Eureka Math

Engage NY Eureka Math Kindergarten Module 1 Lesson 28 Answer Key

Eureka Math Kindergarten Module 1 Lesson 28 Problem Set Answer Key

Listen to my stories. Color the pictures to show what is happening. Write how many in the box.

Bobby picked 4 red flowers. Then, he picked 2 purple flowers. How many flowers did Bobby pick?

Answer:

Janet went to the donut store. She bought 6 chocolate donuts and 3 strawberry donuts. How many donuts did she buy?

Answer:

Some children were sitting in a circle. 4 of them were wearing green shirts. The rest were wearing yellow shirts. How many children were in the circle?

Answer:

Jerry spilled his bag of marbles. Circle the group of grey marbles. Circle the group of black marbles. How many marbles were spilled?

Answer:

Make up a story about the bears. Color the bears to match the story. Tell your story to a friend.

Answer: There were brown bears in a forest they went to drink water from a river near by.they forget the path to go to the river when the bear 4 said to bear 5 that he hears the sound of water after which the bear 3 bear 2 and bear 1 follows the bear 5 along with bear 4 and they reach the river.Thers they play and relax and have lots fun.

Make up a new story. Draw a picture to go with your story. Tell your story to a friend.
Answer: Mom bought 5 apples. She gave 3 red apples to my elder brother .And gave me 2 green apples. we exchanged one each so now i have 1 red and one green apple .

Eureka Math Kindergarten Module 1 Lesson 28 Exit Ticket Answer Key

How many Write how many in the box.

Answer:

Draw 6 circles. Draw 4 triangles.
How many shapes did you draw? Write how many in the box.
Answer:

Eureka Math Kindergarten Module 1 Lesson 28 Homework Answer Key

Make up a story about 10 things in your house. Draw a picture to go with your story. Be ready to share your story at school tomorrow.
Answer: I was playing with my toys when i stamped on a toy train and fell to the gound and got hurt mom used a plaster to cover my wound and i took rest on my bed. In the eveng i was having fever when mom called doctor by taking the number from phone book later when doctor came he checked my temperature using thermometr and checked my weight using weight machine. Mom was worred and intensely looking what doctor was doing with her spectacles on her nose. Doctor examined me and said every thing is fine and gave me one candy and a lolipop.
d

Engage NY Eureka Math Kindergarten Module 2 Lesson 9 Answer Key

Eureka Math Kindergarten Module 2 Lesson 9 Problem Set Answer Key

Circle the pictures of the flat shapes with red. Circle the pictures of the solid shapes with green.

Answer:

Explanation:
The shapes circled red are fat shapes and green are solid shapes.

Eureka Math Kindergarten Module 2 Lesson 9 Homework Answer Key

In each row, circle the one that doesn’t belong. Explain your choice to a grown-up.

Answer:

Explanation:
In the first row there is 1 circle and 2 triangles.So, i circled circle.
In the second row there is 1 hexagon and 2 cylindes.So, i circled hexagon.
In the third row there are 2 circles and 1 semicircle.So, i circled the semicircle.
In the fourth row there is 1 solid shape and 2 flat shapes.So, circled solid shape.
In the last row there is a1 flat shape and 2 solid shapes.So, i circled flat shape.

Engage NY Eureka Math Kindergarten Module 2 Lesson 8 Answer Key

Eureka Math Kindergarten Module 2 Lesson 8 Problem Set Answer Key

Directions: Read to students.
Paste the sphere above the train.
Paste the cube behind the train.
Paste the cylinder in front of the train.
Paste the cone below the train.

Provide one strip for every student.
Answer:

Explanation:
In the above picture I drew the shapes circle above the train, cylinder infront of the train, cube behind the train and cone below the train.

Eureka Math Kindergarten Module 2 Lesson 8 Homework Answer Key

Tell someone at home the names of each solid shape.

Answer:
I told the names of the shapes to my mother.The first shape is a sphere, second is a cylinder, third is cone and fourth is a cube.

Color the car beside the stop sign green.
Circle the next car with blue.
Color the car behind the circled car red.
Draw a road below the cars.
Draw a policeman in front of the cars.
Draw a sun above the cars.
Answer:

Explanation:
In the above picture I colored the car beside the stop sign green, circled the next car with blue, colored the car behind the circled car red, drew a road below the cars, drew a policeman in front of the cars and drew a sun above the cars.

Engage NY Eureka Math Kindergarten Module 2 Lesson 7 Answer Key

Eureka Math Kindergarten Module 2 Lesson 7 Problem Set Answer Key

Circle the cylinders with red.
Circle the cubes with yellow.
Circle the cones with green.
Circle the spheres with blue.

Answer:

Explanation:
In the above picture I circled the cylinders with red, circle the cubes with yellow., circled the cones with green, and circled the spheres with blue.

Eureka Math Kindergarten Module 2 Lesson 7 Homework Answer Key

Cut one set of solid shapes. Sort the 4 solid shapes. Paste onto the chart

Answer:

Explanation:
A cube and a cone has corners and a shpere and a cylinder has no corners.

Cut the other set of solid shapes, and make a rule for how you sorted them. Paste onto the chart.

Answer:

Explanation:
A place where two lines, edges, surfaces meet is called as a corner.

Engage NY Eureka Math Kindergarten Module 2 Lesson 6 Answer Key

Eureka Math Kindergarten Module 2 Lesson 6 Problem Set Answer Key

Match these objects and solids by drawing a line with your ruler from the object to the solid.

Answer:

Explanation:
In the above question i matched the matched the solid shapes with the objects that matches with the shapes.

On the back of the paper, draw solid shapes that you see in the classroom.
Answer:

Explanation:
We see a blackboard, sharpeners and chalks in our classroom.

Eureka Math Kindergarten Module 2 Lesson 6 Homework Answer Key

Find things in your house or in a magazine that look like these solids. Draw the solids or cut out and paste pictures from a magazine.

