{100}{100}\) = 1

Write the total money amount. Then write the amount as a fraction and as a decimal in terms of dollars.

Question 14.
1 quarter 6 dimes 8 pennies
Type below:
_________

Answer:
money amount: $0.39; fraction: \(\frac{39}{100}\) decimal: 0.39 of a dollar

Explanation:
1 dollar = 100 cents
1 quarter = 25 cents
1 dime = 10 cents
1 penny = 1 cent
1 quarter 6 dimes 8 pennies = (25/100) + (6 x 10/100) + (8 x 1/100)
25/100 + 60/100 + 8/100 = 39/100 = 0.39

Question 15.
3 dimes 5 nickels 20 pennies
Type below:
_________

Answer:
money amount: $0.75; fraction: \(\frac{75}{100}\) decimal: 0.75 of a dollar

Explanation:
1 dollar = 100 cents
1 quarter = 25 cents
1 dime = 10 cents
1 penny = 1 cent
3 dimes 5 nickels 20 pennies = (3 x 10/100) + (5 x 5/100) + (20 x 1/100)
30/100 + 25/100 + 20/100 = 75/100 = 0.75

Page No. 516

Make Connections Algebra Complete to tell the value of each digit.

Question 16.
a.
$1.05 = _____ dollar + _____ pennies;

Answer:
$1.05 = 1 dollar + 5 pennies

Explanation:

$1.05 = 1 dollar and 05 pennies
There are 100 pennies in 1 dollar.
So, $1.05 = 105 pennies.

Question 16.
b.
1.05 = _____ one + _____ hundredths

Answer:
1.05 = 1 one and 05 hundredths

Explanation:

1.05 = 1 one and 05 hundredths
There are 100 hundredths in 1 one.
So, 1.05 = 105 hundredths.

Question 17.
a.
$5.18 = _____ dollars + _____ dime + _____ pennies;

Answer:
$5.18 = 5 dollars + 1 dime + 8 pennies;

Explanation:

$5.18 = 5 dollar and 1 dime and 8 pennies
There are 500 pennies in 5 dollars.
1 dime = 10 pennies
So, $5.18 = 518 pennies.

Question 17.
b.
5.18 = _____ ones + _____ tenth + _____ pennies

Answer:
5.18 = 5 ones + 1 tenths + 8 pennies

Explanation:

5.18 = 5 ones and 1 tenths and 8 pennies
There are 100 hundredths in 1 one. So, 500 hundredths in 5 ones.
So, 5.18 = 518 hundredths.

Use the table for 18–19.

Question 18.
The table shows the coins three students have. Write Nick’s total amount as a fraction in terms of dollars.
\(\frac{□}{□}\) of a dollar

Answer:
\(\frac{92}{100}\) of a dollar

Explanation:
Nick’s total amount = 2 quarters + 4 dimes + 0 Nickels + 2 pennies
= (2 x 25/100) + (4 x 10/100) + (2 x 1/100) = 50/100 + 40/100 + 2/100 = 92/100

Question 19.
Kim spent \(\frac{40}{100}\) of a dollar on a snack. Write as a money amount the amount she has left.
$ _____

Answer:
$0.28

Explanation:
Kim’s total amount = 1 quarter + 3 dimes + 2 nickels + 3 pennies
= 25/100 + (3 x 10/100) + (2 x 5/100) + (3 x 1/100) = 25/100 + 30/100 + 10/100 + 3/100 = 68/100.
Kim spent \(\frac{40}{100}\) of a dollar on a snack. So, 68/100 – 40/100 = 28/100 = 0.28

Question 20.
Travis has \(\frac{1}{2}\) of a dollar. He has at least two different types of coins in his pocket. Draw two possible sets of coins that Travis could have.
Type below:
_________

Answer:

Explanation:
1 Quarter + 2 dimes + 5 Pennies = 25/100 + 10/100 + 10/100 + 5/100 = 50/100 = 1/2 of a dollar
1 Quarter + 2 dimes + 1 Nickel = 25/100 + 10/100 + 10/100 + 5/100 = 50/100 = 1/2 of a dollar

Question 21.
Complete the table.

Type below:
_________

Answer:

Common Core – New – Page No. 517

Relate Fractions, Decimals, and Money

Write the total money amount. Then write the amount as a fraction or a mixed number and as a decimal in terms of dollars.

Question 1.

Answer:
$0.18 = \(\frac{18}{100}\) = 0.18

Explanation:
Given that 3 Pennies + 3 Nickels = 3/100 + 15/100 = 18/100

Question 2.

Type below:
_________

Answer:
$0.56 = \(\frac{56}{100}\) = 0.56

Explanation:
Given that 1 Quarter + 3 dime + 1 Pennies = 25/100 + 30/100 + 1/100 = 56/100

Write as a money amount and as a decimal in terms of dollars.

Question 3.
\(\frac{25}{100}\)
Dollars: _____ Decimal: _____

Answer:
Dollars: 1 quarter = $0.25; Decimal: 0.25

Explanation:
25 our of 100 dollars = 1 quarter.
So, 25/100 = 0.25

Question 4.
\(\frac{79}{100}\)
Dollars: _____ Decimal: _____

Answer:
amount: $0.79 decimal: 0.79 of a dollar

Explanation:
\(\frac{79}{100}\) = 0.79

Question 5.
\(\frac{31}{100}\)
Dollars: _____ Decimal: _____

Answer:
amount: $0.31 decimal: 0.31 of a dollar

Explanation:
\(\frac{31}{100}\) = 0.31

Question 6.
\(\frac{8}{100}\)
Dollars: _____ Decimal: _____

Answer:
amount: $0.08 decimal: 0.08 of a dollar

Explanation:
\(\frac{8}{100}\) = 0.08

Question 7.
\(\frac{42}{100}\)
Dollars: _____ Decimal: _____

Answer:
amount: $0.42 decimal: 0.42 of a dollar

Explanation:
\(\frac{42}{100}\) = 0.42

Write the money amount as a fraction in terms of dollars.

Question 8.
$0.87
\(\frac{□}{□}\)

Answer:
\(\frac{87}{100}\) of a dollar

Explanation:

$0.87 = 87 pennies
There are 100 pennies in 1 dollar.
So, $0.87 = \(\frac{87}{100}\) of a dollar.

Question 9.
$0.03
\(\frac{□}{□}\)

Answer:
\(\frac{3}{100}\)

Explanation:

$0.03 = 3 pennies
There are 100 pennies in 1 dollar.
So, $0.03 = \(\frac{3}{100}\).

Question 10.
$0.66
\(\frac{□}{□}\)

Answer:
\(\frac{66}{100}\)

Explanation:

$0.66 = 66 pennies
There are 100 pennies in 1 dollar.
So, $0.66 = \(\frac{66}{100}\).

Question 11.
$0.95
\(\frac{□}{□}\)

Answer:
\(\frac{95}{100}\)

Explanation:

$0.95 = 95 pennies
There are 100 pennies in 1 dollar.
So, $0.95 = \(\frac{95}{100}\).

Question 12.
$1.00
\(\frac{□}{□}\)

Answer:
\(\frac{100}{100}\)

Explanation:

$1.00 = 1 dollar
There are 100 pennies in 1 dollar.
So, $1.00 = \(\frac{100}{100}\).

Write the total money amount. Then write the amount as a fraction and as a decimal in terms of dollars.

Question 13.
2 quarters 2 dimes
Type below:
_________

Answer:
money amount: $0.70; fraction: \(\frac{70}{100}\); decimal: 0.70

Explanation:
Given that 2 quarters 2 dimes = (2 x 25/100) + (2 x 10/100) = 50/100 + 20/100 = 70/100

Question 14.
3 dimes 4 pennies
Type below:
_________

Answer:
money amount: $0.34; fraction: \(\frac{34}{100}\); decimal: 0.34

Explanation:
Given that 3 dimes 4 pennies = (3 x 10/100) + (4 x 1/100) = 30/100 + 4/100 = 34/100

Question 15.
8 nickels 12 pennies
Type below:
_________

Answer:
money amount: $0.57; fraction: \(\frac{57}{100}\); decimal: 0.57

Explanation:
Given that 8 nickels 12 pennies = (8 x 5/100) + (12 x 1/100) = 45/100 + 12/100 = 57/100

Problem Solving

Question 16.
Kate has 1 dime, 4 nickels, and 8 pennies. Write Kate’s total amount as a fraction in terms of a dollar.
\(\frac{□}{□}\)

Answer:
fraction: \(\frac{38}{100}\)

Explanation:
Kate has 1 dime, 4 nickels, and 8 pennies.
10/100 + (4 x 5/100) + (8/100) = 10/100 + 20/100 + 8/100 = 38/100

Question 17.
Nolan says he has \(\frac{75}{100}\) of a dollar. If he only has 3 coins, what are the coins?
_________

Answer:
3 quarters

Explanation:
3 quarters = \(\frac{25}{100}\) + \(\frac{25}{100}\) + \(\frac{25}{100}\) = \(\frac{75}{100}\)

Common Core – New – Page No. 518

Lesson Check

Question 1.
Which of the following names the total money amount shown as a fraction in terms of a dollar?

Options:
a. \(\frac{43}{1}\)
b. \(\frac{43}{10}\)
c. \(\frac{43}{57}\)
d. \(\frac{43}{100}\)

Answer:
d. \(\frac{43}{100}\)

Explanation:
Given that 1 quarter + 1 nickel + 1 dime + 3 pennies = 25/100 + 5/100 + 10/100 + 3/100 = 43/100

Question 2.
Crystal has \(\frac{81}{100}\) of a dollar. Which of the following could be the coins Crystal has?
Options:
a. 3 quarters, 1 dime, 1 penny
b. 2 quarters, 6 nickels, 1 penny
c. 2 quarters, 21 pennies
d. 1 quarter, 4 dimes, 1 nickel, 1 penny

Answer:
b. 2 quarters, 6 nickels, 1 penny

Explanation:
2 quarters, 6 nickels, 1 penny = (2 x 25/100) + (6 x 5/100) + 1/100 = 50/100 + 30/100 + 1/100 = 81/100

Spiral Review

Question 3.
Joel gives \(\frac{1}{3}\) of his baseball cards to his sister. Which fraction is equivalent to \(\frac{1}{3}\)?
Options:
a. \(\frac{3}{5}\)
b. \(\frac{2}{6}\)
c. \(\frac{8}{9}\)
d. \(\frac{4}{10}\)

Answer:
b. \(\frac{2}{6}\)

Explanation:
\(\frac{2}{6}\) is divided by 2. The remaining answer after the dividion is \(\frac{1}{3}\).

