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Engage NY Eureka Math Grade 6 Module 6 Lesson 9 Answer Key

Eureka Math Grade 6 Module 6 Lesson 9 Example Answer Key

Example 1: Variability

In Lesson 8, Robert wanted to decide where he would rather move (New York City or San Francisco). He planned to make his decision by comparing the average monthly temperatures for the two cities. Since the mean of the average monthly temperatures for New York City and the mean for San Francisco turned out to be about the same, he decided instead to compare the cities based on the variability in their monthly average temperatures.

He looked at the two distributions and decided that the New York City temperatures were more spread out from their mean than were the San Francisco temperatures from their mean.

Exercises 1 – 3:

The following temperature distributions for seven other cities all have a mean monthly temperature of approximately 63 degrees Fahrenheit. They do not have the same variability.

Exercise 1.
Which distribution has the smallest variability? Explain your answer.
Answer:
City A has the smallest variability because all the data points are the same.

Exercise 2.
Which distribution or distributions seem to have the most variability? Explain your answer.
Answer:
One or more of the following is acceptable: Cities D, E, and F. They appear to have data points that are the most
spread out.

Exercise 3.
Order the seven distributions from least variability to most variability. Explain why you listed the distributions in
the order that you chose.
Answer:
Several orderings are reasonable. Focus on student’s explanations for choosing the order, making sure that the ordering is consistent with an understanding of spread. There are some that will be hard for students to order, and if students have trouble, use this opportunity to point out that it would be useful to have a more formal way to measure variability in a data set. Such a measure is developed in Example 2.

Example 2: Measuring Variability

Based on just looking at the distributions, there are different orderings of variability that seem to make some sense. Sabina is interested in developing a formula that will produce a number that measures the variability in a data distribution. She would then use the formula to measure the variability in each data set and use these values to order the distributions from smallest variability to largest variability. She proposes beginning by looking at how far the values in a data set are from the mean of the data set.

Exercises 4 – 5:

The dot plot for the monthly temperatures in City G is shown below. Use the dot plot and the mean monthly temperature of 63 degrees Fahrenheit to answer the following questions.

City G

Exercise 4.
Fill in the following table for City G’s temperature deviations.

Answer:

Exercise 5.
What is the sum of the distances to the left of the mean? What is the sum of the distances to the right of the mean?
Answer:
The sum of the distances to the left of the mean is 10 + 6 + 3 + 3 = 22. The sum of the distances to the right of the mean is 1 + 1 + 1 + 1 + 1 + 5 + 5 + 7 = 22.

Example 3: Finding the Mean Absolute Deviation (MAD)

Sabina notices that when there is not much variability in a data set, the distances from the mean are small and that when there is a lot of variability in a data set, the data values are spread out and at least some of the distances from the mean are large. She wonders how she can use the distances from the mean to help her develop a formula to measure variability.

Exercises 6 – 7:

Exercise 6.
Use the data on monthly temperatures for City G given in Exercise 4 to answer the following questions.

a. Fill in the following table.

Answer:

b. The absolute deviation for a data value is its distance from the mean of the data set. For example, for the first temperature value for City G (53 degrees), the absolute deviation is 10. What !s the sum of the absolute deviations?
Answer:
The sum of the absolute deviations is 10 + 6 + 3 + 3 + 1 + 1 + 1 + 1 + 1 + 5 + 5 + 7 = 44.

c. Sabina suggests that the mean of the absolute deviations (the mean of the distances) could be a measure of the variability in a data set. Its value is the average distance of the data values from the mean of the monthly temperatures. It is called the mean absolute deviation and is denoted by the letters MAD. Find the MAD for this data set of City G’s temperatures. Round to the nearest tenth.
Answer:
The MAD (mean absolute deviation) is \(\frac{44}{12^{\prime}}\) or 3.7 degrees to the nearest tenth of a degree.

d. Find the MAD values in degrees Fahrenheit for each of the seven city temperature distributions and use the values to order the distributions from least variability to most variability. Recall that the mean for each data set is 63 degrees Fahrenheit. Looking only at the distributions, does the list that you made in Exercise 2 match the list made by ordering MAD values?

Answer:
If time is a factor in completing this lesson, assign cities to individual students. After each student has calculated the mean deviation, organize the results for the whole class. Direct students to calculate the MAD to the nearest tenth of a degree.

MAD values (in °F):
City A = 0
City B = 5.3
City C = 3.2
City D = 10.5
City E = 10.5
City F = 10.5
City G = 3.7
The order from least to greatest is A, C, G, B, and D, E, and F(all tied).

e. Which of the following is a correct interpretation of the MAD?
i. The monthly temperatures in City G are all within 3. 7 degrees from the approximate mean of 63 degrees.
ii. The monthly temperatures in City G are, on average, 3. 7 degrees from the approximate mean temperature of 63 degrees.
iii. All of the monthly temperatures in City G differ from the approximate mean temperature of 63 degrees by 3. 7 degrees.
Answer:
The answer is (ii). Remind students that the MAD is an average of the distances from the mean, so some distances may be smaller and some larger than the value of the MAD. Point out that the distances from the mean for City G were not all equal to 3.7 and that some were smaller (for example, the distances of 1 and 3) and that some were larger (for example, the distances of 5 and 10).

Exercise 7.
The dot plot for City A’s temperatures follows.
City A

a. How much variability is there in City A’s temperatures? Why?
Answer:
There is no variability in City A’s temperatures. The absolute deviations (distances from the mean) are all 0.

b. Does the MAD agree with your answer In part (a)?
Answer:
The MAD does agree with my answer from part (a). The value of the MAD is 0.

Eureka Math Grade 6 Module 6 Lesson 9 Problem Set Answer Key

Question 1.
Suppose the dot plot on the left shows the number of goals a boys’ soccer team has scored in six games so far this
season, and the dot plot on the right shows the number of goals a girls’ soccer team has scored in six games so far
this season. The mean for both of these teams is 3.

a. Before doing any calculations, which dot plot has the larger MAD? Explain how you know.
Answer:
The graph of the boys’ team has a larger MAD because the data are more spread out and have the larger distances from the mean.

b. Use the following tables to find the MAD for each distribution. Round your calculations to the nearest hundredth.

Answer:

The MAD for the boy’s team is 2 goals because \(\frac{12}{6}\) = 2. The MAD for the girls’ team is 0.67 goal because \(\frac{4}{6}\) ≈ 0.67

c. Based on the computed MAD values, for which distribution is the mean a better indication of a typical value? Explain your answer.
Answer:
The mean is a better indicator of a typical value for the girl’s team because the measure of variability given by the MAD is lower (0.67 goal) than the boys’ MAD (2 goals).

Question 2.
Recall Robert’s problem of deciding whether to move to New York City or to San Francisco. A table of temperatures (in degrees Fahrenheit) and absolute deviations for New York City follows:

a. The absolute deviations for the monthly temperatures are shown in the above table. Use this information to calculate the MAD. Explain what the MAD means in words.
Answer:
The sum of the absolute deviations is 168. The MAD is the average of the absolute deviations. The MAD is 14 degrees because \(\frac{168}{12}\) = 14. On average, the monthly temperatures in New York City differ from the mean of 63 degrees Fahrenheit by 14 degrees.

b. Complete the following table, and then use the values to calculate the MAD for the San Francisco data distribution.