Answer:

Explanation:
In our house we have wallclock in shape of circlr, stool in shape of cube, batteries in shape of cylinder and birthday cap in shape of a cone.

Engage NY Eureka Math Kindergarten Module 2 Lesson 5 Answer Key

Eureka Math Kindergarten Module 2 Lesson 5 Problem Set Answer Key

Cut out all of the shapes, and put them next to your paper with the duck.
Listen to the directions, and glue the objects onto your paper.


Answer:

Explanation:
I have cut out all of the shapes, and put them next to your paper with the duck.
Below the duck-I drew triangle and coloured it green.
Above the duck-I drew square, coloured it blue.
Behind the duck-I drew a yellow circle and red rectangle.
In front of the duck -I drew orange colour hexagon.

Eureka Math Kindergarten Module 2 Lesson 5 Homework Answer Key

• Behind the elephant, draw a shape with 4 straight sides that are exactly the same length. Color it blue.
• Above the elephant, draw a shape with no corners. Color it yellow.
• In front of the elephant, draw a shape with 3 straight sides. Color it green.
• Below the elephant, draw a shape with 4 sides, 2 long and 2 short. Color it red.

Below the elephant, draw a shape with 6 corners. Color it orange.

Answer:

Explanation:
A shape with 4 straight sides that are exactly the same length is a square,
A shape with no corners is a square,
A shape with 3 straight sides is a triangle,
A shape with 4 sides, 2 long and 2 short is a rectangle,
A shape with 6 corners is a hexagon.

On the back of your paper, draw 1 hexagon and 4 triangles. How many shapes did you draw? Put your answer in the circle.

Answer:

Explanation:
I drew 1 hexagon and 4 triangles
1+4=5
The total number of shapes i drew are 5.

Engage NY Eureka Math Kindergarten Module 2 Lesson 4 Answer Key

Eureka Math Kindergarten Module 2 Lesson 4 Problem Set Answer Key

Find the circles, and color them green. Find the hexagons, and color them yellow. Put an X on shapes that are not hexagons or circles.

Answer:

Explanation:
In the above picture i found the circles and coloured them green and found the hexagons and coloured then yellow.

Draw hexagons and circles.
Answer:

Explanation:
In the above picture I drew 2 hexagons and 2 circles.

Eureka Math Kindergarten Module 2 Lesson 4 Homework Answer Key

Color the triangles blue.
Color the rectangles red.
Color the circles green.
Color the hexagons yellow.

Answer:

Explanation:
In the above pictures, i found and coloured the triangles blue, the rectangles red, the circles green and the hexagons yellow.

On the back of your paper, draw 2 triangles and 1 hexagon.
How many shapes did you draw? ______
Answer:

Explanation:
I drew 2 triangles and 1 hexagon
2 tiangles and 1 hexagon
2+1=3
The number of shapes i drew are 3.

Engage NY Eureka Math Kindergarten Module 2 Lesson 3 Answer Key

Eureka Math Kindergarten Module 2 Lesson 3 Problem Set Answer Key

Find the rectangles, and color them red. Put an X on shapes that are not rectangles.

Answer:

Explanation:
In the above question i found and coloured the rectangles red and i put a X mark on the shapes that are not rectangles.

Draw some rectangles.
Answer:

Explanation:
In the above picture i drew some rectangles.

Eureka Math Kindergarten Module 2 Lesson 3 Homework Answer Key

Color all the rectangles red. Color all the triangles green.

Answer:

Explanation:
In the above picture i coloured the rectangles red and the triangles green.

On the back of your paper, draw 2 rectangles and 3 triangles.
Answer:

Explanation:
In the above picture i drew 2 rectangles and 3 triangles.

How many shapes did you draw? Put your answer in the circle.

Answer:

Explanation:
2 Rectangles and 3 Triangles
2+3=5

Engage NY Eureka Math Kindergarten Module 2 Lesson 2 Answer Key

Eureka Math Kindergarten Module 2 Lesson 2 Problem Set Answer Key

Find the triangles, and color them blue. Put an X on shapes that are not triangles.

Answer:

Explanation:
In the above picture i coloured the triangle shapes and i put a cross mark against the shapes that are not triangles.

Draw some triangles.
Answer:

Explanation:
In the above picture i drew some triangles.

Eureka Math Kindergarten Module 2 Lesson 2 Homework Answer Key

Color the triangles red and the other shapes blue.

Answer:

Explanation:
In the above picture i coloured the triangles red and the other shapes blue.

Draw 2 different triangles of your own.
Answer:

Explanation:
In the above picture i drew two different types of triangles.

Engage NY Eureka Math Kindergarten Module 2 Lesson 1 Answer Key

Eureka Math Kindergarten Module 2 Lesson 1 Problem Set Answer Key

Sort the shapes.

Answer:

Explanation:
In the above image the shapes with curve are to the left side of the table and the shapes without curve are to the right side of the table.

Eureka Math Kindergarten Module 2 Lesson 1 Homework Answer Key

Draw a line from the shape to its matching object.

Answer:

Explanation:
In the above picture the shapes are matched with the objects that are in that shape.

Engage NY Eureka Math 4th Grade Module 5 Lesson 3 Answer Key

Eureka Math Grade 4 Module 5 Lesson 3 Problem Set Answer Key

Question 1.
Decompose each fraction modeled by a tape diagram as a sum of unit fractions. Write the equivalent multiplication sentence. The first one has been done for you.
a.

Answer:
3/4 = 1/4 + 1/4 + 1/4.
3/4 = 3 x 1/4.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
3/4 = 1/4 + 1/4 + 1/4.
3/4 = 1/4 + 1 /4 + 1/4.
3/4 = 3 x 1/4.

b.

Answer:
2/5 = 1/5 + 1/5.
2/5 = 2 x 1/5.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
2/5 = 1/5 + 1/5.
2/5 = 1/5 + 1 /5.
2/5 = 2 x 1/5.

c.