Question 4.
Penelope bakes pretzels. She salts \(\frac{3}{8}\) of the pretzels. Which fraction is equivalent to \(\frac{3}{8}\)?
Options:
a. \(\frac{9}{24}\)
b. \(\frac{15}{20}\)
c. \(\frac{3}{16}\)
d. \(\frac{1}{5}\)

Answer:
a. \(\frac{9}{24}\)

Explanation:
a. \(\frac{9}{24}\) is divided by 3. The remaining fraction after the division is \(\frac{3}{8}\).

Question 5.
Which decimal is shown by the model?

Options:
a. 10.0
b. 1.0
c. 0.1
d. 0.01

Answer:
d. 0.01

Explanation:
1 box is shaded out of 100. So, the fraction is 1/100 = 0.01.

Question 6.
Mr. Guzman has 100 cows on his dairy farm. Of the cows, 57 are Holstein. What decimal represents the portion of cows that are Holstein?
Options:
a. 0.43
b. 0.57
c. 5.7
d. 57.0

Answer:
b. 0.57

Explanation:
Mr. Guzman has 100 cows on his dairy farm. Of the cows, 57 are Holstein. So, 57/100 Holstein cows are available.
57/100 = 0.57

Page No. 521

Question 1.
Juan has $3.43. He is buying a paint brush that costs $1.21 to paint a model race car. How much will Juan have after he pays for the paint brush?
First, use bills and coins to model $3.43.

Next, you need to subtract. Remove bills and coins that have a value of $1.21. Mark Xs to show what you remove.
Last, count the value of the bills and coins that are left. How much will Juan have left?
$ _____

Answer:
Juan has $3.43. He is buying a paint brush that costs $1.21 to paint a model race car. Subtract $3.43 – $1.21

2 dollars, 2 dimes, and 2 pennies left.
2 + (2 x 10/100) + (2/100) = 2 + 20/100 + 2/100 = 2 + 22/100 = 2.22.
Juan has left $2.22

Question 2.
What if Juan has $3.43, and he wants to buy a paint brush that costs $2.28? How much money will Juan have left then? Explain.
$ _____

Answer:
$1.15

Explanation:
Juan has $3.43. He wants to buy a paint brush that costs $2.28.
$3.43 – $2.28 = $1.15

Question 3.
Sophia has $2.25. She wants to give an equal amount to each of her 3 young cousins. How much will each cousin receive?
$ _____ each cousin receive

Answer:
$0.75 each cousin receive

Explanation:
Sophia has $2.25. She wants to give an equal amount to each of her 3 young cousins.
Divide $2.25 with 3 = $2.25/3 = $0.75

Page No. 522

Question 4.
Marcus saves $13 each week. In how many weeks will he have saved at least $100?
_____ weeks

Answer:
8 weeks

Explanation:
Marcus saves $13 each week. He saves $100 in $100/$13 weeks = 7.96 weeks that is nearly equal to 8 weeks.

Question 5.
Analyze Relationships Hoshi has $50. Emily has $23 more than Hoshi. Karl has $16 less than Emily. How much money do they have all together?
$ _____

Answer:
$180

Explanation:
Hoshi has $50.
Emily has $23 more than Hoshi = $50 + $23 = $73.
Karl has $16 less than Emily = $73 – $16 = $57.
All together = $50 +$73 + $57 = $180.

Question 6.
Four girls have $5.00 to share equally. How much money will each girl get? Explain.
$ _____ each girl

Answer:
$1.25 for each girl

Explanation:
Four girls have $5.00 to share equally. So, each girl get $5.00/4 = $1.25

Question 7.
What if four girls want to share $5.52 equally? How much money will each girl get? Explain.
$ _____

Answer:
$1.38

Explanation:
Four girls have $5.52 to share equally. So, each girl get $5.52/4 = $1.38. If the amount shares equally, each girl get 1 dollar, 1 dime, 8 pennies.

Question 8.
Aimee and three of her friends have three quarters and one nickel. If Aimee and her friends share the money equally, how much will each person get? Explain how you found your answer.
$ _____

Answer:
$0.2

Explanation:
Aimee and three of her friends have three quarters and one nickel. If Aimee and her friends share the money equally. Four members shared (3 x 25/100) + 5/100 = 75/100 + 5/100 = 80/100 = 0.8.
Four members shared $0.8 equally, $0.8/4 = $0.2.

Common Core – New – Page No. 523

Problem Solving Money

Use the act it out strategy to solve.

Question 1.
Carl wants to buy a bicycle bell that costs $4.50. Carl has saved $2.75 so far. How much more money does he need to buy the bell?
Use 4 $1 bills and 2 quarters to model $4.50. Remove bills and coins that have a value of $2.75. First, remove 2 $1 bills and 2 quarters.
Next, exchange one $1 bill for 4 quarters and remove 1 quarter.
Count the amount that is left. So, Carl needs to save $1.75 more.

Answer:

Question 2.
Together, Xavier, Yolanda, and Zachary have $4.44. If each person has the same amount, how much money does each person have?
$ __________

Answer:
$1.11

Explanation:
Together, Xavier, Yolanda, and Zachary have $4.44. If each person has the same amount, $4.44/4 = $1.11

Question 3.
Marcus, Nan, and Olive each have $1.65 in their pockets. They decide to combine the money. How much money do they have altogether?
$ __________

Answer:
$4.95

Explanation:
Marcus, Nan, and Olive each have $1.65 in their pockets. They decide to combine the money. So, $1.65 + $1.65 + $1.65 = $4.95

Question 4.
Jessie saves $6 each week. In how many weeks will she have saved at least $50?
__________ weeks

Answer:
9 weeks

Explanation:
Jessie saves $6 each week. To save $50, $50/$6 = 9 weeks (approximately)

Question 5.
Becca has $12 more than Cece. Dave has $3 less than Cece. Cece has $10. How much money do they have altogether?
$ __________

Answer:
$39

Explanation:
Cece has $10.
Becca has $12 more than Cece = $10 + $12 = $22.
Dave has $3 less than Cece = $10 – $3 = $7.
All together = $10 + $22 + $7 = $39.

Common Core – New – Page No. 524

Lesson Check

Question 1.
Four friends earned $5.20 for washing a car. They shared the money equally. How much did each friend get?
Options:
a. $1.05
b. $1.30
c. $1.60
d. $20.80

Answer:
b. $1.30

Explanation:
Four friends earned $5.20 for washing a car. They shared the money equally.
$5.20/4 = $1.30

Question 2.
Which represents the value of one $1 bill and 5 quarters?
Options:
a. $1.05
b. $1.25
c. $1.50
d. $2.25

Answer:
d. $2.25

Explanation:
one $1 bill and 5 quarters. 5 quarters = 5 x 0.25 = 1.25.
$1 + $1.25 = $2.25

Spiral Review

Question 3.
Bethany has 9 pennies. What fraction of a dollar is this?
Options:
a. \(\frac{9}{100}\)
b. \(\frac{9}{10}\)
c. \(\frac{90}{100}\)
d. \(\frac{99}{100}\)

Answer:
a. \(\frac{9}{100}\)

Explanation:
1 dollar = 100 pennies.
So, 9 pennies = 9/100 of a dollar

Question 4.
Michael made \(\frac{9}{12}\) of his free throws at practice. What is \(\frac{9}{12}\) in simplest form?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{3}{9}\)
c. \(\frac{1}{2}\)
d. \(\frac{3}{4}\)

Answer:
d. \(\frac{3}{4}\)

Explanation:
\(\frac{9}{12}\) is divided by 3 that is equal to d. \(\frac{3}{4}\).

Question 5.
I am a prime number between 30 and 40. Which number could I be?
Options:
a. 31
b. 33
c. 36
d. 39

Answer:
a. 31

Explanation:
31 has fractions 1 and 31.

Question 6.
Georgette is using the benchmark \(\frac{1}{2}\) to compare fractions. Which statement is correct?
Options:
a. \(\frac{3}{8}>\frac{1}{2}\)
b. \(\frac{2}{5}<\frac{1}{2}\)
c. \(\frac{7}{12}<\frac{1}{2}\)
d. \(\frac{9}{10}=\frac{1}{2}\)

Answer:
b. \(\frac{2}{5}<\frac{1}{2}\)

Explanation:
From the given details, \(\frac{2}{5}<\frac{1}{2}\) is the correct answer.

Page No. 525

Choose the best term from the box to complete the sentence.

Question 1.
A symbol used to separate the ones and the tenths place is called a __________.
__________

Answer:
decimal point

Question 2.
The number 0.4 is written as a ____________.
__________

Answer:
4 tenths or 40 hundredths

Question 3.
A ______________ is one of one hundred equal parts of a whole.
__________

Answer:
hundredth

Write the fraction or mixed number and the decimal shown by the model.

Question 4.

Type below:
________

Answer:
\(\frac{4}{10}\) = 0.4

Explanation:
From the given model, 4 boxes are shaded out of 10 boxes. So, the fraction is \(\frac{4}{10}\) = 0.4

Question 5.

Type below:
________

Answer:
1\(\frac{3}{100}\) = 1.03

Explanation:
The model is divided into 100 equal parts. Each part represents the one-hundredth.
1\(\frac{3}{100}\) is 1 whole and 3 hundredths.

Write the number as hundredths in fraction form and decimal form.