Answer:
The sum of the absolute deviations is 42. The MAD is the mean of the absolute deviations. The MAD is 3.5 degrees because \(\frac{42}{12}\) = 3. 5.

c. Comparing the MAD values for New York City and San Francisco, which city would Robert choose to move to if he is interested in having a lot of variability in monthly temperatures? Explain using the MAD.
Answer:
New York City has a MAD of 14 degrees, as compared to 3.5 degrees in San Francisco. Robert should choose
New York City if he wants to have more variability in monthly temperatures.

Question 3.
Consider the following data of the number of green jelly beans in seven bags sampled from each of five different candy manufacturers (Awesome, Delight, Finest, Sweeties, YumYum). Note that the mean of each distribution is 42 green jelly beans.

a. Complete the following table of the absolute deviations for the seven bags for each candy manufacturer.

Answer:

b. Based on what you learned about MAD, which manufacturer do you think will have the lowest MAD? Calculate the MAD for the manufacturer you selected.

Answer:
Use the MAD for each manufacturer to evaluate student’s responses.

Eureka Math Grade 6 Module 6 Lesson 9 Exit Ticket Answer Key

Question 1.
The mean absolute deviation (MAD) is a measure of variability for a data set. What does a data distribution look like if its MAD equals zero? Explain.
Answer:
If the MAD is zero, then all of the absolute deviations are zero. The MAD measures the average distance from the mean, and the distance is never negative. The only way the MAD could average to zero is if all the absolute deviations are zero. For example, City A had a dot plot where all of the temperatures were the same. Because all of the temperatures were the same, all of the absolute deviations were zero, which indicates that there was no variability in the temperatures.

Question 2.
Is it possible to have a negative value for the MAD of a data set?
Answer:
Because a MAD is the average of distances, which can never be negative, the MAD is always zero or a positive number.

Question 3.
Suppose that seven students have the following numbers of pets: 1, 1, 1, 2, 4, 4, 8.

a. The mean number of pets for these seven students is 3 pets. Use the following table to find the MAD for this distribution of number of pets.

Answer:
\(\frac{14}{7}\)
The MAD number of pets is 2.

b. Explain in words what the MAD means for this data set.
Answer:
On average, the number of pets for these students differs by 2 from the mean of 3 pets.

Engage NY Eureka Math 4th Grade Module 1 Lesson 15 Answer Key

Eureka Math Grade 4 Module 1 Lesson 15 Problem Set Answer Key

Question 1.
Use the standard subtraction algorithm to solve the problems below.
a.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 101,660 is the minuend, the number 91,680 is the subtrahend and the number 9,980 is the difference.
b.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 101,660 is the minuend, the number 9,980 is the subtrahend and the number 91,680 is the difference.
c.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 242,561 is the minuend, the number 44,702 is the subtrahend and the number 197,859 is the difference.
d.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 242,561 is the minuend, the number 74,987 is the subtrahend and the number 167,574 is the difference.

e.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 1,000,000 is the minuend, the number 592,000 is the subtrahend and the number 408,000 is the difference.

f.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 1,000,000 is the minuend, the number 592,500 is the subtrahend and the number 407,500 is the difference.

g.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 600,658 is the minuend, the number 592,569 is the subtrahend and the number 8,089 is the difference.

h.

Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 600,000 is the minuend, the number 592,569 is the subtrahend and the number 7,431 is the difference.

Use tape diagrams and the standard algorithm to solve the problems below. Check your answers.

Question 2.
David is flying from Hong Kong to Buenos Aires. The total flight distance is 11,472 miles. If the plane has 7,793 miles left to travel, how far has it already traveled?
Answer:
Total flight distance = 11,472 miles
Number of more miles Flight has to travel is = 7,793.
Number of miles the flight has traveled = ?

Question 3.
Tank A holds 678,500 gallons of water. Tank B holds 905,867 gallons of water. How much less water does Tank A hold than Tank B?
Answer:
Answer:
Total gallons of water Tank A holds = 678,500 gallons
Total gallons of water Tank B holds = 905,867 gallons

Question 4.
Mark had $25,081 in his bank account on Thursday. On Friday, he added his paycheck to the bank account, and he then had $26,010 in the account. What was the amount of Mark’s paycheck?
Answer:
Money in Mark bank account on Thursday = $25,081
After adding the paycheck to the bank account on Friday he have = $26,010
The amount on the Mark’s paycheck = ? = 26,010 – 25,081

Eureka Math Grade 4 Module 1 Lesson 15 Exit Ticket Answer Key

Draw a tape diagram to model each problem and solve.

Question 1.
956,204 – 780,169 =_______________
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 956,204 is the minuend, the number 780,169 is the subtrahend and the number 176,035 is the difference.

Question 2.
A construction company was building a stone wall on Main Street. 100,000 stones were delivered to the site. On Monday, they used 15,631 stones. How many stones remain for the rest of the week? Write your answer as a statement.
Answer:
Total stones delivered to the site = 100,000 stones
Number of stones used on Monday = 15,631 stones.
Number of stones remaining for rest of the week = 100,000 – 15,631

Eureka Math Grade 4 Module 1 Lesson 15 Homework Answer Key

Question 1.
Use the standard subtraction algorithm to solve the problems below.
a.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 9,656 is the minuend, the number 838 is the subtrahend and the number 8,818 is the difference.

b.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 59,656 is the minuend, the number 5,880 is the subtrahend and the number 53,776 is the difference.

c.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 759,656 is the minuend, the number 579,989 is the subtrahend and the number 179,667 is the difference.

d.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 294,150 is the minuend, the number 166,370 is the subtrahend and the number 127,780 is the difference.

e.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 294,150 is the minuend, the number 239,089 is the subtrahend and the number 55,061 is the difference.

f.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 294,150 is the minuend, the number 96,400 is the subtrahend and the number 197,750 is the difference.

g.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 800,500 is the minuend, the number 79,989 is the subtrahend and the number 720,511 is the difference.

h.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 800,500 is the minuend, the number 45,500 is the subtrahend and the number 755,000 is the difference.

i.

Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 800,500 is the minuend, the number 276,664 is the subtrahend and the number 523,836 is the difference.

Use tape diagrams and the standard algorithm to solve the problems below. Check your answers.