Answer:
5/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6.
5/6 = 5 x 1/6.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
5/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6.
5/6 = 1/6 + 2 /6 + 1/6 + 1/6.
5/6 = 5/6 x 1/6.

d.

Answer:
6/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 +1/8.
6/8 = 6/8 x 1/8.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
6/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 +1/8.
6/8 = 1/8 + 2 /8 + 2/8 + 1/8.
6/8 = 6/8 x 1/8.

e.

Answer:
1 = 1/4 + 1/4 + 1/4 + 1/4.
1/4 = 1 x 1/4.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
1 = 1/4 + 1/4 + 1/4 + 1/4.
1 = 1/4 + 2/4 + 1/4.
1/4 = 1 x 1/4.

Question 2.
Write the following fractions greater than 1 as the sum of two products.
a.

Answer:
1 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5.
1= 1 x 1/5.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
1 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5.
1 = 1/5 + 2/5 + 1/5.
1 = 1 x 1/5.

b.

Answer:
1 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6.
1/6 = 1 x 1/6.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
1 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6.
1 = 1/6 x 1.
1/6 = 1 x 1/6.

Question 3.
Draw a tape diagram, and record the given fraction’s decomposition into unit fractions as a multiplication sentence.
a. \(\frac{4}{5}\)

Answer:
4/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5.
4/5 = 4 x 1/5.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
4/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5.
4/5 = 1/5 + 2/5 + 1/5.
4/5 = 4 x 1/5.

b. \(\frac{5}{8}\)

Answer:
5/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8.
5/8 = 5 x 1/8.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
5/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8.
5/8 = 1/8 + 2/8 + 2/8.
5/8 = 5 x 1/8.

c. \(\frac{7}{9}\)

Answer:
7/9 = 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9.
7/9 = 7 x 1/9.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
7/9 = 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9.
7/9 = 1/9 + 2/9 + 2/9 + 2/9.
7/9 = 7 x 1/9.

d. \(\frac{7}{4}\)

Answer:
7/4 = 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4.
7/4 = 7 x 1/4.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
7/4 = 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4.
7/4 = 1/4 + 2/4 + 2/4 + 2/4.
7/4 = 7 x 1/4.

e. \(\frac{7}{6}\)

Answer:
7/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6.
7/6 = 7 x 1/6.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
7/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6.
7/6 = 1/6 + 2/6 + 2/6 + 2/6.
7/6 = 7 x 1/6.

Eureka Math Grade 4 Module 5 Lesson 3 Exit Ticket Answer Key

Question 1.
Decompose each fraction modeled by a tape diagram as a sum of unit fractions. Write the equivalent multiplication sentence.
a.

Answer:
2/3 = 1/3 + 1/3.
2/3 = 2 x 1/3.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
2/3 = 1/3 + 1/3.
2/3 = 2 x 1/3.

b.

Answer:
1 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5.
1 = 1 x 1/5.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
1 = 1/5 + 1/5.
1 = 1 x 1/5.

Question 2.
Draw a tape diagram, and record the given fraction’s decomposition into unit fractions as a multiplication sentence.
\(\frac{6}{9}\)

Answer:
6/9 = 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9.
6/9 = 6 x 1/9.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
6/9 = 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9.
6/9 = 1/9 + 2/9 + 2/9 + 1/9.
6/9 = 6 x 1/9.

Eureka Math Grade 4 Module 5 Lesson 3 Homework Answer Key

Question 1.
Decompose each fraction modeled by a tape diagram as a sum of unit fractions. Write the equivalent multiplication sentence. The first one has been done for you.
a.
b.

Answer:
3/4 = 1/4 + 1/4 + 1/4.
3/4 = 3 x 1/4.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
3/4 = 1/4 + 1/4 + 1/4.
3/4 = 1/4 + 2/4.
3/4 = 3 x 1/4.

c.

Answer:
4/5 = 1/5 + 1/5 + 1/5 + 1/5.
4/5 = 4 x 1/5.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
4/5 = 1/5 + 1/5 + 1/5 + 1/5.
4/5 = 1/5 + 2/5 + 1/5.
4/5 = 4 x 1/5.

d.

Answer:
5/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6.
5/6 = 5 x 1/6.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
5/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6.
5/6 = 1/6 + 2/6 + 2/6
5/6 = 5 x 1/6.

Question 2.
Write the following fractions greater than 1 as the sum of two products.
a.

Answer:
1 = 1/4 + 1/4 + 1/4 + 1/4.
1 = 1 x 1/4.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
1 = 1/4 + 2/4 + 1/4.
1 = 1 x 1/4.

b.

Answer:
1 = 1/8 + 1/8 + 1/8 + 1/8.
1 = 1 x 1/8.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
1 = 1/8 + 1/8 + 1/8 + 1/8.
1 = 1/8 + 2/8 + 1/8.
1 = 1 x 1/8.

Question 3.
Draw a tape diagram, and record the given fraction’s decomposition into unit fractions as a multiplication sentence.
a. \(\frac{3}{5}\)

Answer:
3/5 = 1/5 + 1/5 + 1/5.
3/5 = 3 x 1/5.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
3/5 = 1/5 + 1/5 + 1/5.
3/5 = 1/5 + 2/5.
3/5 = 3 x 1/5.

b. \(\frac{3}{8}\)

Answer:
3/8 = 1/8 + 1/8 + 1/8.
3/8 = 3 x 1/8.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
3/8 = 1/8 + 1/8 + 1/8.
3/8 = 1/8 + 2/8.
3/8 = 3 x 1/8.

c. \(\frac{5}{9}\)

Answer:
5/9 = 1/9 + 1/9 + 1/9 + 1/9 + 1/9.
5/9 = 5 x 1/9.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
5/9 = 1/9 + 1/9 + 1/9 + 1/9 + 1/9.
5/9 = 1/9 + 2/9 + 2/9.
5/9 = 5 x 1/9.

d. \(\frac{8}{5}\)

Answer:
8/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5.
8/5 = 8 x 1/5.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
8/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5.
8/5 = 1/5 + 2/5 + 3/5 + 2/5.
8/5 = 8 x 1/5.

e. \(\frac{12}{4}\)

Answer:
12/4 = 1/4 + 2/4+ 3/4 + 4/4 + 1/4.
12/4 = 12 x 1/4.