Question 6.
\(\frac{8}{10}\)
Type below:
________

Answer:
\(\frac{80}{100}\)

0.80

Explanation:
Write \(\frac{8}{10}\) as an equivalent fraction.
\(\frac{8}{10}\) =\(\frac{8 × 10}{10× 10}\) = \(\frac{80}{100}\)
8 tenths is the same as 8 tenths 0 hundredths. So the decimal form = 0.80

Question 7.
0.5
Type below:
________

Answer:
\(\frac{50}{100}\)

0.50

Explanation:
Write 0.5 = \(\frac{5}{10}\) as an equivalent fraction.
\(\frac{5}{10}\) =\(\frac{5 × 10}{10× 10}\) = \(\frac{50}{100}\)
5 tenths is the same as 5 tenths 0 hundredths and also 0.50

Question 8.
Type below:
________

Answer:
b. \(\frac{2}{5}<\frac{1}{2}\)

Explanation:

Write the fraction or mixed number as a money amount, and as a decimal in terms of dollars.

Question 9.
\(\frac{95}{100}\)
amount: $ _____ decimal: _____ of a dollar

Answer:
amount: $0.95; decimal: 0.95

Explanation:
Write down 95 with the decimal point 2 spaces from the right (because 100 has 2 zeros)

Question 10.
1 \(\frac{48}{100}\)
amount: $ _____ decimal: _____ of a dollar

Answer:
amount: $1.48; decimal: 1.48

Explanation:
1\(\frac{48}{100}\) = \(\frac{148}{100}\)
Write down 148 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 1.48 is the answer

Question 11.
\(\frac{4}{100}\)
amount: $ _____ decimal: _____ of a dollar

Answer:
amount: $0.04; decimal: 0.04

Explanation:
Write down 4 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, the answer is 0.04

Page No. 526

Question 12.
Ken’s turtle competed in a 0.50-meter race. His turtle had traveled \(\frac{4}{100}\)
meter when the winning turtle crossed the finish line. What is \(\frac{4}{100}\) written as a decimal?
_____

Answer:
decimal: 0.04

Explanation:
Write down 4 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, the answer is 0.04

Question 13.
Alex lives eight tenths of a mile from Sarah. What is eight tenths written as a decimal?
_____

Answer:
decimal: 0.8

Explanation:
Write down 8 with the decimal point 1 space from the right (because 100 has 1 zero). The decimal value of eight tenths is 0.8

Question 14.
What fraction and decimal, in hundredths, is equivalent to \(\frac{7}{10}\)?
Type below:
________

Answer:
\(\frac{7 x 10}{10 x 10}\) = 0.70

Explanation:
\(\frac{7}{10}\) = \(\frac{7 x 10}{10 x 10}\) = 0.70

Question 15.
Elaine found the following in her pocket. How much money was in her pocket?

$ _____

Answer:
$\(\frac{140}{100}\)

Explanation:
Given that 1 dollar, 1 quarter, 1 dime, 1 Nickel.
1 + 25/100 + 10/100 + 5/100 = 1 + 40/100 = 140/100

Question 16.
Three girls share $0.60. Each girl gets the same amount. How much money does each girl get?
$ _____

Answer:
$0.20

Explanation:
Three girls share $0.60. Each girl gets the same amount. So, $0.60/3 = $0.20

Question 17.
The deli scale weighs meat and cheese in hundredths of a pound. Sam put \(\frac{5}{10}\) pound of pepperoni on the deli scale. What weight does the deli scale show?
_____ hundredths

Answer:
50 hundredths

Explanation:
\(\frac{5}{10}\) = \(\frac{5 x 10}{10 x 10}\) = \(\frac{50}{100}\).
\(\frac{50}{100}\) written as 50 hundredths.

Page No. 529

Question 1.
Find \(\frac{7}{10}+\frac{5}{100}\)
Think: Write the addends as fractions with a common denominator.
\(\frac{■}{100}\) + \(\frac{■}{100}\) = \(\frac{■}{■}\)
\(\frac{□}{□}\)

Answer:
\(\frac{75}{100}\)

Explanation:
\(\frac{7}{10}+\frac{5}{100}\).
Write the addends as fractions with a common denominator
\(\frac{7}{10}\) = \(\frac{7 X 10}{10 X 10}\) = \(\frac{70}{100}\).
\(\frac{70}{100}+\frac{5}{100}\) = \(\frac{75}{100}\)

Find the sum.

Question 2.
\(\frac{1}{10}+\frac{11}{100}\) = \(\frac{□}{□}\)

Answer:
\(\frac{21}{100}\)

Explanation:
\(\frac{1}{10}+\frac{11}{100}\).
Write the addends as fractions with a common denominator
\(\frac{1}{10}\) = \(\frac{1 X 10}{10 X 10}\) = \(\frac{10}{100}\).
\(\frac{10}{100}+\frac{11}{100}\) = \(\frac{21}{100}\)

Question 3.
\(\frac{36}{100}+\frac{5}{10}\) = \(\frac{□}{□}\)

Answer:
\(\frac{86}{100}\)

Explanation:
\(\frac{36}{100}+\frac{5}{10}\).
Write the addends as fractions with a common denominator
\(\frac{5}{10}\) = \(\frac{5 X 10}{10 X 10}\) = \(\frac{50}{100}\).
\(\frac{36}{100}+\frac{50}{100}\) = \(\frac{86}{100}\).

Question 4.
$0.16 + $0.45 = $ _____

Answer:
$0.61

Explanation:
Think 0.16 as 16 hundredths = \(\frac{16}{100}\).
Think 0.45 as 45 hundredths = \(\frac{45}{100}\).
Write the addends as fractions with a common denominator
\(\frac{16}{100}\) + \(\frac{45}{100}\) = \(\frac{61}{100}\) = 0.61

Question 5.
$0.08 + $0.88 = $ _____

Answer:
$0.96

Explanation:
Think 0.08 as 8 hundredths = \(\frac{8}{100}\).
Think 0.88 as 88 hundredths = \(\frac{88}{100}\).
Write the addends as fractions with a common denominator.
\(\frac{8}{100}\) + \(\frac{88}{100}\) = \(\frac{96}{100}\) = 0.96

Question 6.
\(\frac{6}{10}+\frac{25}{100}\) = \(\frac{□}{□}\)

Answer:
\(\frac{85}{100}[/latex

Explanation:
[latex]\frac{6}{10}+\frac{25}{100}\)
Write the addends as fractions with a common denominator.
\(\frac{6}{10}\) = \(\frac{6 X 10}{10 X 10}\) = \(\frac{60}{100}\).
\(\frac{60}{100}+\frac{25}{100}\) = \(\frac{85}{100}\).

Question 7.
\(\frac{7}{10}+\frac{7}{100}\) = \(\frac{□}{□}\)

Answer:
50 hundredths

Explanation:
\(\frac{7}{10}+\frac{7}{100}\)
Write the addends as fractions with a common denominator.
\(\frac{7}{10}\) = \(\frac{7 X 10}{10 X 10}\) = \(\frac{70}{100}\).
\(\frac{70}{100}+\frac{7}{100}\) = \(\frac{77}{100}\).

Question 8.
$0.55 + $0.23 = $ _____

Answer:
$0.78

Explanation:
Think 0.55 as 55 hundredths = \(\frac{55}{100}\).
Think 0.23 as 23 hundredths = \(\frac{23}{100}\).
Write the addends as fractions with a common denominator.
\(\frac{55}{100}\) + \(\frac{23}{100}\) = \(\frac{78}{100}\) = 0.78.

Question 9.
$0.19 + $0.13 = $ _____

Answer:
$0.32

Explanation:
Think 0.19 as 19 hundredths = \(\frac{19}{100}\).
Think 0.13 as 13 hundredths = \(\frac{13}{100}\).
Write the addends as fractions with a common denominator.
\(\frac{19}{100}\) + \(\frac{13}{100}\) = \(\frac{32}{100}\) = 0.32.

Reason Quantitatively Algebra Write the number that makes the equation true.

Question 10.
\(\frac{20}{100}+\frac{■}{10}\) = \(\frac{60}{100}\)
■ = _____

Answer:
■ = 4

Explanation:
\(\frac{20}{100}+\frac{■}{10}\) = \(\frac{60}{100}\).
Let the unknown number = s.
If s = 4,
\(\frac{20}{100}+\frac{4}{10}\).
Write the addends as fractions with a common denominator.
\(\frac{4}{10}\) = \(\frac{4 X 10}{10 X 10}\) = \(\frac{40}{100}\).
\(\frac{20}{100}+\frac{40}{100}\) = \(\frac{60}{100}\).
So, the unknown number is 4.

Question 11.
\(\frac{2}{10}+\frac{■}{100}\) = \(\frac{90}{100}\)
■ = _____

Answer:
■ = 70

Explanation:
\(\frac{2}{10}+\frac{■}{100}\) = \(\frac{90}{100}\).
Let the unknown number = s.
If s = 70,
\(\frac{2}{10}+\frac{7}{100}\).
Write the addends as fractions with a common denominator.
\(\frac{2}{10}\) = \(\frac{2 X 10}{10 X 10}\) = \(\frac{20}{100}\).
\(\frac{20}{100}+\frac{70}{100}\) = \(\frac{90}{100}\).
So, the unknown number is 70.

Question 12.
Jerry had 1 gallon of ice cream. He used \(\frac{3}{10}\) gallon to make chocolate milkshakes and 0.40 gallon to make vanilla milkshakes. How much ice cream does Jerry have left after making the milkshakes?
_____ gallon

Answer:
0.30 gallon

Explanation:
Jerry had 1 gallon of ice cream. He used \(\frac{3}{10}\) gallon to make chocolate milkshakes and 0.40 gallon to make vanilla milkshakes.
So, write 0.40 as \(\frac{40}{100}\) gallon.
She used \(\frac{3}{10}\) + \(\frac{40}{100}\).
\(\frac{3}{10}\) = \(\frac{3 X 10}{10 X 10}\) = \(\frac{30}{100}\).
\(\frac{30}{100}\) + \(\frac{40}{100}\) = \(\frac{70}{100}\)
Jerry have left 1 – \(\frac{70}{100}\) = \(\frac{30}{100}\) = 0.30 gallon

Page No. 530

Use the table for 13−16.