Question 2.
A fishing boat was out to sea for 6 months and traveled a total of 8,578 miles. In the first month, the boat traveled 659 miles. How many miles did the fishing boat travel during the remaining 5 months?
Answer:
Total distance traveled by a fishing boat in 6 months = 8,578 miles
The distance traveled by the fishing boat in the 1st month = 659 miles
The distance traveled by the fishing boat in 5 months = ? = 8,578 – 659

Question 3.
A national monument had 160,747 visitors during the first week of September. A total of 759,656 people visited the monument in September. How many people visited the monument in September after the first week?
Answer:
Number of visitors during the first week of September  at a national monument = 160,747
Total number of people visited the monument in September = 759,656
Number of people visited the monument in September after the first week = 759,656 – 160,747

Question 4.
Shadow Software Company earned a total of $800,000 selling programs during the year 2012. $125,300 of that amount was used to pay expenses of the company. How much profit did Shadow Software Company make in the year 2012?
Answer:
Total amount earned by the Shadow Software Company by selling the programs during the year 2012 = $800,000
The amount payed for the expenses of he company = $125,300
Profit made by the Shadow Software Company in the year 2012 = $800,000 – $125,300

Question 5.
At the local aquarium, Bubba the Seal ate 25,634 grams of fish during the week. If, on the first day of the week, he ate 6,987 grams of fish, how many grams of fish did he eat during the remainder of the week?
Answer:
At the Local aquarium
The amount of fish ate by Bubba the seal during the week = 25,634 grams
The amount of fish he ate on the first day of the week = 6,987 grams.
The amount of fish did he eat during the remaining week= 25,634 – 6,987

Engage NY Eureka Math 4th Grade Module 1 Lesson 14 Answer Key

Eureka Math Grade 4 Module 1 Lesson 14 Problem Set Answer Key

Question 1.
Use the standard algorithm to solve the following subtraction problems.
a.
Answer:

b.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones = 0 – 0 = 0.
Tens =  6 – 7 = 16 – 7 = 9.
6 is less than 7 so we borrow  1 from the 4 hundred  place  and make 4 hundred  as 3 hundred  and make 6  ten  as 16 ten and we subtract 7 from 16.
Hundreds = After borrowing 1 from hundred 4 becomes 3 . 3 – 4 = 13 – 4 = 9.
3 is less than 4 so we again borrow  1 from the 2 Thousands  place  and make 2 Thousands   as 1 Thousands and make 3 hundreds  as 13 hundreds and we subtract 4 from 13.
Thousands = 1 – 1 = 0
The number 2,460 is the minuend, the number 1,470 is the subtrahend and the number 990 is the difference.
c.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones = 4 – 0 = 4.
Tens =  8 – 0 = 8.
Hundreds = 6 – 7 = 16 – 7 = 9.
6 is less than 7 so we borrow  1 from the 7 thousands  place  and make 7 thousands  as 6 thousands  and make 6  hundreds  as 16 hundreds and we subtract 7 from 16.
Thousands =After borrowing 1 from thousands place 7 becomes 6. 6 – 9 = 16 – 9 = 7.
6 is less than 9 so we again borrow  1 from the 9 ten thousands place  and make 9 ten thousands  as 8 ten thousands and make 6  thousands as 16 thousands and we subtract 9 from 16.
Ten Thousands = 8 – 4 = 4.
The number 97,684 is the minuend, the number 49,700 is the subtrahend and the number 47,984 is the difference.
d.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones = 0 – 2 = 10 – 2 = 8.
0 is less than 2 so we borrow  1 from the 6 tens  place  and make 6 tens  as 5 tens  and make 0 ones  as 10 ones and we subtract 2 from 10.
Tens =After borrowing 1 from tens place 6 becomes 5.  5 – 7 = 15 – 7 = 8.
5 is less than 7 so we borrow  1 from the 4 hundred  place  and make 4 hundred  as 3 hundred  and make 5  tens  as 15 tens and we subtract 7 from 15.
Hundreds = After borrowing 1 from hundred 4 becomes 3 . 3 – 4 = 13 – 4 = 9.
3 is less than 4 so we borrow  1 from the 2 Thousands  place  and make 2 Thousands   as 1 Thousands and make 3 hundreds  as 13 hundreds and we subtract 4 from 13.
Thousands = 1 – 1 = 0
The number 2,460 is the minuend, the number 1,472 is the subtrahend and the number 988 is the difference.
e.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Since, ones place and tens place values are less then the subtrahend we borrow 1 from the hundreds place and increase the value of tens.
Tens =After borrowing 1 from hundreds place 0 ten becomes 10 ten. So, After borrowing  1 from the 3 hundred  place. 3 hundred becomes 2 hundred .
Ones = 6 – 7 = 16 – 7 = 9.
6 is less than 7 so we borrow  1 from the 10 tens  place  and make 10 tens  as 9 tens  and make 6 ones  as 16 ones and we subtract 7 from 16.
Tens : After borrowing 1 from tens place. 10 becomes 9. 9 – 1 = 8.
Hundreds = After borrowing 1 from hundred 3 becomes 2 . 2 – 1 = 1.
Thousands : 4 – 1 = 3.
Ten Thousand : 2 – 3 = 12 – 3 = 9.
2 is less than 3 so we borrow  1 from the 1 hundred Thousands  place  and make 1 hundred Thousands   as 0  hundred Thousands and make 2 thousand  as 12 thousand and we subtract 3 from 12.
Hundred thousands = 0.
The number 124,306 is the minuend, the number 31,117 is the subtrahend and the number 93,189 is the difference.
f.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones = 4 – 5 = 14 – 5 = 9.
4 is less than 5 so we borrow  1 from the 8 hundred  place  and make 8 hundred  as 7 hundred  and make 4  ten  as 14 ten and we subtract 5 from 14.
Tens =  7 – 0 = 7
Hundreds =6 – 7 = 16 – 7 = 9
6 is less than 7 so we borrow  1 from the 7 Thousands  place  and make 7 Thousands   as 6 Thousands and make 6 hundreds  as 16 hundreds and we subtract 7 from 16.
Thousands = 6 – 4  = 2
Ten Thousand = 9.
The number 97,684 is the minuend, the number 4,705 is the subtrahend and the number 92,979 is the difference.
g.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
The minuend ones , tens , hundreds all the three places are less then the subtrahend.
First
Ones = 6 – 7 = 16 – 7 = 9.
6 is less than 7 so we borrow  1 from the 0 ten place  and make 0 tens as 9 tens  and make 6  ones  as 16 ones and we subtract 7 from 16.
Tens = After borrowing 1 from hundred 0 becomes 9. 9 -1 = 8.
Hundreds = After borrowing 1 from thousand 0 becomes 9 . 9 – 1 = 8.
Thousands = 3 – 1 =  2.
Ten thousand = 2 – 2 = 0.
Hundred thousand = 1 – 1 = 0.
The number 124,006 is the minuend, the number 121,117 is the subtrahend and the number 2,889 is the difference.