Explanation:
In the above-given question,
given that,
write the equivalent multiplication sentence.
12/4 = 1/4 + 2/4+ 3/4 + 4/4 + 1/4.
12/4 = 1/4 + 4/4 + 2/4 + 3/4 + 2/4.
12/4 = 12 x 1/4.

Engage NY Eureka Math 4th Grade Module 5 Lesson 4 Answer Key

Eureka Math Grade 4 Module 5 Lesson 4 Problem Set Answer Key

Question 1.
The total length of each tape diagram represents 1. Decompose the shaded unit fractions as the sum of smaller unit fractions in at least two different ways. The first one has been done for you.
a.

Answer:
1/2 = 1/4 + 1/4 .
1/2 = 1/8 + 1/8 + 1/8 + 1/8.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
1/2 = 1/4 + 1/4 .
1/2 = 1/8 + 1/8 + 1/8 + 1/8.

b.

Answer:
1/3 = 1/6 + 1/6.
1/3 = 1/12 + 1/12 + 1/12 + 1/12.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
1/3 = 1/6 + 1/6.
1/3 = 1/12 + 1/12 + 1/12 + 1/12.

c.

Answer:
1/4 = 1/8 + 1/8.
1/4 = 1/ 16+ 1/16 + 1/16 + 1/16.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
1/4 = 1/8 + 1/8.
1/4 = 1/ 16+ 1/16 + 1/16 + 1/16.

d.

Answer:
1/5 = 1/10 + 1/10.
1/5 = 1/ 15+ 1/15 + 1/15 + 1/15.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
1/5 = 1/10 + 1/10.
1/5 = 1/ 15+ 1/15 + 1/15 + 1/15.

Question 2.
The total length of each tape diagram represents 1. Decompose the shaded fractions as the sum of smaller unit fractions in at least two different ways.
a.

Answer:
2/3 = 4/6 + 4/6.
2/3 = 8/ 9+ 8/9 + 8/9 + 8/9.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
2/3 = 4/6 + 4/6.
2/3 = 8/9 + 8/9 + 8/9 + 8/9.

b.

Answer:
3/5 =6/10 + 6/10.
3/5 = 9/ 15+ 9/15 + 9/15 + 9/15.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
3/5 = 6/10 + 6/10.
3/5 = 9/ 15 + 9/15 + 9/15.

Question 3.
Draw and label tape diagrams to prove the following statements. The first one has been done for you.
a. \(\frac{2}{5}\) = \(\frac{4}{10}\)

Answer:
2/5 = 4/10 + 4/10.
2/5 = 8/ 20+ 8/20 + 8/20 + 8/20.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
2/5 = 4/10 + 4/10.
2/5 = 8/ 20+ 8/20 + 8/20 + 8/20

b. \(\frac{2}{6}\) = \(\frac{4}{12}\)

Answer:
2/6 = 4/12 + 4/12.
2/6 = 4/18 + 4/18 + 4/18 + 4/18.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
2/6 = 4/12 + 4/12.
2/6 = 4/18 + 4/18 + 4/18 + 4/18.

c. \(\frac{3}{4}\) = \(\frac{6}{8}\)

Answer:
3/4 = 6/8 + 6/8.
3/4 = 9/12 + 9/12 + 9/12 + 9/12.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
3/4 = 6/8 + 6/8.
3/4 = 9/12 + 9/12 + 9/12 + 9/12.

d. \(\frac{3}{4}\) = \(\frac{9}{12}\)

Answer:
3/4 = 6/8 + 6/8.
3/4 = 9/12 + 9/12 + 9/12 + 9/12.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
3/4 = 6/8 + 6/8.
3/4 = 9/12 + 9/12 + 9/12 + 9/12.

Question 4.
Show that \(\frac{1}{2}\) is equivalent to \(\frac{4}{8}\) using a tape diagram and a number sentence.

Answer:
1/2 = 1/4 + 1/4.
1/2 = 1/8 + 1/8 + 1/8 + 1/8 = 4/8.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
1/2 = 1/4 + 1/4.
1/2 = 1/8 + 1/8 + 1/8 + 1/8 = 4/8.

Question 5.
Show that \(\frac{2}{3}\) is equivalent to \(\frac{6}{9}\) using a tape diagram and a number sentence.

Answer:
2/3 = 4/6 + 4/6.
2/3 = 6/9 + 6/9 + 6/9 + 6/9 = 6/9.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
2/3 = 4/6 + 4/6.
2/3 = 6/9 + 6/9 + 6/9 + 6/9 = 6/9.

Question 6.
Show that \(\frac{4}{6}\) is equivalent to \(\frac{8}{12}\) using a tape diagram and a number sentence.

Answer:
4/6 = 8/12 + 8/12.
4/6 = 12/18 + 12/18.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
4/6 = 8/12 + 8/12.
4/6 = 12/18 + 12/18.

Engage NY Math 4th Grade Module 5 Lesson 4 Exit Ticket Answer Key

Question 1.
The total length of the tape diagram represents 1. Decompose the shaded unit fraction as the sum of smaller unit fractions in at least two different ways.

Answer:
1/6 = 1/12 + 1/12 .
1/6 = 1/18 + 1/18 + 1/18 + 1/18.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
1/6 = 1/12 + 1/12 .
1/6 = 1/18 + 1/18 + 1/18 + 1/18.