Question 13.
Dean selects Teakwood stones and Buckskin stones to pave a path in front of his house. How many meters long will each set of one Teakwood stone and one Buckskin stone be?
_____ meter

Answer:
\(\frac{71}{100}\) meter

Explanation:
Dean selects Teakwood stones and Buckskin stones to pave a path in front of his house.
Teakwood stone and one Buckskin stone = \(\frac{3}{10}\) + \(\frac{41}{100}\).
Write the addends as fractions with a common denominator.
\(\frac{3}{10}\) = \(\frac{3 X 10}{10 X 10}\) = \(\frac{30}{100}\).
\(\frac{30}{100}\) + \(\frac{41}{100}\) = \(\frac{71}{100}\)

Question 14.
The backyard patio at Nona’s house is made from a repeating pattern of one Rose stone and one Rainbow stone. How many meters long is each pair of stones?
_____ meter

Answer:
\(\frac{68}{100}\) meter

Explanation:
The backyard patio at Nona’s house is made from a repeating pattern of one Rose stone and one Rainbow stone.
Each pair of stone = \(\frac{8}{100}\) + \(\frac{6}{10}\).
\(\frac{6}{10}\) = \(\frac{6 X 10}{10 X 10}\) = \(\frac{60}{100}\).
Each pair of stone = \(\frac{8}{100}\) + \(\frac{60}{100}\) = \(\frac{68}{100}\).

Question 15.
For a stone path, Emily likes the look of a Rustic stone, then a Rainbow stone, and then another Rustic stone. How long will the three stones in a row be? Explain.
_____ meter

Answer:
\(\frac{90}{100}\) meter

Explanation:
For a stone path, Emily likes the look of a Rustic stone, then a Rainbow stone, and then another Rustic stone. If three stones in a row, then
\(\frac{15}{100}\) + \(\frac{6}{10}\) + \(\frac{15}{100}\).
\(\frac{30}{100}\) + \(\frac{6}{10}\).
\(\frac{6}{10}\) = \(\frac{6 X 10}{10 X 10}\) = \(\frac{60}{100}\).
\(\frac{30}{100}\) + \(\frac{60}{100}\) = \(\frac{90}{100}\).

Question 16.
Which two stones can you place end-to-end to get a length of 0.38 meter? Explain how you found your answer.
Type below:
________

Answer:
If you add Teakwood stones and Rose stones, then you get a length of 0.38 meter.
\(\frac{3}{10}\) + \(\frac{8}{100}\).
\(\frac{3}{10}\) = \(\frac{3 X 10}{10 X 10}\) = \(\frac{30}{100}\).
\(\frac{30}{100}\) + \(\frac{8}{100}\) = latex]\frac{38}{100}[/latex] = 0.38.
If you add any other two stones, the answer will not equal to 0.38.

Question 17.
Christelle is making a dollhouse. The dollhouse is \(\frac{6}{10}\) meter tall without the roof. The roof is \(\frac{15}{100}\) meter high. What is the height of the dollhouse with the roof? Choose a number from each column to complete an equation to solve.

\(\frac{□}{□}\) meter

Answer:
\(\frac{60}{100}\) + \(\frac{15}{100}\) = \(\frac{75}{100}\) meter

Explanation:
\(\frac{6}{10}\) + \(\frac{15}{100}\).
\(\frac{6}{10}\) = \(\frac{6 X 10}{10 X 10}\) = \(\frac{60}{100}\).
\(\frac{60}{100}\) + \(\frac{15}{100}\) = \(\frac{75}{100}\).

Common Core – New – Page No. 531

Add Fractional Parts of 10 and 100

Find the sum.

Question 1.
\(\frac{2}{10}+\frac{43}{100}\) Think: Write \(\frac{2}{10}\) as a fraction with a denominator of 100: \(\frac{2 \times 10}{10 \times 10}=\frac{20}{100}\)

Answer:
\(\frac{63}{100}\)

Explanation:
Think: Write \(\frac{2}{10}\) as a fraction with a denominator of 100: \(\frac{2 \times 10}{10 \times 10}=\frac{20}{100}\)

Question 2.
\(\frac{17}{100}+\frac{6}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{77}{100}\)

Explanation:
\(\frac{17}{100}+\frac{6}{10}\).
\(\frac{6 \times 10}{10 \times 10}=\frac{60}{100}\)
\(\frac{17}{100}+\frac{60}{100}\) = \(\frac{77}{100}\)

Question 3.
\(\frac{9}{100}+\frac{4}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{49}{100}\)

Explanation:
\(\frac{9}{100}+\frac{4}{10}\).
\(\frac{4 \times 10}{10 \times 10}=\frac{40}{100}\)
\(\frac{9}{100}+\frac{40}{100}\) = \(\frac{49}{100}\)

Question 4.
\(\frac{7}{10}+\frac{23}{100}\)
\(\frac{□}{□}\)

Answer:
\(\frac{93}{100}\)

Explanation:
\(\frac{7}{10}+\frac{23}{100}\).
\(\frac{7 \times 10}{10 \times 10}=\frac{70}{100}\)
\(\frac{70}{100}+\frac{23}{100}\) = \(\frac{93}{100}\)

Question 5.
$0.48 + $0.30
$ _____

Answer:
$0.78

Explanation:
Think $0.48 as \(\frac{48}{100}\).
Think $0.30 as \(\frac{30}{100}\).
\(\frac{48}{100}+\frac{30}{100}\) = \(\frac{78}{100}\) = $0.78

Question 6.
$0.25 + $0.34
$ _____

Answer:
$0.59

Explanation:
Think $0.25 as \(\frac{25}{100}\).
Think $0.34 as \(\frac{34}{100}\).
\(\frac{25}{100}+\frac{34}{100}\) = \(\frac{59}{100}\) = $0.59

Question 7.
$0.66 + $0.06
$ _____

Answer:
$0.72

Explanation:
Think $0.66 as \(\frac{66}{100}\).
Think $0.06 as \(\frac{6}{100}\).
\(\frac{66}{100}+\frac{6}{100}\) = \(\frac{72}{100}\) = $0.72

Problem Solving

Question 8.
Ned’s frog jumped \(\frac{38}{100}\) meter. Then his frog jumped \(\frac{4}{10}\) meter. How far did Ned’s frog jump in all?
\(\frac{□}{□}\)

Answer:
\(\frac{78}{100}\) meter

Explanation:
Ned’s frog jumped \(\frac{38}{100}\) meter. Then his frog jumped \(\frac{4}{10}\) meter.
So, together \(\frac{38}{100}\) + \(\frac{4}{10}\) jumped.
\(\frac{4}{10}\) = \(\frac{4 \times 10}{10 \times 10}=\frac{40}{100}\).
\(\frac{38}{100}\) + \(\frac{40}{100}\) = \(\frac{78}{100}\).

Question 9.
Keiko walks \(\frac{5}{10}\) kilometer from school to the park. Then she walks \(\frac{19}{100}\) kilometer from the park to her home. How far does Keiko walk in all?
\(\frac{□}{□}\)

Answer:
\(\frac{69}{100}\) kilometer

Explanation:
Keiko walks \(\frac{5}{10}\) kilometer from school to the park. Then she walks \(\frac{19}{100}\) kilometer from the park to her home.
Total = \(\frac{5}{10}\) + \(\frac{19}{100}\) kilometer.
\(\frac{5}{10}\) = \(\frac{5 \times 10}{10 \times 10}=\frac{50}{100}\).
\(\frac{50}{100}\) + \(\frac{19}{100}\) = \(\frac{69}{100}\).

Common Core – New – Page No. 532

Lesson Check

Question 1.
In a fish tank, \(\frac{2}{10}\) of the fish were orange and \(\frac{5}{100}\) of the fish were striped. What fraction of the fish were orange or striped?
Options:
a. \(\frac{7}{10}\)
b. \(\frac{52}{100}\)
c. \(\frac{25}{100}\)
d. \(\frac{7}{100}\)

Answer:
c. \(\frac{25}{100}\)

Explanation:
In a fish tank, \(\frac{2}{10}\) of the fish were orange and \(\frac{5}{100}\) of the fish were striped.
To find the raction of the fish were orange or striped Add \(\frac{2}{10}\) and \(\frac{5}{100}\).
\(\frac{2}{10}\) = \(\frac{2 \times 10}{10 \times 10}=\frac{20}{100}\).
\(\frac{20}{100}\) + \(\frac{5}{100}\) = \(\frac{25}{100}\).

Question 2.
Greg spends $0.45 on an eraser and $0.30 on a pen. How much money does Greg spend in all?
Options:
a. $3.45
b. $0.75
c. $0.48
d. $0.15

Answer:
b. $0.75

Explanation:
Think $0.45 as \(\frac{45}{100}\).
Think $0.30 as \(\frac{30}{100}\).
\(\frac{45}{100}+\frac{30}{100}\) = \(\frac{75}{100}\) = $0.75.

Spiral Review

Question 3.
Phillip saves $8 each month. How many months will it take him to save at least $60?
Options:
a. 6 months
b. 7 months
c. 8 months
d. 9 months

Answer:
c. 8 months

Explanation:
Phillip saves $8 each month.
To save at least $60, \(\frac{60}{8}\) = 8 months (approximately)

Question 4.
Ursula and Yi share a submarine sandwich. Ursula eats \(\frac{2}{8}\) of the sandwich. Yi eats \(\frac{3}{8}\) of the sandwich. How much of the sandwich do the two friends eat?
Options:
a. \(\frac{1}{8}\)
b. \(\frac{4}{8}\)
c. \(\frac{5}{8}\)
d. \(\frac{6}{8}\)

Answer:
c. \(\frac{5}{8}\)

Explanation:
Ursula and Yi share a submarine sandwich. Ursula eats \(\frac{2}{8}\) of the sandwich. Yi eats \(\frac{3}{8}\) of the sandwich.
Two friends eat \(\frac{2}{8}\) + \(\frac{3}{8}\) = \(\frac{5}{8}\)

Question 5.
A carpenter has a board that is 8 feet long. He cuts off two pieces. One piece is 3 \(\frac{1}{2}\) feet long and the other is 2 \(\frac{1}{3}\) feet long. How much of the board is left?
Options:
a. 2 \(\frac{1}{6}\)
b. 2 \(\frac{5}{6}\)
c. 3 \(\frac{1}{6}\)
d. 3 \(\frac{5}{6}\)

Answer:
a. 2 \(\frac{1}{6}\)

Explanation:
3 \(\frac{1}{2}\) = \(\frac{7}{2}\).
2 \(\frac{1}{3}\) = \(\frac{7}{3}\).
A carpenter has a board that is 8 feet long. He cuts off two pieces. One piece is 3 \(\frac{1}{2}\) feet long and the other is 2 \(\frac{1}{3}\) feet long.
\(\frac{7}{2}\) + \(\frac{7}{3}\) = \(\frac{7 \times 3}{2\times 3} + [latex]\frac{7 \times 2}{3\times 2} = [latex]\frac{21}{6}\) + \(\frac{14}{6}\) = \(\frac{35}{6}\) = 5\(\frac{5}{6}\).
He left 8 – 5\(\frac{5}{6}\).
7\(\frac{6}{6}\) – 5\(\frac{5}{6}\) = 2\(\frac{1}{6}\)

Question 6.
Jeff drinks \(\frac{2}{3}\) of a glass of juice. Which fraction is equivalent to \(\frac{2}{3}\)?
Options:
a. \(\frac{1}{3}\)
b. \(\frac{3}{2}\)
c. \(\frac{3}{6}\)
d. \(\frac{8}{12}\)

Answer:
d. \(\frac{8}{12}\)

Explanation:
\(\frac{8}{12}\) is divided by 4. So, \(\frac{8}{12}\) = \(\frac{2}{3}\).