h.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones = 4 – 5 = 14 – 5 = 9.
4 is less than 5 so we borrow  1 from the 8 Tens place  and make 8 Tens  as 7 Tens  and make 6  ones  as 16 ones and we subtract 5 from 14.
Tens =  7 – 0 = 7.
Hundreds = 6 – 7 = 16 – 7 = 9.
6 is less than 7 so we borrow  1 from the 7 Thousands  place  and make 7 Thousands   as 6 Thousands and make 6 hundreds  as 16 hundreds and we subtract 7 from 16.
Thousands = 6 – 7 = 16 – 7 = 9.
6 is less than 7 so we borrow  1 from the 9 ten Thousands  place  and make 9  ten Thousands   as 8 ten Thousands and make 6 hundreds  as 16 hundreds and we subtract 7 from 16.
ten thousand = 8 – 4 = 4.
The number 97,684 is the minuend, the number 47,705 is the subtrahend and the number  49,979 is the difference.
i.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones = 0 – 7 = 10 – 7 = 3.
0 is less than 7 so we borrow  1 from the 6 Tens place  and make 6 Tens  as 5 Tens  and make 0  ones  as 10 ones and we subtract 7 from 10.
Tens =  5 – 1 = 4.
Hundreds =0 – 1 = 1 – 1 = 9.
0 is less than 1 so we borrow  1 from the 4 Thousands  place  and make 4 Thousands   as 3 Thousands and make 0 hundreds  as 10 hundreds and we subtract 1 from 10.
Thousands = 3 – 1 = 2.
Ten thousand= 2 – 3 = 12 – 3 = 9.
2 is less than 3 so we borrow  1 from the 1 hundred Thousands  place  and make 1 hundred Thousands   as 0  hundred Thousands and make 2 ten thousand as 12 ten thousand and we subtract 3 from 12.
The number 124,060 is the minuend, the number 31,117 is the subtrahend and the number 92,943 is the difference.

Draw a tape diagram to represent each problem. Use numbers to solve, and write your answer as a statement. Check your answers.

Question 2.
There are 86,400 seconds in one day. If Mr. Liegel is at work for 28,800 seconds a day, how many seconds a day is he away from work?
Answer:
Total seconds in one day = 86,400
Number of seconds Mr. Liegel at work in a day = 28,800
Number of seconds Mr. Leigel away from work = 86,400 – 28,800

Question 3.
A newspaper company delivered 240,900 newspapers before 6 a.m. on Sunday. There were a total of 525,600 newspapers to deliver. How many more newspapers needed to be delivered on Sunday?
Answer:
Number of newspapers delivered by the company on Sunday before 6 a.m = 240,900
Total number of newspapers to be delivered = 525,600.
How many more newspaper to be delivered= ?

Question 4.
A theater holds a total of 2,013 chairs. 197 chairs are in the VIP section. How many chairs are not in the VIP section?
Total number of chairs a theater holds = 2,013
Number of chairs in the VIP Section = 197
Number of chairs which are not in the VIP section = B

Question 5.
Chuck’s mom spent $19,155 on a new car. She had $30,064 in her bank account. How much money does Chuck’s mom have after buying the car?
Answer:
Money spent by Chuck’s mom on new car = $19,155
Total money she had in her bank account = $30,064
Money left with her after buying the car = 30,064 – 19,155

Eureka Math Grade 4 Module 1 Lesson 14 Exit Ticket Answer Key

Use the standard algorithm to solve the following subtraction problems.

Question 1.

Answer:

Question 2.
32,010 – 2,546
Answer:

Draw a tape diagram to represent the following problem. Use numbers to solve, and write your answer as a statement. Check your answer.

Question 3.
A doughnut shop sold 1,232 doughnuts in one day. If they sold 876 doughnuts in the morning, how many doughnuts were sold during the rest of the day?
Answer:
Total doughnut sold by the doughnut shop in one day  = 1,232
Number of doughnuts sold in the morning = 876
Number of doughnuts sold during the rest of the day = A

Eureka Math Grade 4 Module 1 Lesson 14 Homework Answer Key

Question 1.
Use the standard algorithm to solve the following subtraction problems.
a.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 71,989 is the minuend, the number 21,492 is the subtrahend and the number 50,497 is the difference.

b.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 371,989 is the minuend, the number 96,492 is the subtrahend and the number 275,497 is the difference.
c.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 371,089 is the minuend, the number 25,192 is the subtrahend and the number 345,897 is the difference.

d.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 879,989 is the minuend, the number 721,492 is the subtrahend and the number 158,497 is the difference.

e.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 879,009 is the minuend, the number 788,492 is the subtrahend and the number 90,517 is the difference.
f.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 879,989 is the minuend, the number 21,070 is the subtrahend and the number 858,919 is the difference.
g.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 879,000 is the minuend, the number 21,989 is the subtrahend and the number 857,011 is the difference.
h.
Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 279,389 is the minuend, the number 191,492 is the subtrahend and the number 87,897 is the difference.
i.

Answer:

Explanation:
In subtraction if the minuend place values are less than the subtrahend then 1 is borrowed from the higher place value like
ones borrow from tens
tens borrow from hundreds
hundreds borrow  from thousands
thousands borrow from ten thousands
ten thousands borrow from hundred thousands
hundred thousands borrow from million.
if there are successive place values less  than the subtrahend we borrow from the highest place value whose value is higher than the subtrahend.
The number 500,989 is the minuend, the number 242,000 is the subtrahend and the number 258,989 is the difference.

Draw a tape diagram to represent each problem. Use numbers to solve, and write your answer as a statement. Check your answers.

Question 2.
Jason ordered 239,021 pounds of flour to be used in his 25 bakeries. The company delivering the flour showed up with 451,202 pounds. How many extra pounds of flour were delivered?
Answer:
Total flour ordered by Jason to use in his 25 bakeries = 239,021 pounds
Total flour showed by the company at delivering = 451,202 pounds.
Extra pounds of flour delivered by the company =  A = 451,202 – 239,021

Question 3.
In May, the New York Public Library had 124,061 books checked out. Of those books, 31,117 were mystery books. How many of the books checked out were not mystery books?
Answer:
Number of books checked out from the New York Public Library = 124,061 books
Out of the checked out books the Number of Mystery books are =  31,117 books

Question 4.
A Class A dump truck can haul 239,000 pounds of dirt. A Class C dump truck can haul 600,200 pounds of dirt. How many more pounds can a Class C truck haul than a Class A truck?
Answer:
Number of pounds of dust A Class A dump truck can haul = 239,000 pounds
Number of pounds of dust A Class C dump truck can haul = 600,200 pounds
The number of more pounds of dust A Class C truck can haul than a Class A truck = ?

Engage NY Eureka Math 4th Grade Module 1 Lesson 12 Answer Key

Eureka Math Grade 4 Module 1 Lesson 12 Problem Set Answer Key

Estimate and then solve each problem. Model the problem with a tape diagram. Explain if your answer is reasonable.

Question 1.
For the bake sale, Connie baked 144 cookies. Esther baked 49 more cookies than Connie.
a. About how many cookies did Connie and Esther bake? Estimate by rounding each number to the nearest ten before adding.
Answer:
Number of cookies Connie baked = 144 cookies
Number of cookies  Esther baked = 49 more than Connie = 49 + 144 = 193 cookies
Total number of cookies baked by both  = 144 + 193
rounding each number to the nearest ten = 144 ~ 140  and  193 ~ 190.
Adding both 140 + 190 = 330 cookies.

b. Exactly how many cookies did Connie and Esther bake?
Answer:

They both Baked 337 cookies exactly.
c. Is your answer reasonable? Compare your estimate from (a) to your answer from (b). Write a sentence to explain your reasoning.
Answer:
In the (a) bit the estimate answer was 330 cookies  but the answer in (b)  is 337 cookies on rounding it the nearest ten it would be 340 cookies.