Question 2.
Draw a tape diagram to prove the following statement.
\(\frac{2}{3}\) = \(\frac{4}{6}\)

Answer:
2/3 = 4/6 + 4/6.
2/3 = 8/12 + 8/12 + 8/12 + 8/12.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
2/3 = 4/6 + 4/6.
2/3 = 8/12 + 8/12 + 8/12 + 8/12.

Eureka Math 4th Grade Module 5 Lesson 4 Homework Answer Key

Question 1.
The total length of each tape diagram represents 1. Decompose the shaded unit fractions as the sum of smaller unit fractions in at least two different ways. The first one has been done for you.
a.

Answer:
1/2 = 1/6 + 1/6 + 1/6.
1/2 = 1/10 + 1/10 + 1/10 + 1/10 + 1/10.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
1/2 = 1/6 + 1/6 + 1/6.
1/2 = 1/10 + 1/10 + 1/10 + 1/10 + 1/10.
b.

Answer:
1/4 = 1/8 + 1/8.
1/4 = 1/12 + 1/12 + 1/12 + 1/12.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
1/4 = 1/8 + 1/8.
1/4 = 1/12 + 1/12 + 1/12 + 1/12.

Question 2.
The total length of each tape diagram represents 1. Decompose the shaded fractions as the sum of smaller unit fractions in at least two different ways.
a.

Answer:
3/4 = 6/8 + 6/8.
3/4 = 9/12 + 9/12 + 9/12 + 9/12.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
3/4 = 6/8 + 6/8.
3/4 = 9/12 + 9/12 + 9/12 + 9/12

b.

Answer:
4/5 = 8/10 + 8/10.
4/5 = 12/15 + 12/15 + 12/15 + 12/15.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
4/5 = 8/10 + 8/10.
4/5 = 12/15 + 12/15 + 12/15 + 12/15.

c.

Answer:
4/6 = 8/12 + 8/12.
4/6 = 12/18 + 12/18 + 12/18 + 12/18.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
4/6 = 8/12 + 8/12.
4/6 = 12/18 + 12/18 + 12/18 + 12/18.

Question 3.
Draw tape diagrams to prove the following statements. The first one has been done for you.
a. \(\frac{2}{5}\) = \(\frac{4}{10}\)

Answer:
2/5 = 4/10 + 4/10.
2/5 = 4/10 + 4/10 + 4/10 + 4/10.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
2/5 = 4/10 + 4/10.
2/5 = 4/10 + 4/10 + 4/10 + 4/10.

b. \(\frac{3}{6}\) = \(\frac{6}{12}\)

Answer:
3/6 = 6/12 + 6/12.
3/6 = 12/24 + 12/24 + 12/24 + 12/24.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
3/6 = 6/12 + 6/12.
3/6 = 12/24 + 12/24 + 12/24 + 12/24.

c. \(\frac{2}{6}\) = \(\frac{6}{18}\)

Answer:
2/6 = 4/12 + 4/12.
2/6 = 6/18 + 6/18 + 6/18 + 6/18.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
2/6 = 4/12 + 4/12.
2/6 = 6/18 + 6/18 + 6/18 + 6/18.

d. \(\frac{3}{4}\) = \(\frac{12}{16}\)

Answer:
3/4 = 6/8 + 6/8.
3/4 = 12/16 + 12/16 + 12/16 + 12/16.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
3/4 = 6/8 + 6/8.
3/4 = 12/16 + 12/16 + 12/16 + 12/16.

Question 4.
Show that \(\frac{1}{2}\) is equivalent to \(\frac{6}{12}\) using a tape diagram and a number sentence.

Answer:
1/2 = 1/4 + 1/4.
1/2 = 1/8 + 1/8 + 1/8 + 1/8.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
1/2 = 1/4 + 1/4.
1/2 = 1/8 + 1/8 + 1/8 + 1/8

Question 5.
Show that \(\frac{2}{3}\) is equivalent to \(\frac{8}{12}\) using a tape diagram and a number sentence.

Answer:
2/3 = 4/6 + 4/6.
2/3 = 8/12 + 8/12 + 8/12 + 8/12.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
2/3 = 4/6 + 4/6.
2/3 = 8/12 + 8/12 + 8/12 + 8/12.

Question 6.
Show that \(\frac{4}{5}\) is equivalent to \(\frac{12}{15}\) using a tape diagram and a number sentence.

Answer:
4/5 = 8/10 + 8/10.
4/5 = 12/15 + 12/15 + 12/15 + 12/15.

Explanation:
In the above-given question,
given that,
shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
4/5 = 8/10 + 8/10.
4/5 = 12/15 + 12/15 + 12/15 + 12/15.

Engage NY Eureka Math 4th Grade Module 5 Lesson 1 Answer Key

Eureka Math Grade 4 Module 5 Lesson 1 Problem Set Answer Key

Question 1.
Draw a number bond, and write the number sentence to match each tape diagram. The first one is done for you.
a.

Answer:
1 = 1/3 + 1/3 + 1/3.

Explanation:
In the above-given question,
given that,
total there are 3 boxes.
the 3 boxes are filled.
1 = 1/3 + 1/3 + 1/3.
b.

Answer:
4/5 = 1/5 + 2/5 + 1/5.

Explanation:
In the above-given question,
given that,
total there are 5 boxes.
the 4 boxes are filled.
4/5 = 1/5 + 2/5 + 1/5.

c.

Answer:
3/4 = 1/4 + 1/4 + 1/4.

Explanation:
In the above-given question,
given that,
total there are 4 boxes.
the 3 boxes are filled.
3/4 = 1/4 + 1/4 + 1/4.

d.

Answer:
4/6 = 2/6 + 2/6.

Explanation:
In the above-given question,
given that,
total there are 6 boxes.
the 4 boxes are filled.
4/6 = 2/6 + 2/6 .

e.

Answer:
6/8 = 2/8 + 2/8 + 2/8.

Explanation:
In the above-given question,
given that,
total there are 8 boxes.
the 6 boxes are filled.
6/8 = 2/8 + 2/8 + 2/8.

f.