Page No. 535

Question 1.
Compare 0.39 and 0.42. Write <, >, or =.
Shade the model to help.

0.39 ____ 0.42

Answer:

0.39 < 0.42

Compare. Write <, >, or =.

Question 2.

0.26 ____ 0.23

Answer:
0.26 > 0.23

Explanation:

The digits in the one’s and tenths place are the same. Compare the digits in the hundredths place. 6 > 3. So, 0.26 > 0.23.

Question 3.

0.7 ____ 0.54

Answer:
0.7 > 0.54

Explanation:

The digits in the ones place are the same. Compare the digits in the tenths place. 0.7 = 0.70. 7 > 5. So, 0.70 > 0.54.

Question 4.

1.15 ____ 1.3

Answer:
1.15 < 1.3

Explanation:

The digits in the ones place are the same. Compare the digits in the tenths place. 1 < 3. So, 1.15 < 1.3

Question 5.

4.5 ____ 2.89

Answer:
4.5 > 2.89

Explanation:

Compare one’s digits. 4 > 2 . So, 4.5 > 2.89

Compare. Write <, >, or =.

Question 6.
0.9 ____ 0.81

Answer:
0.9 > 0.81

Explanation:
0.9 is 9 tenths, which is equivalent to 90 hundredths.
0.81 is 81 hundredths.
90 hundredths > 81 hundredths. So, 0.9 > 0.81.

Question 7.
1.06 ____ 0.6

Answer:
1.06 > 0.6

Explanation:
1.06 is 106 hundredths.
0.6 is 6 tenths, which is equivalent to 60 hundredths.
106 hundredths > 60 hundredths. So, 1.06 > 0.6.

Question 8.
0.25 ____ 0.3

Answer:
0.25 < 0.3

Explanation:
0.25 is 25 hundredths.
0.3 is 3 tenths, which is equivalent to 30 hundredths.
25 hundredths < 30 hundredths. So, 0.25 < 0.3.

Question 9.
2.61 ____ 3.29

Answer:
2.61 < 3.29

Explanation:
2.61 is 261 hundredths.
3.29 is 329 hundredths.
261 hundredths < 329 hundredths. So, 2.61 < 3.29.

Reason Quantitatively Compare. Write <, >, or =.

Question 10.
0.30 ____ \(\frac{3}{10}\)

Answer:
0.30 = \(\frac{3}{10}\)

Explanation:
0.30 is 30 hundredths.
\(\frac{3}{10}\) is 3 tenths, which is equal to 30 hundredths.
30 hundredths = 30 hundredths. So, 0.30 = \(\frac{3}{10}\).

Question 11.
\(\frac{4}{100}\) ____ 0.2

Answer:
\(\frac{4}{100}\) < 0.2

Explanation:
\(\frac{4}{100}\) is 4 hundredths.
0.2 is 2 tenths, which is equal to 20 hundredths.
4 hundredths < 20 hundredths. So, \(\frac{4}{100}\) < 0.2

Question 12.
0.15 ____ \(\frac{1}{10}\)

Answer:
0.15 > \(\frac{1}{10}\)

Explanation:
0.15 is 15 hundredths.
\(\frac{1}{10}\) is 1 tenths, which is equal to 10 hundredths.
15 hundredths > 10 hundredths. So, 0.15 > \(\frac{1}{10}\).

Question 13.
\(\frac{1}{8}\) ____ 0.8

Answer:
latex]\frac{1}{8}[/latex] < 0.8

Explanation:
\(\frac{1}{8}\) = 0.25 is 25 hundredths.
0.8 is 8 tenths, which is equal to 80 hundredths.
25 hundredths < 80 hundredths. So, \(\frac{1}{8}\) < 0.8

Question 14.
Robert had $14.53 in his pocket. Ivan had $14.25 in his pocket. Matt had $14.40 in his pocket. Who had more money, Robert or Matt? Did Ivan have more money than either Robert or Matt?
________

Answer:
Robert had more money.
No, Ivan didn’t have more money than either Robert or Matt.

Explanation:
Compare Robert, Ivan, and Matt money to know who had more money.
The digits in the one’s place are the same. Compare the digits in the tenths place. 5 > 4 > 2. So, Robert had more money.

Page No. 536

Question 15.
Ricardo and Brandon ran a 1500-meter race. Ricardo finished in 4.89 minutes. Brandon finished in 4.83 minutes. What was the time of the runner who finished first?
a. What are you asked to find?–
Type below:
________

Answer:
The time of the runner who finished first.

Question 15.
b. What do you need to do to find the answer?
Type below:
________

Answer:
I have to compare the times to find the time that is less.

Question 15.
c. Solve the problem.
Type below:
________

Answer:
Use place-value chart

The digits of the one’s and tenths are equal. So, compare hundredths to find greater time.
9 > 3.
4.83 minutes are less than 4.89.

Question 15.
d. What was the time of the runner who finished first?
______ minutes

Answer:
4.83 minutes

Question 15.
e. Look back. Does your answer make sense? Explain.
_____

Answer:
Yes. The time of the runner who finished first is the lesser time of the two. Since 4.83, 4.89, then 4.83 minutes is the time of the runner who finished first.

Question 16.
The Venus flytrap closes in 0.3 second and the waterwheel plant closes in 0.2 second. What decimal is halfway between 0.2 and 0.3? Explain.
_____

Answer:
0.2 is 2 tenths, which is equal to the 20 hundredths.
0.3 is 3 tenths, which is equal to 30 hundredths.
The halfway between 20 hundredths and 30 hundredths is 25 hundredths.
So, the answer is 0.25.

Question 17.
For numbers 17a–17c, select True or False for the inequality.
a. 0.5 > 0.53
i. True
ii. False

Answer:
ii. False

Explanation:
0.5 is 50 hundredths.
0.53 is 53 hundredths.
50 hundredths < 53 hundredths. So, 0.5 < 0.53. So, the answer is false.

Question 17.
b. 0.35 < 0.37
i. True
ii. False

Answer:
i. True

Explanation:
0.35 is 35 hundredths.
0.37 is 37 hundredths.
35 hundredths < 37 hundredths.
0.35 < 0.37.
So, the answer is true.

Question 17. c. $1.35 > $0.35
i. True
ii. False

Answer:
i. True

Explanation:
$1.35 is 135 hundredths.
$0.35 is 35 hundredths.
135 hundredths > 35 hundredths.
$1.35 > $0.35.
So, the answer is correct.

Common Core – New – Page No. 537

Compare Decimals

Compare. Write <. >, or =.

Question 1.

Think: 3 tenths is less than 5 tenths. So, 0.35 < 0.53

Answer:
0.35 < 0.53

Explanation:
3 tenths is less than 5 tenths. So, 0.35 < 0.53

Question 2.
0.6 ______ 0.60

Answer:
0.6 = 0.60

Explanation:
0.6 is 6 tenths can write as 6 tenths and 0 hundredths. So, 0.6 = 0.60.

Question 3.
0.24 ______ 0.31

Answer:
0.24 < 0.31

Explanation:
2 tenths is less than 3 tenths. So, 0.24 < 0.31.

Question 4.
0.94 ______ 0.9

Answer:
0.94 > 0.9

Explanation:
The digits of tenths are equal. So, compare hundredths. 4 hundredths is greater than 0 hundredths. So, 0.94 > 0.9.

Question 5.
0.3 ______ 0.32

Answer:
0.3 < 0.32

Explanation:
The digits of tenths are equal. So, compare hundredths. 0 hundredths is less than 2 hundredths. So, 0.3 < 0.32.

Question 6.
0.45 ______ 0.28

Answer:
0.45 > 0.28

Explanation:
4 tenths is greater than 2 tenths. So, 0.45 > 0.28.

Question 7.
0.39 ______ 0.93

Answer:
0.39 < 0.93

Explanation:
3 tenths is less than 9 tenths. So, 0.39 < 0.93.

Use the number line to compare. Write true or false.

Question 8.
0.8 > 0.78
______

Answer:
true

Explanation:
0.78 is in between 0.7 and 0.8 that is less than 0.8. So, 0.8 > 0.78.

Question 9.
0.4 > 0.84
______

Answer:
false

Explanation:
0.4 is less than 0.84 and the left side of the number line. So, 0.4 < 0.84. The answer is false.

Question 10.
0.7 > 0.70
______

Answer:
false

Explanation:
0.7 is 7 tenths and 70 hundredths. 0.7 = 0.70. So, the answer is false.

Question 11.
0.4 > 0.04
______

Answer:
true

Explanation:
0.04 is less than 0.4 and it is left side of the 0.1 on the number line. 0.1 is less than 0.4. So, the given answer is true.

Compare. Write true or false.

Question 12.
0.09 > 0.1
______

Answer:
false

Explanation:
0 tenths is less than 1 tenths. So, 0.09 < 0.1. So, the answer is false.