Queens 2.
Raffle tickets were sold for a school fundraiser to parents, teachers, and students. 563 tickets were sold to teachers. 888 more tickets were sold to students than to teachers. 904 tickets were sold to parents.
a. About how many tickets were sold to parents, teachers, and students? Round each number to the nearest hundred to find your estimate.
Answer:

b. Exactly how many tickets were sold to parents, teachers, and students?
Answer:

c. Assess the reasonableness of your answer in (b). Use your estimate from (a) to explain.
Answer:
In (b) the answer is 2,918 on rounding it ti nearest hundred we get 2,900. But in (a) the answer is 3,000 on rounding to the nearest hundred. The difference is 100 tickets .

Queens 3.
From 2010 to 2011, the population of Queens increased by 16,075. Brooklyn’s population increased by 11,870 more than the population increase of Queens.
a. Estimate the total combined population increase of Queens and Brooklyn from 2010 to 2011.
(Round the addends to estimate.)
Answer:

b. Find the actual total combined population increase of Queens and Brooklyn from 2010 to 2011.
Answer:

c. Assess the reasonableness of your answer in (b). Use your estimate from (a) to explain.
Answer:
The answer in (b) is 44,020 population but on rounding to the nearest thousand the value is 44,000 in (a). There is a difference of 20 between the both value. Both the values are relatively closed.

Question 4.
During National Recycling Month, Mr. Yardley’s class spent 4 weeks collecting empty cans to recycle.

a. During Week 2, the class collected 1,256 more cans than they did during Week 1. Find the total number of cans Mr. Yardley’s class collected in 4 weeks.
Answer:

b. Assess the reasonableness of your answer in (a) by estimating the total number of cans collected.
Answer:
On rounding the number to the nearest thousand we get 53,000 as total and the difference will be of 443 cans. both my estimation and actual are relatively close.

Engage NY Math 4th Grade Module 1 Lesson 12 Exit Ticket Answer Key

Model the problem with a tape diagram. Solve and write your answer as a statement.

In January, Scott earned $8,999. In February, he earned $2,387 more than in January. In March, Scott earned the same amount as in February. How much did Scott earn altogether during those three months? Is your answer reasonable? Explain.
Answer:
In January Scott earned = $8,999
In February Scott earned = $2,387
In March Scott earned same amount as February = $2,387
Total earnings in the three months =

Yes my answer is  reasonable. Because my actual and estimation both are relatively close.

Eureka Math 4th Grade Module 1 Lesson 12 Homework Answer Key

Estimate and then solve each problem. Model the problem with a tape diagram. Explain if your answer is reasonable.

Question 1.
There were 3,905 more hits on the school’s website in January than February. February had 9,854 hits. How many hits did the school’s website have during both months?
Answer:
In February there were 9,854 hits on school’s website
In January  there were more hits than February = 3,905 + 9,854 = 13,759
a. About how many hits did the website have during January and February?
Answer:

b. Exactly how many hits did the website have during January and February?
Answer:

c. Is your answer reasonable? Compare your estimate from (a) to your answer from (b). Write a sentence to explain your reasoning.
Answer:
The actual number of hits 23,613 is reasonable because it is relatively close to the estimation 24,000.

Question 2.
On Sunday, 77,098 fans attended a New York Jets game. The same day, 3,397 more fans attended a New York Giants game than attended the Jets game. Altogether, how many fans attended the games?
Answer:
Number of fans attended a New York Jets game = 77,098
Number of fans attended the Giants game = 3,397 more than New York Jets = 3,397 + 77,098
a. What was the actual number of fans who attended the games?
Answer:

b. Is your answer reasonable? Round each number to the nearest thousand to find an estimate of how many fans attended the games.
Answer:
Rounding each number to the nearest thousand
80,495 ~ 90,000               77,098 ~ 77,000

Yes my answer is reasonable. The real value and the estimation values are close .

Question 3.
Last year on Ted’s farm, his four cows produced the following number of liters of milk:

a. Betsy produced 986 more liters of milk than Buttercup. How many liters of milk did all 4 cows produce?
Answer:
Number of liters of milk produced by Daisy = 5,098
Number of liters of milk produced by Mary = 9,980
Number of liters of milk produced by Buttercup = 7,087
Number of liters of milk produced by Betsy = 986 more liters of milk than Buttercup =986 + 7,087

b. Is your answer reasonable? Explain.
Answer:

Engage NY Eureka Math 4th Grade Module 1 Lesson 13 Answer Key2ureka Math Grade 4 Module 1 Lesson 13 Problem Set Answer Key

Question 1.
Use the standard algorithm to solve the following subtraction problems.
a.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones =  5 – 2 = 3.
Tens =  2 – 0 = 2.
Hundreds = 5 – 5 = 0.
Thousands = 7 – 3 = 4.
The number 7,525 is the minuend, the number 3,502 is the subtrahend and the number 4,023 is the difference.
b.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones =  5 – 2 = 3.
Tens =  2 – 0 = 2.
Hundreds = 5 – 5 = 0.
Thousands = 7 – 3 = 4.
Ten thousands = 1 – 1 = 0.
The number 17,525 is the minuend, the number 13,502 is the subtrahend and the number 04,023 is the difference.