Answer:
1 = 1/5 + 1/5 + 1/5.

Explanation:
In the above-given question,
given that,
total there are 5 boxes.
the 5 boxes are filled.
1 = 1/5 + 1/5 + 1/5 + 1/5.

g.

Answer:
1 = 1/5 + 2/5 + 3/5 + 1/5.

Explanation:
In the above-given question,
given that,
total there are 5 boxes.
the 5 boxes are filled.
1 = 1/5 + 2/5 + 3/5 +1/5.

h.

Answer:
1 = 1/11 + 2/11 + 2/11 + 4/11 +1/11 + 8/11.

Explanation:
In the above-given question,
given that,
total there are 11 boxes.
the 11 boxes are filled.
1 = 1/11 + 2/11 + 2/11 + 4/11 + 1/11 + 8/1.

Question 2.
Draw and label tape diagrams to model each decomposition.
a. 1 = \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\)

Answer:
1 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6.

Explanation:
In the above-given question,
given that,
total there are 6 boxes.
the 6 boxes are filled.
1 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6.

b. \(\frac{4}{5}\) = \(\frac{1}{5}+\frac{2}{5}+\frac{1}{5}\)

Answer:
4/5 = 1/5 + 2/5 + 1/5.

Explanation:
In the above-given question,
given that,
total there are 5 boxes.
the 4 boxes are filled.
4/5 = 1/5 + 2/5 + 1/5.

c. \(\frac{7}{8}\) = \(\frac{3}{8}+\frac{3}{8}+\frac{1}{8}\)

Answer:
7/8 = 3/8 + 3/8 + 1/8.

Explanation:
In the above-given question,
given that,
total there are 8 boxes.
the 7 boxes are filled.
7/8 = 3/8 + 3/8 + 1/8.

d. \(\frac{11}{8}\) = \(\frac{7}{8}+\frac{1}{8}+\frac{3}{8}\)

Answer:
11/8 = 7/8 + 1/8 + 3/8.

Explanation:
In the above-given question,
given that,
total there are 11 boxes.
the 8 boxes are filled.
11/8 = 7/8 + 1/8 + 3/8.

e. \(\frac{12}{10}\) = \(\frac{6}{10}+\frac{4}{10}+\frac{2}{10}\)

Answer:
12/10 = 6/10 + 4/10 + 2/10.

Explanation:
In the above-given question,
given that,
total there are 12 boxes.
the 10 boxes are filled.
12/10 = 6/10 + 4/10 + 2/10.

f. \(\frac{15}{12}\) = \(\frac{8}{12}+\frac{3}{12}+\frac{4}{12}\)

Answer:
15/12 = 8/12 + 3/12 + 4/12.

Explanation:
In the above-given question,
given that,
total there are 15 boxes.
the 12 boxes are filled.
15/12 = 8/12 + 3/12 + 4/12.

g. 1\(\frac{2}{3}\) = 1 + \(\frac{2}{3}\)

Answer:
2/3 = 1 + 2/3.

Explanation:
In the above-given question,
given that,
total there are 3 boxes.
the 2 boxes are filled.
2/3 = 1 + 2/3.

h. 1\(\frac{5}{8}\) = 1 + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{3}{8}\)

Answer:
5/8 = 1 + 1/8 + 1/8 + 3/8.

Explanation:
In the above-given question,
given that,
total there are 8 boxes.
the 5 boxes are filled.
5/8 =1 + 1/8 + 1/8 + 3/8.

Eureka Math Grade 4 Module 5 Lesson 1 Exit Ticket Answer Key

Question 1.
Complete the number bond, and write the number sentence to match the tape diagram.

Answer:
1 = 1/4 + 1/4 + 1/4 + 1/4.

Explanation:
In the above-given question,
given that,
total there are 4 boxes.
the 4 boxes are filled.
1 = 1/4 + 1/4 + 1/4 + 1/4.

Question 2.
Draw and label tape diagrams to model each number sentence.
a. 1 = \(\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}\)

Answer:
1 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5.

Explanation:
In the above-given question,
given that,
total there are 5 boxes.
the 5 boxes are filled.
1 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5.

b. \(\frac{5}{6}\) = \(\frac{2}{6}+\frac{2}{6}+\frac{1}{6}\)

Answer:
5/6 = 2/6 + 2/6 + 1/6.

Explanation:
In the above-given question,
given that,
total there are 6 boxes.
the 5 boxes are filled.
5/6 = 2/6 + 2/6 + 1/6.

Eureka Math Grade 4 Module 5 Lesson 1 Homework Answer Key

Draw a number bond, and write the number sentence to match each tape diagram. The first one is done for you.

a.
b.

Answer:
2/4 = 1/4 + 1/4 .

Explanation:
In the above-given question,
given that,
total there are 4 boxes.
the 2 boxes are filled.
2/4 = 1/4 + 1/4 .

c.

Answer:
3/5 = 1/5 + 2/5.

Explanation:
In the above-given question,
given that,
total there are 5 boxes.
the 3 boxes are filled.
3/5 = 1/5 + 2/5.

d.

Answer:
6/7 = 3/7 + 2/7 + 1/7.

Explanation:
In the above-given question,
given that,
total there are 7 boxes.
the 6 boxes are filled.
6/7 = 3/7 + 2/7 + 1/7.

e.

Answer:
3/8 = 2/8 + 1/8 .

Explanation:
In the above-given question,
given that,
total there are 8 boxes.
the 3 boxes are filled.
3/8 = 2/8 + 1/8.

f.

Answer:
1 = 1/6 + 1/7.

Explanation:
In the above-given question,
given that,
total there are 7 boxes.
the 6 boxes are filled.
1 = 1/6 + 1/7.

g.

Answer:
1 = 3/6 + 2/6 + 1/6.

Explanation:
In the above-given question,
given that,
total there are 6 boxes.
the 6 boxes are filled.
1 = 3/6 + 2/6 + 1/6.

h.