Question 13.
0.24 = 0.42
______

Answer:
false

Explanation:
2 tenths is less than 4 tenths. So, 0.24 < 0.42. So, the answer is false.

Question 14.
0.17 < 0.32 ______

Answer:
true

Explanation:
1 tenths is less than 3 tenths. So, 0.17 < 0.32. So, the answer is true.

Question 15.
0.85 > 0.82
______

Answer:
true

Explanation:
The digits of tenths are equal. So, compare hundredths. 5 hundredths is greater than 2 hundredths. So, 0.85 > 0.82.

Question 16.
Kelly walks 0.7 mile to school. Mary walks 0.49 mile to school. Write an inequality using <, > or = to compare the distances they walk to school.
0.7 ______ 0.49

Answer:
0.7 > 0.49

Explanation:
7 tenths is greater than 4 tenths. So, 0.7 > 0.49.

Question 17.
Tyrone shades two decimal grids. He shades 0.03 of the squares on one grid blue. He shades 0.3 of another grid red. Which grid has the greater part shaded?
0.03 ______ 0.3

Answer:
0.03 < 0.3

Explanation:
0.03 is 3 hundredths.
0.3 is 3 tenths, which is equal to 30 hundredths.
3 hundredths < 30 hundredths. So, 0.03 < 0.3.

Common Core – New – Page No. 538

Lesson Check

Question 1.
Bob, Cal, and Pete each made a stack of baseball cards. Bob’s stack was 0.2 meter high. Cal’s stack was 0.24 meter high. Pete’s stack was 0.18 meter high.
Which statement is true?
Options:
a. 0.02 > 0.24
b. 0.24 > 0.18
c. 0.18 > 0.2
d. 0.24 = 0.2

Answer:
b. 0.24 > 0.18

Explanation:
2 tenths is greater than 1 tenth. So, 0.24 > 0.18.

Question 2.
Three classmates spent money at the school supplies store. Mark spent 0.5 dollar, Andre spent 0.45 dollar, and Raquel spent 0.52 dollar. Which
statement is true?
Options:
a. 0.45 > 0.5
b. 0.52 < 0.45
c. 0.5 = 0.52
d. 0.45 < 0.5

Answer:
d. 0.45 < 0.5

Explanation:
4 tenths is less than 5 tenth. So, 0.45 > 0.5.

Spiral Review

Question 3.
Pedro has $0.35 in his pocket. Alice has $0.40 in her pocket. How much money do Pedro and Alice have in their pockets altogether?
Options:
a. $0.05
b. $0.39
c. $0.75
d. $0.79

Answer:
c. $0.75

Explanation:
Pedro has $0.35 in his pocket. Alice has $0.40 in her pocket.
Together = $0.35 + $0.40 = $0.75.

Question 4.
The measure 62 centimeters is equivalent to \(\frac{62}{100}\) meter. What is this measure written as a decimal?
Options:
a. 62.0 meters
b. 6.2 meters
c. 0.62 meter
d. 0.6 meter

Answer:
c. 0.62 meter

Explanation:
\(\frac{62}{100}\) = 0.62 meter.

Question 5.
Joel has 24 sports trophies. Of the trophies, \(\frac{1}{8}\) are soccer trophies. How many soccer trophies does Joel have?
Options:
a. 2
b. 3
c. 4
d. 6

Answer:
b. 3

Explanation:
Joel has 24 sports trophies. Of the trophies, \(\frac{1}{8}\) are soccer trophies.
So, \(\frac{1}{8}\) X 24 = 3 soccer trophies.

Question 6.
Molly’s jump rope is 6 \(\frac{1}{3}\) feet long. Gail’s jump rope is 4 \(\frac{2}{3}\) feet long. How much longer is Molly’s jump rope?
Options:
a. 1 \(\frac{1}{3}\) feet
b. 1 \(\frac{2}{3}\) feet
c. 2 \(\frac{1}{3}\) feet
d. 2 \(\frac{2}{3}\) feet

Answer:
b. 1 \(\frac{2}{3}\) feet

Explanation:
6 \(\frac{1}{3}\) feet = \(\frac{19}{3}\) feet.
4 \(\frac{2}{3}\) feet = \(\frac{14}{3}\) feet.
\(\frac{19}{3}\) – \(\frac{14}{3}\) = \(\frac{5}{3}\) feet = b. 1 \(\frac{2}{3}\) feet.

Page No. 539

Question 1.
Select a number shown by the model. Mark all that apply.

Type below:
________

Answer:
1 \(\frac{4}{10}\) = \(\frac{14}{10}\) = 1.4

Explanation:
from the given image, there is one whole number and \(\frac{4}{10}\) of another model. So, 1 \(\frac{4}{10}\) = \(\frac{14}{10}\) = 1.4

Question 2.
Rick has one dollar and twenty-seven cents to buy a notebook. Which names this money amount in terms of dollars? Mark all that apply.
Options:
a. 12.7
b. 1.027
c. $1.27
d. 1.27
e. 1 \(\frac{27}{100}\)
f. \(\frac{127}{10}\)

Answer:
c. $1.27
d. 1.27
e. 1 \(\frac{27}{100}\)

Explanation:
one dollar and twenty-seven cents = 1 \(\frac{27}{100}\) = 1.27 = $1.27

Question 3.
For numbers 3a–3e, select True or False for the statement.
a. 0.9 is equivalent to 0.90.
i. True
ii. False

Answer:
i. True

Explanation:
0.9 is 9 tenths, which is equal to 90 hundredths. 0.9 = 0.90. So, the answer is true.

Question 3.
b. 0.20 is equivalent to \(\frac{2}{100}\)
i. True
ii. False

Answer:
ii. False

Explanation:
\(\frac{2}{100}\) = 0.02. So, the given answer is false.

Question 3.
c. \(\frac{80}{100}\) is equivalent to \(\frac{8}{10}\).
i. True
ii. False

Answer:
i. True

Explanation:
Divide \(\frac{80}{100}\) by 10 = \(\frac{8}{10}\). So, the answer is true.

Question 3.
d. \(\frac{6}{10}\) is equivalent to 0.60.
i. True
ii. False

Answer:
i. True

Explanation:
\(\frac{6}{10}\) is 0.6. 0.6 is 6 tenths, which is equal to 6 tenths and 0 hundredths. 0.60. So, 0.6 =0.60. The answer is true.

Question 3.
e. 0.3 is equivalent to \(\frac{3}{100}\)
i. True
ii. False

Answer:
ii. False

Explanation:
0.3 is 3 tenths, which is equal to 3 tenths and 0 hundredths. \(\frac{3}{100}\) is 0 tenths. So, the answer is false.

Page No. 540

Question 4.
After selling some old books and toys, Gwen and her brother Max had 5 one-dollar bills, 6 quarters, and 8 dimes. They agreed to divide the money equally.
Part A
Wat is the total amount of money that Gwen and Max earned?
Explain.
$ _____

Answer:
$7.30

Explanation:
After selling some old books and toys, Gwen and her brother Max had 5 one-dollar bills, 6 quarters, and 8 dimes.
5 + (6 X 25/100) + (8 X 10/100) = 5 + 150/100 + 80/100 = 5 + 230/100 = 730/100 = 7.30

Question 4.
Part B
Max said that he and Gwen cannot get equal amounts of money because 5 one-dollar bills cannot be divided evenly. Do you agree with Max?
Explain.
_____

Answer:
ii. False

Explanation:
No; they can share the 3 quarters and 4 dimes each. Then, they can change the 5 dollar bills into quarters. 1 dollar = 4 quarters. So, 5 dollars = 5 X 4 or 20 quarters. They can each get 10 quarters. So, each person has a total of 13 quarters and 4 dimes. $3.25 + $0.40 = $3.65

Question 5.
Harrison rode his bike \(\frac{6}{10}\) of a mile to the park. Shade the model. Then write the decimal to show how far Harrison rode his bike.

Harrison rode his bike _______ mile to the park.
_____

Answer:

Harrison rode his bike 0.6 mile to the park.

Explanation:
6 boxes are shaded out of 10.

Question 6.
Amaldo spent \(\frac{88}{100}\) of a dollar on a souvenir pencil from Zion National Park in Utah. What is \(\frac{88}{100}\) written as a decimal in terms of dollars?
_____

Answer:
0.88

Explanation:
Write down 88 with the decimal point 2 spaces from the right (because 100 has 2 zeros). 0.88

Question 7.
Tran has $5.82. He is saving for a video game that costs $8.95.
Tran needs _______ more to have enough money for the game.
_____

Answer:
$3.13

Explanation:
Tran has $5.82. He is saving for a video game that costs $8.95. To know more amount need to buy a video game = $8.95 – $5.82 = $3.13

Page No. 541

Question 8.
Cheyenne lives \(\frac{7}{10}\) mile from school. A fraction in hundredths equal to \(\frac{7}{10}\) is
\(\frac{□}{□}\)

Answer:
\(\frac{70}{100}\)

Explanation:
\(\frac{7}{10}\) = \(\frac{7 \times 10}{10 \times 10}\) = \(\frac{70}{100}\)

Question 9.
Write a decimal in tenths that is less than 2.42 but greater than 2.0.
Type below:
__________

Answer:
2.1, 2.2, 2.3, 2.4

Explanation:
The decimal in greater than 2.0 and below the 2.4 are 2.1, 2.2, 2.3, 2.4

Question 10.
Kylee and two of her friends are at a museum. They find two quarters and one dime on the ground.
Part A
If Kylee and her friends share the money equally, how much will each person get? Explain how you found your answer.
$ _____
Explain:
__________

Answer:
$0.20; Two quarters and one dime are equal to $0.50 + $0.10 = $0.60. Take $0.60 as 6 dimes. When 6 dimes divide equally, each person will receive 2 dimes or $0.20.

Question 10.
Part B
Kylee says that each person will receive \(\frac{2}{10}\) of the money that was found. Do you agree? Explain.
__________

Answer:
No; Each person receives $0.20, which is 2/10 of a dollar, not 2/10 of the money that was found. Since there are 3 people who share the money equally, each person will receive 1/3 of the money.