c.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones =  5 – 7 = 8.
5 is less than 7 so we borrow  1 from the 2 tens place and make 2 tens as 1 tens and make 5 ones as 15 ones and we subtract 7 from 15.
Tens =  1 – 1 = 0.
Hundreds = 6 – 4 = 2.
Thousands = 6 – 4 = 2.
The number 6,625 is the minuend, the number 4,417 is the subtrahend and the number 2,208 is the difference.
d.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones =  5 – 5 = 0.
Tens =  2 – 3 =  12 – 3 = 9.
2 is less than 3 so we borrow  1 from the 6 hundreds place  and make 6 hundreds as 5 hundreds and make 2 tens as 12 tens and we subtract 3 from 12.
Hundreds = 5 – 4 = 1.
Thousands = 4 – 0 = 4.
The number 4,625 is the minuend, the number 435 is the subtrahend and the number 4,190 is the difference.
e.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones =  0 – 0 = 0.
Tens =  0 – 7 =  10 – 7 = 3.
0 is less than 7 so we borrow  1 from the 5 hundreds place  and make 5 hundreds as 4 hundreds and make 0 tens as 10 tens and we subtract 7 from 10.
Hundreds = 4 – 4 = 0 .
Thousands = 6 – 0 = 6.
The number 6,500 is the minuend, the number 470 is the subtrahend and the number 6,030 is the difference.
f.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones =  5 – 2 = 3.
Tens =  2 – 0 =  2.
Hundreds = 0 – 5 = 10 – 5 = 5.
0 is less than 5 so we borrow  1 from the 6 Thousands place  and make 6 Thousands as 5 Thousands and make 0 hundreds as 10 hundreds and we subtract 5 from 10.
Thousands = 5 – 3 = 2.
The number 6,025 is the minuend, the number 3,502 is the subtrahend and the number 2,502 is the difference.
g.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones =  0 – 0  = 0.
Tens =  4 – 3 = 1
Hundreds = 6 – 6 = 0.
Thousands = 3 – 4 = 13 – 4 = 9.
3 is less than 4 so we borrow  1 from the 2 ten Thousands place  and make 2 Thousands as 1 ten Thousands and make 3 hundreds as 13 hundreds and we subtract 4 from 13.
Ten Thousands = 1 – 1 = 0
The number 23,640 is the minuend, the number 14,630 is the subtrahend and the number 09,010 is the difference.
h.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones =  5 – 5 = 0.
Tens =  2 – 1 =  1.
2 is less than 3 so we borrow  1 from the 6 hundreds place  and make 6 hundreds as 5 hundreds and make 2 tens as 12 tens and we subtract 3 from 12.
Hundreds = 9 – 8 = 1.
Thousands = 1 – 4 = 11 – 4 = 7.
1 is less than 4 so we borrow  1 from the 3 ten thousands place  and make 3 ten thousands as 2 ten thousands and make 1 thousands as 11 thousands and we subtract 4 from 11.
Ten thousand =2 – 0 = 2.
Hundred thousand = 4 – 2 = 2.
The number 431,925 is the minuend, the number 204,815 is the subtrahend and the number 227,110 is the difference.
i.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones =  5 – 5 = 0.
Tens =  2 – 0 =  2.
Hundreds = 9 – 7 = 2.
Thousands = 9 – 1 = 8
Ten thousand =1 – 2 = 11 – 2 = 9.
1 is less than 2 so we borrow  1 from the 2 hundred thousands place  and make 2 hundred thousands as 1 hundred thousands and make 1  ten thousands as 11 ten thousands and we subtract 2 from 11.
Hundred thousand = 1 – 1 = 0.
The number 219,925 is the minuend, the number 121,705 is the subtrahend and the number 098,220 is the difference.

Draw a tape diagram to represent each problem. Use numbers to solve, and write your answer as a statement. Check your answers.

Question 2.
What number must be added to 13,875 to result in a sum of 25,884?
Answer:

12,009 must be added to 13,875 to get the sum of 25,884.

Question 3.
Artist Michelangelo was born on March 6, 1475. Author Mem Fox was born on March 6, 1946. How many years after Michelangelo was born was Fox born?
Answer:
Artist Michelangelo was born on March 6, 1475.
Artist Mem Fox was born on March 6, 1946
The difference between the their years = 1946 – 1475 = 471 years.

Question 4.
During the month of March, 68,025 pounds of king crab were caught. If 15,614 pounds were caught in the first week of March, how many pounds were caught in the rest of the month?
Answer:
Number of pounds of king crabs caught in the month of March = 68,025 pounds.
Number of pounds of king crabs caught in the first week of March = 15,614 pounds.
Number of pounds were caught in the rest of the month = 68,025 – 15,614 = 52,411.

Question 5.
James bought a used car. After driving exactly 9,050 miles, the odometer read 118,064 miles. What was the odometer reading when James bought the car?
Answer:
James bought a used car after driving exactly = 9,050 miles.
The reading of the Odometer  = 118,064 miles.
The odometer reading when James bought the car = 118,064 – 9,050 =

Eureka Math Grade 4 Module 1 Lesson 13 Exit Ticket Answer Key

Question 1.
Use the standard algorithm to solve the following subtraction problems.
a.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones =  2 – 1 = 1.
Tens =  1 – 0 = 1.
Hundreds = 5 – 5 = 0.
Thousands = 8 – 2 = 6.
The number 8,512 is the minuend, the number 2,501 is the subtrahend and the number 6,011 is the difference.

b.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones =  2 – 2 = 0.
Tens =  4 – 2 =  2.
Hundreds = 0 – 1 = 10 – 1 = 9.
0 is less than 1 so we borrow  1 from the 8 thousands place  and make 8 thousands as 7 thousands and make 0 hundred as 10 hundred and we subtract 1 from 10.
Thousands = 7 – 4 = 3.
Ten thousand =1.
The number 18,042 is the minuend, the number 4,122 is the subtrahend and the number 13,920 is the difference.
c.
Answer:

Explanation:
The rules of subtraction we first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
Ones =  2 – 1 = 1.
Tens =  7- 6 =  1.
Hundreds = 0 – 5 = 10 – 5 = 5.
0 is less than 5 so we borrow  1 from the 8 thousands place  and make 8 thousands as 7 thousands and make 0 hundred as 10 hundred and we subtract 5 from 10.
Thousands = 7 – 1 = 6.
The number 8,072 is the minuend, the number 1,561 is the subtrahend and the number 6,511 is the difference.

Draw a tape diagram to represent the following problem. Use numbers to solve. Write your answer as a statement. Check your answer.

Question 2.
What number must be added to 1,575 to result in a sum of 8,625?
Answer:
Sum = 8,625
One Addend = 1,575
Second Addend = sum –  one addend = 8,625 – 1,575 =

Eureka Math Grade 4 Module 1 Lesson 13 Homework Answer Key

Question 1.
Use the standard algorithm to solve the following subtraction problems.

a.
Answer:

b.
Answer:

c.
Answer:

d.
Answer:

e.
Answer:

f.
Answer:

g. 2,431 – 920 =
Answer:

h. 892,431 – 520,800 =
Answer:

Question 2.
What number must be added to 14,056 to result in a sum of 38,773?
Answer:

Draw a tape diagram to model each problem. Use numbers to solve, and write your answers as a statement. Check your answers.

Question 3.
An elementary school collected 1,705 bottles for a recycling program. A high school also collected some bottles. Both schools collected 3,627 bottles combined. How many bottles did the high school collect?
Answer:

The High School have collected 1,922 bottles.

Question 4.
A computer shop sold $356,291 worth of computers and accessories. It sold $43,720 worth of accessories. How much did the computer shop sell in computers?
Answer:
Total worth of computers and accessories a computer shop = $356,291
The worth of  accessories = $43,720.
The worth of computers  = A

Question 5.
The population of a city is 538,381. In that population, 148,170 are children.
a. How many adults live in the city?
b. 186,101 of the adults are males. How many adults are female?
Answer:
Total population of the city = 538,381
Number of children in the city = 148,170
Answer:

Engage NY Eureka Math 4th Grade Module 1 Lesson 11 Answer Key

Eureka Math Grade 4 Module 1 Lesson 11 Problem Set Answer Key

Question 1.
Solve the addition problems below using the standard algorithm.
a.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 6,311 and 268
first adding the ones place = 1 + 8 = 9.
ten place : 1 + 6 = 7
hundreds place = 3 + 2 = 5
thousands place = 6
Sum = 6,579
b.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 6,311 and 1,268
first adding the ones place = 1 + 8 = 9.
ten place : 1 + 6 = 7
hundreds place = 3 + 2 = 5
thousands place = 6 + 1 = 7
Sum = 7,579
c.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 6,314 and 1,268
first adding the ones place =  4 + 8 = 12. 12 is represented as 10 ones + 2 ones  that’s 10 ones make 1 ten and 2 ones. So 1 is carried to the tens place and added to the tens place values.
ten place : 1 + 6 + 1 = 8
hundreds place = 3+ 2 = 5
thousands place = 6 + 1 = 7
Sum = 7,582.
d.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 6,314 and 2,493
first adding the ones place =  4 + 3 = 7.
ten place : 1 + 9  = 10. 10 tens make 1 hundred . So 1 is carried to the hundreds place and added to the hundreds place values and 0 is represented in tens place
hundreds place = 3+ 4 + 1 = 8
thousands place = 6 + 2 = 8
Sum = 8,807
e.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 8,314 and 2,493
first adding the ones place = 4 + 3 = 7.
ten place : 1 + 9 = 10. 10 tens make 1 hundred . So 1 is carried to the hundreds place and added to the hundreds place values and 0 is represented in tens place
hundreds place = 3 + 4 + 1 = 8
thousands place = 8 + 2 = 10. 10 thousands make 1 ten thousands . So 1 is carried to the ten thousands place and added to the ten thousands place values and 0 is represented in thousands place
ten thousands = 1
Sum = 10,807.
f.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 12,378 and 5,463
first adding the ones place = 8 + 3 = 11. 10 ones + 1 ones = 11. 10 ones make 1 ten . So 1 is carried to the tens place and added to the tens place values and 1 is represented in ones place
ten place : 7 + 6 + 1(carry on) = 14. 10 ten and 4 tens = 14 .10 tens make 1 hundred . So 1 is carried to the hundreds place and added to the hundreds place values and 4 is represented in tens place
hundreds place = 3 + 4 + 1(carry on) = 8
thousands place = 2 + 5 = 7
ten thousands = 1
Sum = 17,841

g.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 52,098 and 6,048
first adding the ones place = 8 + 8 = 16. 10 ones + 6 ones = 16. 10 ones make 1 ten . So 1 is carried to the tens place and added to the tens place values and 6 is represented in ones place
ten place : 9 + 4 + 1(carry on) = 14. 10 ten and 4 tens = 14 .10 tens make 1 hundred . So 1 is carried to the hundreds place and added to the hundreds place values and 4 is represented in tens place
hundreds place = 0 + 0 + 1(carry on) = 1
thousands place = 2 + 6 = 8
ten thousands = 5
Sum = 58,146
h.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 34,698 and 71,840
first adding the ones place = 8 + 0 = 8.
ten place : 9 + 4 = 13. 10 tens + 3 tens = 13 .10 tens make 1 hundred . So 1 is carried to the hundreds place and added to the hundreds place values and 3 is represented in tens place
hundreds place = 6 +8 + 1(carried number) = 15 = 10 hundred + 5 hundred . 10 hundreds make 1 thousands . So 1 is carried to the thousands place and added to the thousands place values and 5 is represented in hundreds place
thousands place = 4 + 1 + 1(carried number) = 6.
ten thousands = 3 + 7 = 10 .10  ten thousands make 1 hundred thousands . So 1 is carried to the hundred thousands place and added to the hundred thousands place values and 0 is represented in ten thousands place
Hundred thousands = 1(carried number) = 1
Sum = 106,538.
i.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 34,698 and 71,840
first adding the ones place = 1 + 5 = 6.
ten place : 1 + 4 = 5.
hundreds place = 8 + 4 = 12 = 10 hundred + 2 hundred . 10 hundreds make 1 thousands . So 1 is carried to the thousands place and added to the thousands place values and 2 is represented in hundreds place
thousands place = 4 + 6 + 1(carried number) = 11 =10 thousand + 1 thousand. 10   thousands make 1 ten thousands . So 1 is carried to the ten thousands place and added to the ten thousands place values and 1 is represented in  thousands place
ten thousands = 4 + 5 + 1(carried number) = 10 .10  ten thousands make 1 hundred thousands . So 1 is carried to the hundred thousands place and added to the hundred thousands place values and 0 is represented in ten thousands place
Hundred thousands = 1(carried number) = 5 + 3 + 1(carried number) = 9
Sum = 901,256.
j. 527 + 275 + 752
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 527 , 275 and 752
first adding the ones place = 7 + 5 + 2 = 14 = 10 ones + 4 ones . 10 ones make 1 tens . So 1 is carried to the tens place and added to the tens place values and 4 is represented in ones place
ten place : 2 + 7 + 5 + 1(carried number) = 15 = 10 tens + 5 tens.  10 tens make 1 hundred . So 1 is carried to the hundreds place and added to the hundreds place values and 5 is represented in tens place
hundreds place = 5 +2 + 7 + 1(carried number)= 15 = 10 hundred + 5 hundred . 10 hundreds make 1 thousands . So 1 is carried to the thousands place and added to the thousands place values and 5 is represented in hundreds place
thousands place = 4 + 6 + 1(carried number) = 11 =10 thousand + 1 thousand. 10   thousands make 1 ten thousands . So 1 is carried to the ten thousands place and added to the ten thousands place values and 1 is represented in  thousands place
ten thousands = 4 + 5 + 1(carried number) = 10 .10  ten thousands make 1 hundred thousands . So 1 is carried to the hundred thousands place and added to the hundred thousands place values and 0 is represented in ten thousands place
Hundred thousands = 1(carried number) = 5 + 3 + 1(carried number) = 9
Sum = 1,554
k. 38,193 + 6,376 + 241,457
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 38,193 + 6,376 + 241,457
first adding the ones place = 3 + 6 + 7= 16 = 10 ones + 6 ones . 10 ones make 1 tens . So 1 is carried to the tens place and added to the tens place values and 6 is represented in ones place
ten place : 9 + 7 + 5 + 1(carried number) = 22 = 20 tens + 2 tens.  20 tens make 2 hundred . So 1 is carried to the hundreds place and added to the hundreds place values and 2 is represented in tens place
hundreds place = 1 + 3 + 4  + 1(carried number)= 10. 10 hundreds make 1 thousands . So 1 is carried to the thousands place and added to the thousands place values and 0 is represented in hundreds place
thousands place = 8 + 6 + 1 +1(carried number) = 16 =10 thousand + 6 thousand. 10   thousands make 1 ten thousands . So 1 is carried to the ten thousands place and added to the ten thousands place values and 6 is represented in  thousands place
ten thousands =3 + 4 + 1(carried number) = 8 .
Hundred thousands = 2
Sum = 286,026.

Draw a tape diagram to represent each problem. Use numbers to solve, and write your answer as a statement.