Answer:
1 = 3/12 + 2/12 + 1/12 + 3/12 + 3/12.

Explanation:
In the above-given question,
given that,
total there are 12 boxes.
the 12 boxes are filled.
1 = 3/12 + 2/12 + 1/12 + 3/12 + 3/12.

Question 2.
Draw and label tape diagrams to match each number sentence.
a. \(\frac{5}{8}\) = \(\frac{2}{8}+\frac{2}{8}+\frac{1}{8}\)

Answer:
5/8 = 2/8 + 2/8 + 1/8.

Explanation:
In the above-given question,
given that,
total there are 8 boxes.
the 5 boxes are filled.
5/8 = 2/8 + 2/8 + 1/8.

b. \(\frac{12}{8}\) = \(\frac{6}{8}+\frac{2}{8}+\frac{4}{8}\)

Answer:
12/8 = 6/8 + 2/8 + 4/8.

Explanation:
In the above-given question,
given that,
total there are 12 boxes.
the 8 boxes are filled.
12/8 = 6/8 + 2/8 + 4/8.

c. \(\frac{11}{10}\) = \(\frac{5}{10}+\frac{5}{10}+\frac{1}{10}\)

Answer:
11/10 = 5/10 + 5/10 + 1/10.

Explanation:
In the above-given question,
given that,
total there are 11 boxes.
the 10 boxes are filled.
11/10 = 5/10 + 5/10 + 1/10.

d. \(\frac{13}{12}\) = \(\frac{7}{12}+\frac{1}{12}+\frac{5}{12}\)

Answer:
13/12 = 7/12 + 1/12 + 5/12.

Explanation:
In the above-given question,
given that,
total there are 13 boxes.
the 12 boxes are filled.
13/12 = 7/12 + 1/12 + 5/12.

e. 1\(\frac{1}{4}\) = 1 + \(\frac{1}{4}\)

Answer:
5/4 = 1 + 1/4.

Explanation:
In the above-given question,
given that,
total there are 5 boxes.
the 4 boxes are filled.
5/4 = 1 + 1/4.

f. 1\(\frac{2}{7}\) = 1 + \(\frac{2}{7}\)

Answer:
9/7 = 1 + 2/7.

Explanation:
In the above-given question,
given that,
total there are 9 boxes.
the 7 boxes are filled.
9/7 = 1 + 2/7.

Engage NY Eureka Math 5th Grade Module 2 End of Module Assessment Answer Key

Eureka Math Grade 5 Module 2 End of Module Assessment Task Answer Key

Question 1.
Express the missing divisor using a power of 10. Explain your reasoning using a place value model.
a. 5.2 ÷ __100___ = 0.052

Answer:
5.2/100 = 0.052.

Explanation:
In the above-given question,
given that,
Express the missing divisor using a power of 10.
10 x 10 = 100.
5.2/100.
52/10/100.
0.052.

b. 7,650 ÷ ____1000_______ = 7.65

Answer:
7650/1000 = 7.65.

Explanation:
In the above-given question,
given that,
Express the missing divisor using a power of 10.
100 x 10 = 1000.
7650/1000.
7.65.

Question 2.
Estimate the quotient by rounding the expression to relate to a one-digit fact. Explain your thinking in the space below.
a. 432 ÷ 73 ≈ ___60________

Answer:
432/73 = 60.

Explanation:
In the above-given question,
given that,
432 / 73 = 5.917.
432/73.
5.917 = 60.

b. 1,275 ÷ 588 ≈ __2_________

Answer:
1275/588 = 2.

Explanation:
In the above-given question,
given that,
1275/588.
1275/588.
2.1683.
2.1683 = 2.

Question 3.
Generate and solve another division problem with the same quotient and remainder as the two problems below. Explain your strategy for creating the new problem.

Answer:
30/6 = 12.
27/5 = 12.

Explanation:
In the above-given question,
given that,
30/6 = 12.
6 x 3 = 18.
30-18 = 12.
27/5 = 12.
5 x 3 = 15.
27-15 = 12.

Question 4.
Sarah says that 26 ÷ 8 equals 14 ÷ 4 because both are “3 R2.” Show her mistake using decimal division.

Answer:
30/6 = 12.
27/5 = 12.

Explanation:
In the above-given question,
given that,
30/6 = 12.
6 x 3 = 18.
30-18 = 12.
27/5 = 12.
5 x 3 = 15.
27-15 = 12.

Question 5.
A rectangular playground has an area of 3,392 square meters. If the width of the rectangle is 32 meters, find the length.

Answer:
The length of the rectangular playground = 106 m.

Explanation:
In the above-given question,
given that,
A rectangular playground has an area of 3392 square meters.
width of the rectangle = 32 m.
3392 = l x 32.
l = 3392/32.
l = 106.

Question 6.
A baker uses 5.5 pounds of flour daily.
a. How many ounces of flour will he use in two weeks? Use words, numbers, or pictures to explain your thinking. (1 lb = 16 oz)

Answer:
The ounces of flour will he use in two weeks = 77 ounces.

Explanation:
In the above-given question,
given that,
A baker uses 5.5 pounds of flour daily.
5.5 x 14.
77 ounces.
The number of ounces of flour will he use in two weeks = 77 ounces.

b. The baker’s recipe for a loaf of bread calls for 12 ounces of flour. If he uses all of his flour to make loaves of bread, how many full loaves can he bake in two weeks?

Answer:
The full loaves can he bake in two weeks = 168.

Explanation:
In the above-given question,
given that,
the baker’s recipe for a loaf of bread calls for 12 ounces of flour.
14 x 12.
168.

c. The baker sends all his bread to one store. If he can pack up to 15 loaves of bread in a box for shipping, what is the minimum number of boxes required to ship all the loaves baked in two weeks? Explain your reasoning.

Answer:
The minimum number of boxes required to ship all the loaves = 210.