Question 11.
Shade the model to show 1 \(\frac{52}{100}\). Then write the mixed number in decimal form.

_____

Answer:

1.52

Page No. 542

Question 12.
Henry is making a recipe for biscuits. A recipe calls for \(\frac{5}{10}\) kilogram flour and \(\frac{9}{100}\) kilogram sugar.
Part A
If Henry measures correctly and combines the two amounts, how much flour and sugar will he have? Show your work.
\(\frac{□}{□}\) kilogram

Answer:
\(\frac{59}{100}\) kilogram

Explanation:
Henry is making a recipe for biscuits. A recipe calls for \(\frac{5}{10}\) kilogram flour and \(\frac{9}{100}\) kilogram sugar. So, add \(\frac{5}{10}\) kilogram flour and \(\frac{9}{100}\) kilogram flour.
\(\frac{5}{10}\) = \(\frac{5 \times 10}{10 \times 10}\) = \(\frac{50}{100}\).
\(\frac{50}{100}\) + \(\frac{9}{100}\) = \(\frac{59}{100}\).

Question 12.
Part B
How can you write your answer as a decimal?
__________ kilogram

Answer:
0.59 kilogram

Explanation:
\(\frac{59}{100}\) = 0.59

Question 13.
An orchestra has 100 musicians. \(\frac{4}{10}\) of them play string instruments—violin, viola, cello, double bass, guitar, lute, and harp. What decimal is equivalent to \(\frac{4}{10}\)?
__________

Answer:
0.4 or 0.40

Explanation:
\(\frac{4}{10}\) = 0.4 = 0.40

Question 14.
Complete the table.

Answer:

Question 15.
The point on the number line shows the number of seconds it took an athlete to run the forty-yard dash. Write the decimal that correctly names the point.

Answer:
\(\frac{70}{100}\)

Explanation:
The point is in between 5\(\frac{5}{10}\) and 6.0. The point after the 5\(\frac{5}{10}\) is 5\(\frac{6}{10}\) = 5.6

Page No. 543

Question 16.
Ingrid is making a toy car. The toy car is \(\frac{5}{10}\) meter high without the roof. The roof is \(\frac{18}{100}\) meter high. What is the height of the toy car with the roof? Choose a number from each column to complete an equation to solve.

Type below:
__________

Answer:
\(\frac{50}{100}\) + \(\frac{18}{100}\) = \(\frac{68}{100}\) meter high

Explanation:
\(\frac{5}{10}\) = \(\frac{5 \times 10}{10 \times 10}\) = \(\frac{50}{100}\).
\(\frac{50}{100}\) + \(\frac{18}{100}\) = \(\frac{68}{100}\).

Question 17.
Callie shaded the model to represent the questions she answered correctly on a test. What decimal represents the part of the model that is shaded?

represents _____

Answer:
0.81

Explanation:
81 boxes are shaded out of 100. So, \(\frac{81}{100}\) = 0.81

Question 18.
For numbers 18a–18f, select True or False for the inequality.
a. 0.21 < 0.27
i. True
ii. False

Answer:
i. True

Explanation:
The digits in the one’s and tenths place are the same. Compare the digits in the hundredths place. 1 < 7. So, 0.21 < 0.27. The answer is true.

Question 18. b. 0.4 > 0.45

i. True
ii. False

Answer:
ii. False

Explanation:
0.4 = 0.40
The digits in the one’s and tenths place are the same. Compare the digits in the hundredths place. 0 < 5. So, 0.4 < 0.46. The answer is false.

Question 18.
c. $3.21 > $0.2
i. True
ii. False

Answer:
i. True

Explanation:
3 ones is greater than 0’s. So, $3.21 > $0.2

Question 18.
d. 1.9 < 1.90
i. True
ii. False

Answer:
ii. False

Explanation:
1.9 = 1.90. So, the answer is false

Question 18. e. 0.41 = 0.14
i. True
ii. False

Answer:
ii. False

Explanation:
The digits in the one’s are the same. Compare the digits in the tenths place. 4 > 1. So, 0.41 > 0.14. The answer is false.

Question 18. f. 6.2 > 6.02
i. True
ii. False

Answer:
i. True

Explanation:
2 tenths is greater than 0 tenths. So, 6.2 > 6.02. The answer is true.

Question 19.
Fill in the numbers to find the sum.

Type below:
__________

Answer:
\(\frac{4}{10}\) + \(\frac{40}{100}\) = \(\frac{8}{10}\)

Explanation:
Let the unknown numbers are A and B.
\(\frac{4}{10}\) + \(\frac{A}{100}\) = \(\frac{8}{B}\)
If A = 40 and B = 10, then \(\frac{4}{10}\) + \(\frac{40}{100}\) = \(\frac{8}{10}\).

Page No. 544

Question 20.
Steve is measuring the growth of a tree. He drew this model to show the tree’s growth in meters. Which fraction, mixed number, or decimal does the model show? Mark all that apply.

Options:
a. 1.28
b. 12.8
c. 0.28
d. 2 \(\frac{8}{100}\)
e. 1 \(\frac{28}{100}\)
f. 1 \(\frac{28}{10}\)

Answer:
a. 1.28
e. 1 \(\frac{28}{100}\)

Explanation:
From the given image, it has one model of 1 whole number and other model is shades 24 boxes out of 100. So, 1 \(\frac{28}{100}\) = \(\frac{128}{100}\) = 1.28 is the answer.

Question 21.
Luke lives 0.4 kilometer from a skating rink. Mark lives 0.25 kilometer from the skating rink.
Part A
Who lives closer to the skating rink? Explain.
_____

Answer:
Mark lives closer to the skating rink

Explanation:
0.4 is 4 tenths and 0.25 is 2 tenths 5 hundredths. Compare the tenths, since
4 tenths > 2 tenths. Luke lives farther from the rink. So, Mark lives closer.

Question 21.
Part B
How can you write each distance as a fraction? Explain.
Type below:
__________

Answer:
\(\frac{4}{10}\) and \(\frac{25}{100}\)

Explanation:
0.4 is 4 tenths. So, \(\frac{4}{10}\) and 0.25 is 25 hundredths. So, \(\frac{25}{100}\).

Question 21.
Part C
Luke is walking to the skating rink to pick up a practice schedule. Then he is walking to Mark’s house. Will he walk more than a kilometer or less than a kilometer? Explain.
__________

Answer:
Less than a kilometer; \(\frac{4}{10}\) < \(\frac{5}{10}\) or \(\frac{1}{2}\) and \(\frac{25}{100}\) < \(\frac{50}{100}\) or \(\frac{1}{2}\).
\(\frac{4}{10}\) + \(\frac{25}{100}\) < \(\frac{1}{2}\) + \(\frac{1}{2}\). So, \(\frac{1}{2}\) + \(\frac{1}{2}\) = 1.
Therefore, \(\frac{4}{10}\) + \(\frac{25}{100}\) < 1.

Page No. 551

Question 1.
Draw and label \(\overline{A B}\) in the space at the right.
\(\overline{A B}\) is a __________ .
__________

Answer:

\(\overline{A B}\) is a line segment.

Draw and label an example of the figure.

Question 2.
\(\underset { XY }{ \longleftrightarrow } \)
Type below:
__________

Answer:

\(\underset { XY }{ \longleftrightarrow } \) is a line

Question 3.
obtuse ∠K
Type below:
__________

Answer:

Angle K is greater than a right angle and less than a straight angle.

Question 4.
∠CDE
Type below:
__________

Answer:

angle CDE

Use Figure M for 5 and 6.

Question 5.
Name a line segment.
Type below:
__________

Answer:
line segment TU

Explanation:
TU line is a straight path of points that continues without an end in both directions.

Question 6.
Name a right angle.
Type below:
__________

Answer:
Angle TUW

Explanation:
TUW is a right angle that forms a square corner.

Draw and label an example of the figure.

Question 7.
\(\overrightarrow{P Q}\)
Type below:
__________

Answer:

\(\overrightarrow{P Q}\) is a ray.

Question 8.
acute ∠RST
Type below:
__________

Answer:

Angle RST

Question 9.
straight ∠WXZ
Type below:
__________

Answer:

Use Figure F for 10–15.

Question 10.
Name a ray.
Type below:
__________

Answer:
Ray K

Explanation:
K is a ray that has one endpoint and continues without an end in one direction.

Question 11.
Name an obtuse angle.
Type below:
__________

Answer:
Angle ABK

Explanation:
ABK is an obtuse angle that is greater than a right angle and less than a straight angle.

Question 12.
Name a line.
Type below:
__________

Answer:
Line AC

Explanation:
AC is a line that is a straight path of points that continues without end in
both directions.

Question 13.
Name a line segment.
Type below:
__________

Answer:
Line Segment PQ

Explanation:
PQ is a line segment that is part of a line between two endpoints.

Question 14.
Name a right angle.
Type below:
__________

Answer:
Angle PRC

Explanation:
PRC is a right angle that forms a square corner.

Question 15.
Name an acute angle.
Type below:
__________

Answer:
Angle ABJ

Explanation:
ABJ is an acute angle that is less than a right angle.

Page No. 552

Use the picture of the bridge for 16 and 17.

Question 16.
Classify ∠A.
_____ angle

Answer:
Right Angle

Explanation:
A is the right angle that forms a square corner.

Question 17.
Which angle appears to be obtuse?
∠ _____

Answer:
∠C

Explanation:
C is an obtuse angle that is greater than a right angle and less than a straight angle.

Question 18.
How many different angles are in Figure X?
List them.

Type below:
__________

Answer:
4 Angles;
Right Angle = Angle EBC;
Obtuse angle = Angle DBF;
Acute angle = Angle DBE;
Straight angle = Angle ABC.

Explanation:

Question 19.
Vanessa drew the angle at the right and named it ∠TRS. Explain why Vanessa’s name for the angle is incorrect. Write a correct name for the angle.

Type below:
__________

Answer:
Vanessa’s name for the angle is incorrect. Because She drew ∠TSR. The two rays R and T have the same endpoint at S called the angle. Also, the TSR is an acute angle that is less than a right angle.

Question 20.
Write the word that describes the part of Figure A.


\(\overline{B G}\) _________
\(\underset { CD }{ \longleftrightarrow } \) _________
∠FBG _________
\(\overrightarrow{B E}\) _________
∠AGD _________

Answer:
\(\overline{B G}\) Line Segment.
\(\underset { CD }{ \longleftrightarrow } \) Line.
∠FBG Right Angle.
\(\overrightarrow{B E}\) Ray.
∠AGD an acute angle.

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Common Core – Page No. 87000

Lessons 4.1–4.2

Find the product.

Question 1.
4 × 2 = ______

Answer:
4 × 2 = 8.

Explanation:
Double 2×2 to get 4×2.
2 x 2 = 4.
Double: 4 + 4 = 8.
4 x 2 = 8.

Question 2.
8 × 5 = ______

Answer:
8 x 5 = 40

Explanation:
Factor 8 is an even number. 4+ 4
5 x 4 = 20.
20 doubled is 40.
8 x 5 = 40.

Question 3.
10 × 7 = ______

Answer:
10 × 7 = 70

Explanation:
A multiple of 10 is any product that has 10 as one of its factors. So, the multiplication of any number with 10 is 10’s of that particular number. The answer is 10 × 7 = 70.

Question 4.
2 × 9 = ______

Answer:
2 x 9 = 18

Explanation:
Double the given number 6 to get the final answer. The answer is 9 + 9 = 18.
2 x 9 = 18.

Question 5.
6
× 1 0
——-
______

Answer:
6 x 10 = 60

Explanation:
Using doubles, we can find a 6 x 10 value. First, multiply the factor with half of 6. So, now we can do 3 x 10 = 30. Now, we can double the value of 3 x 10. That is 30 + 30 = 60. So, the answer for 6 x 10 = 60.

Question 6.
5
× 7
——-
______

Answer:
5 x 7 = 35.

Explanation:

Skip count by 5’s until you say 7 numbers. 5, 10, 15, 20, 25, 30, 35. Now, the count of the number is 7. So, the answer for 5 x 7 is 35.

Question 7.
2
× 1 0
——-
______

Answer:
2 x 10 = 20.

Explanation:
Double 10 to get the answer of 2 x 10.
10 + 10 = 20.
2 x 10 = 20.

Question 8.
4
× 5
——-
______

Answer:
4 x 5 =20

Explanation:
Multiply 2×5 to get the answer for 4×5. Double the answer of 2×5 to get the final answer.
2 x 5 =10.
Double: 10 + 10 = 20.
4 x 5 =20.

Lessons 4.3–4.5

Find the product.

Question 9.
6
× 2
——-
______

Answer:
6 x 2 = 12.

Explanation:
Use doubles to find the answer of 6 x 2.
Multiply 3 x 2 = 6.
Double: 6 + 6 = 12.
The answer for 6 x 2 is 12.

Question 10.
3
× 9
——-
______

Answer:
3 x 9 = 27.

Explanation:

Skip count by 3’s until you say 9 numbers. Write like 3, 6, 9, 12, 15, 18, 21, 24, 27. The answer for 3 x 9 is 27.

Question 11.
7
× 3
——-
______

Answer:
7 x 3 = 21

Explanation:
Write 7 x 3 as 3 x 7 according to the Commutative Law of Multiplication.
Skip count by 3’s until you say 7 numbers. Write like 3, 6, 9, 12, 15, 18, 21. The answer for 3 x 7 is 21. So, 7 x 3 = 21.

Question 12.
8
× 6
——-
______

Answer:
8 × 6 = 48

Explanation:
8 × 6 = (2 x 4) x 6
Use the Associative Property.
8 × 6 = 2 x (4 x 6)
Multiply. 4 × 6
8 × 6 = 2 x 24
Double the product.
8 × 6 = 24 + 24
8 × 6 = 48.

Write one way to break apart the array. Then find the product.

Question 13.

Type below:
__________

Answer:
36

Explanation:
Draw a line to seperate the columns. Divide the columns with 4 and 5 factors.
The array is 4 x 9 = 4 x (5 + 4)
(4 x 5) + (4 x 4) = 20 + 16 = 36.

Find the product.

Question 14.
5 × 7 = ______

Answer:
5 x 7 = 35

Explanation:
Skip count by 5’s until you say 7 numbers. 5, 10, 15, 20, 25, 30, 35. Now, the count of the number is 7. So, the answer for 5 x 7 is 35.

Question 15.
2 × 6 = ______

Answer:
2 x 6 = 12

Explanation:
Double 6 to get the answer. 6 + 6 = 12.
2 x 6 = 12.

Question 16.
4 × 7 = ______

Answer:
Double 2 x 7 to find 4 x 7.
2 x 7 = 14.
Double: 14 + 14 = 28.
4 x 7 = 28.

Explanation:

Question 17.
8 × 3 = ______

Answer:
8 × 3 = 24

Explanation:
8 × 3 = (2 x 4) x 3
Use the Associative Property.
8 × 3 = 2 x (4 x 3)
Multiply. 4 × 3
8 × 3 = 2 x 12
Double the product.
8 × 3 = 12 + 12
8 × 3 = 24.

Question 18.
Abby has 5 stacks of cards with 7 cards in each stack. How many cards does she have in all?
______ cards

Answer:
35 cards

Explanation:
5 x 7 = 35.
Abby has 35 cards.

Question 18.
Noah has 3 sisters. He gave 6 balloons to each sister. How many balloons did Noah give away in all?
______ balloons

Answer:
18 balloons

Explanation:
3 x 6 = 18.
Noah gave 18 balloons to his sisters.

Common Core – Page No. 88000

Lesson 4.6

Write another way to group the factors. Then find the product.

Question 1.
(3 × 2) × 5 = ______
Explain:
__________

Answer:
3 × (2 × 5)
30

Explanation:
Using Associative Property of Multiplication, we can write (3 × 2) × 5 = 3 × (2 × 5).
Find (3 × 2) × 5. Multiply 3 x 2 = 6. Then, multiply 6 x 5 = 30.
Find 3 x (2 x 5). Multiply 2 x 5 = 10. Then, multiply 3 x 10 = 30.
So, (3 × 2) × 5 = 3 × (2 × 5). The product value is 30.

Question 2.
2 × (5 × 3) = ______
Explain:
__________

Answer:
(2 x 5) x 3
30

Explanation:
Using the Associative Property of Multiplication, we can write 2 × (5 × 3) = (2 x 5) x 3.
Find 2 × (5 × 3). Multiply 5 x 3 = 15. Then, multiply 2 x 15 = 30.
Find (2 x 5) x 3. Multiply 2 x 5 = 10. Then, multiply 10 x 3 = 30.
So, 2 × (5 × 3) = (2 x 5) x 3. The product value is 30.

Question 3.
(1 × 4) × 2 = ______
Explain:
__________

Answer:
1 x (4 x 2)

Explanation:
Using the Associative Property of Multiplication, we can write (1 × 4) × 2 = 1 x (4 x 2).
Find 1 × (4 × 2). Multiply 4 x 2 = 8. Then, multiply 1 x 8 = 8.
Find (1 x 4) x 2. Multiply 1 x 4 = 4. Then, multiply 4 x 2 = 8.
So, (1 × 4) × 2 = 1 x (4 x 2). The product value is 8.

Lesson 4.7

Is the product even or odd?
Write even or odd.

Question 4.
6 × 6
______

Answer:
Even

Explanation:
6 x 6 = 36. The numbers end with 0, 2, 4, 6, 8 are even numbers. So, 36 is even number. The 6 x 6 is an even number.

Question 5.
2 × 3
______

Answer:
even

Explanation:
Products with 2 as a factor are even.

Question 6.
3 × 9
______

Answer:
odd

Explanation:
The product of two odd numbers is an odd number. The answer is odd. So, 3 x 9 = 27.

Lessons 4.8–4.9

Find the product.

Question 7.
8 × 2 = ______

Answer:
16

Explanation:
Factor 8 is an even number. 4+ 4
2 x 4 = 8.
8 doubled is 16.
8 x 2 = 16.

Question 8.
5 × 9 = ______

Answer:
5 × 9 = 45

Explanation:
The multiplication of 5 × 9 is calculated as Skip-count by 5’s 9 times. You can write as 5, 10, 15, 20, 25, 30, 35, 40, 45. The final answer for 5 × 9 is 45.

Question 9.
______ = 3 × 9

Answer:
27 = 3 x 9

Explanation:
Skip count by 3’s until you say 9 numbers. Write like 3, 6, 9, 12, 15, 18, 21, 24, 27. The answer for 3 x 9 is 27.

Question 10.
4 × 8 = ______

Answer:
2 × 5 = 10

Explanation:
Double 2×8 to get 4×8.
2 x 8 = 16.
16 + 16 = 32.
4 x 8 = 32.

Question 11.
______ = 9 × 4

Answer:
36

Explanation:
9 = 3 + 6
9 × 4 = (3 + 6) x 4
Multiply each addend by 4.
9 × 4 = (3 x 4) + (6 x 4)
Add the products.
9 × 4 = 12 + 24
9 × 4 = 36.

Question 12.
6 × 8 = ______

Answer:
48

Explanation:
Use doubles to find the answer of 6 x 8. Firstly, multiply 3 x 8 = 24. Then, double the value of 3 x 8. 24 + 24 = 48. The answer for 6 x 8 is 48.

Lesson 4.10

Question 13.
Leo has a total of 45¢. He has some dimes and pennies. How many different combinations of dimes and pennies could Leo have? Make a table to solve.
Leo could have ______ combinations of 45¢.

Answer:
Leo could have 4 combinations of 45¢.

Explanation:
1 dime 35 pennies
2 dimes 25 pennies
3 dimes 15 pennies
4 dimes 5 pennies.

Question 13.

Number of Dimes	____1_____	_____2____	___3______	_____4____
Number of Pennies	____35_____	_____25____	___15______	______5___
Total Value	45¢	45¢	45¢	45¢

Conclusion

Above listed are the Comprehensive Solutions for Grade 3 Chapter 4 Multiplication Facts and Strategies. Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Extra Practice is a reliable source to improve on the fundamentals. Make your learning way effective taking help from this page and stand out from the crowd.