Explanation:
In the above-given question,
given that,
the baker sends all his bread to one store.
15 x 14.
210.
so the minimum number of boxes required to ship all the loaves = 210.

d. The baker pays $0.80 per pound for sugar and $1.25 per pound for butter. Write an expression that shows how much the baker will spend if he buys 6 pounds of butter and 20 pounds of sugar.

Answer:
The baker will spend if he buys 6 pounds of butter and 20 pounds of sugar =

Explanation:
In the above-given question,
given that,
The baker pays $0.80 per pound for sugar and $1.25 per pound of butter.
6 x 0.80 = $4.8.
20 x 1.25 = $25.

e. Chocolate sprinkles cost as much per pound as sugar. Find \(\frac{1}{10}\) the baker’s total cost for 100 pounds of chocolate sprinkles. Explain the number of zeros and the placement of the decimal in your answer using a place value chart.

Answer:
1/10 = 0.1.

Explanation:
In the above-given question,
given that,
Chocolate sprinkles cost as much per pound as sugar.
1/10.
0.1.

Engage NY Eureka Math 5th Grade Module 2 Mid Module Assessment Answer Key

Eureka Math Grade 5 Module 2 Mid Module Assessment Task Answer Key

Question 1.
Fill in the chart.

Answer:
a. 5000.

Explanation:
In the above-given question,
given that,
50 times the sum of 64 and 36.
50 x (64 + 36).
50 x (100).
5000.

Answer:
b. 100.

Explanation:
In the above-given question,
given that,
Divide the difference between 1,200 and 700 by 5
1200 – 700/5.
500/5.
100.

Answer:
c. 300.

Explanation:
In the above-given question,
given that,
The sum of 3 fifteens and 17 fifteens
(3 x 15) + (17 x 15).
45 + 255
300.

Answer:
d. 300.

Explanation:
In the above-given question,
given that,
15 times the sum of 14 and 6
15 x (14 + 6).
15 x (20).
300.

Answer:
e. 2950.

Explanation:
In the above-given question,
given that,
10 times the sum of 250 and 45
10 x (250 + 45).
10 x (295).
2950.

Answer:
f.14000.

Explanation:
In the above-given question,
given that,
14 times the sum of 440 and 560
14 x (440 + 560).
14 x (1000).
14000.

Question 2.
Compare the two expressions using < , > , or = . For each, explain how you can determine the answer without calculating.
a. 100 × 8 25 × (4 × 9)

Answer:
100 x 8  > 25 x (4 x 9)

Explanation:
In the above-given question,
given that,
100 x 8 = 800.
25 x (4 x 9).
25 x (36).
25 x 36 = 72.
so 100 > 72.

b. 48 × 12 50 twelves – 3 twelves

Answer:
48 x 12 > 50 twelves – 3 twelves.

Explanation:
In the above-given question,
given that,
48 x 12 = 576.
50 x 12 = 600.
3 x 12 = 36.
600 – 36.
564.
576 > 564.

c. 24 × 36 18 twenty-fours, doubled

Answer:
24 x 36  <  18 twenty-fours, doubled.

Explanation:
In the above-given question,
given that,
24 x 36 = 864.
18 x 24 = 432.
432 x 432 = 186624.
864 < 186624.

Question 3.
Solve. Use words, numbers, or pictures to explain how your answers to Parts (a) and (b) are related.
a. 25 × 30 = ____750_______

Answer:
25 x 30 = 750.

Explanation:
In the above-given question,
given that,
25 x 30.
750.

b. 2.5 × 30 = _____2.5______ tenths × 30 = _____75______

Answer:
2.5 x 30 = 75.

Explanation:
In the above-given question,
given that,
2.5 x 30.
25/10 = 2.5.
2.5/30 = 75.

Question 4.
Multiply using the standard algorithm. Show your work below each problem. Write the product in the blank.
a. 514 × 33 = ____16962_______

Answer:
514 x 33 = 16962.

Explanation:
In the above-given question,
given that,
514 x 33
16962.

b. 546 × 405 = __2,21,130_________

Answer:
546 x 405 = 2,21,130.

Explanation:
In the above-given question,
given that,
546 x 405.
2,21,130.

Question 5.
For a field trip, the school bought 47 sandwiches for $4.60 each and 39 bags of chips for $1.25 each. How much did the school spend in all?

Answer:
The school spending in all = $264.95.

Explanation:
In the above-given question,
given that,
For a field trip, the school bought 47 sandwiches for $4.60 each and 39 bags of chips for $1.25 each.
47 x $4.60 = 216.2.
39 x $1.25 = 48.75.
216.2 + 48.75 = 264.95.

Question 6.
Jeanne makes hair bows to sell at the craft fair. Each bow requires 1.5 yards of ribbon.
a. At the fabric store, ribbon is sold by the foot. If Jeanne wants to make 84 bows, how many feet of ribbon must she buy? Show all your work.

Answer:
The number of feet of ribbon must she buy = 126 feet.

Explanation:
In the above-given question,
given that,
Jeanne makes hair bows to sell at the craft fair.
Each bow requires 1.5 yards of ribbon.
84 x 1.5.
126.

b. If the ribbon costs 10¢ per foot, what is the total cost of the ribbon in dollars? Explain your reasoning, including how you decided where to place the decimal.

Answer:
The total cost of ribbon in dollars = 0.1.

Explanation:
In the above-given question,
given that,
If the ribbon costs 10 cents per foot.
1 cents = 0.01 dollar.
10 x 0.01 = 0.1$
the total cost of the ribbon = 0.1.

c. A manufacturer is making 1,000 times as many bows as Jeanne to sell in stores nationwide. Write an expression using exponents to show how many yards of ribbon the manufacturer will need. Do not calculate the total.

Answer:
The number of yards of ribbon the manufacturer will need = 1500 yards.

Explanation:
In the above-given question,
given that,
A manufacturer is making 1000 times as many bows.
1000 x 1.5.
1500 yards.