Question 2.
In September, Liberty Elementary School collected 32,537 cans for a fundraiser. In October, they collected 207,492 cans. How many cans were collected during September and October?
Answer:
Number of cans collected by the Liberty Elementary School for a fundraiser in September are = 32,537
Number of cans collected by the Liberty Elementary School for a fundraiser in October are = 207,492
Total number of cans collected during September and October are = 32,537 + 207,492 =

Question 3.
A baseball stadium sold some burgers. 2,806 were cheeseburgers. 1,679 burgers didn’t have cheese. How many burgers did they sell in all?
Answer:
Number of cheeseburgers sold at baseball stadium = 2,806
Number of burgers without cheese sold at baseball stadium are = 1,679
Total number of burgers sold in all are = 2,806 + 1,679

Question 4.
On Saturday night, 23,748 people attended the concert. On Sunday, 7,570 more people attended the concert than on Saturday. How many people attended the concert on Sunday?
Answer:
Number of people attended the concert on Saturday night = 23,748
Number of people attended the concert on Sunday are =  7,570 more than on Saturday
Total people attended the concert on Sunday = 23,748 + 7, 570

Eureka Math Grade 4 Module 1 Lesson 11 Exit Ticket Answer Key

Question 1.
Solve the addition problems below using the standard algorithm.
a.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 23,607 and 2,307
first adding the ones place = 7 + 7 = 14. 14 is represented as 10 + 4 that’s 1 ten and 4 ones. So 1 is carried to the tens place and added to the tens place values.
ten place : 0 + 0 + 1 = 1
hundreds place = 6 + 3 = 9
thousands place = 3 + 2 = 5
ten thousands place = 2
Sum = 25,914.

b.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 3,948 and 278
first adding the
ones place = 8 + 8 = 16. 16 is represented as 10 + 6 that’s 1 ten and 6 ones. So 1 is carried to the tens place and added to the tens place values and 6 is represented in ones place.
ten place : 4 + 7 + 1(carried number) = 12 = 10 + 2 that’s 1 hundred and 2 tens. So 1 is carried to the hundreds place and added to the hundreds place values and 2 is represented in tens place.
hundreds place = 9 + 2 + 1(carried number) = 12 = 10 + 2 that’s 1 thousand and 2 hundred. So 1 is carried to the thousands place and added to the thousands place values and 2 is represented in hundreds place.
thousands place = 3 + 1(carried number) = 4
Sum = 4,226.
c. 5,983 + 2,097
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 5,983 and 2,097
first adding the
ones place = 3 + 7 = 10. 10 is represented as 10 + 0 that’s 1 ten and 0 ones. So 1 is carried to the tens place and added to the tens place values and 0 is represented in ones place.
ten place : 8 + 9 + 1(carried number) = 18 = 10 + 8 that’s 1 hundred and 8 tens. So 1 is carried to the hundreds place and added to the hundreds place values and 8 is represented in tens place.
hundreds place = 9 + 0 + 1(carried number) = 10 = 10 + 0 that’s 1 thousand and 0 hundred. So 1 is carried to the thousands place and added to the thousands place values and 0 is represented in hundreds place.
thousands place = 5 + 2 + 1(carried number) = 8
Sum = 8,080

Question 2.
The office supply closet had 25,473 large paper clips, 13,648 medium paper clips, and 15,306 small paper clips. How many paper clips were in the closet?
Answer:
Number of large paper clips = 25,473
Number of medium paper clips = 13,648
Number of small paper clips = 15,306
Total number of paper clips = 25,473 + 13,648 + 15,306

Eureka Math Grade 4 Module 1 Lesson 11 Homework Answer Key

Question 1.
Solve the addition problems below using the standard algorithm.
a.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 7,909 and 1,044
first adding the ones place = 9 + 4 = 13 = 10 ones + 3 ones . 10 ones make 1 tens . So 1 is carried to the tens place and added to the tens place values and 3 is represented in ones place
ten place : 0 + 4 + 1(carried number) = 5
hundreds place = 9 + 0 = 9.
thousands place = 7 + 1 = 8.
Sum = 8,953.
b.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 27,909 and 9,740
first adding the ones place = 9 + 0 = 9
ten place : 0 + 4 = 4.
hundreds place = 9 + 7 = 16. 10 hundreds make 1 thousands . So 1 is carried to the thousands place and added to the thousands place values and 6 is represented in hundreds place
thousands place = 7 + 9 +1(carried number) = 17 =10 thousand + 7 thousand. 10   thousands make 1 ten thousands . So 1 is carried to the ten thousands place and added to the ten thousands place values and 7 is represented in  thousands place.
ten thousands =2 + 1(carried number) = 3 .
Sum = 37,649.
c.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 827,909 and 42,989
first adding the ones place = 9 + 9= 18 = 10 ones + 8 ones . 10 ones make 1 tens . So 1 is carried to the tens place and added to the tens place values and 8 is represented in ones place
ten place : 0 + 8  + 1(carried number) = 8.
hundreds place = 9 + 9 = 18. 10 hundreds make 1 thousands . So 1 is carried to the thousands place and added to the thousands place values and 8 is represented in hundreds place
thousands place = 7 + 2 +1(carried number) = 10 =10 thousand + 0 thousand. 10   thousands make 1 ten thousands . So 1 is carried to the ten thousands place and added to the ten thousands place values and 0 is represented in  thousands place
ten thousands =2+ 4 + 1(carried number) = 7 .
Hundred thousands = 8
Sum = 870,898.
d.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 289,205 and 11,845
first adding the ones place = 5 + 5 = 10 = 10 ones + 0 ones . 10 ones make 1 tens . So 1 is carried to the tens place and added to the tens place values and 0 is represented in ones place
ten place : 0 + 4 + 1(carried number) = 5.
hundreds place = 2 + 8 = 10. 10 hundreds make 1 thousands . So 1 is carried to the thousands place and added to the thousands place values and 0 is represented in hundreds place
thousands place = 9 + 1 +1(carried number) = 11 =10 thousand + 1 thousand. 10   thousands make 1 ten thousands . So 1 is carried to the ten thousands place and added to the ten thousands place values and 1 is represented in  thousands place
ten thousands =8 + 1 + 1(carried number) =10. 10 ten thousands make 1 hundred thousands . So 1 is carried to the hundred thousands place and added to the hundred thousands place values and 1 is represented in  ten thousands place
Hundred thousands = 2 + 1(carried over number) = 3
Sum = 301,050.
e.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 547,982 and 114,849
first adding the ones place = 2 + 9 = 11 = 10 ones + 1 ones . 10 ones make 1 tens . So 1 is carried to the tens place and added to the tens place values and 1 is represented in ones place
ten place : 8 + 4 + 1(carried number) = 13. 10 tens make 1 hundred . So 1 is carried to the hundreds place and added to the hundreds place values and 3 is represented in tens place
hundreds place = 9 + 8 + 1(carried number)= 18. 10 hundreds make 1 thousands . So 1 is carried to the thousands place and added to the thousands place values and 8 is represented in hundreds place
thousands place = 7 + 4 +1(carried number) = 12 =10 thousand + 2 thousand. 10   thousands make 1 ten thousands . So 1 is carried to the ten thousands place and added to the ten thousands place values and 2 is represented in  thousands place
ten thousands =4 + 1 + 1(carried number) = 6.
Hundred thousands = 5 + 1 = 6.
Sum = 662,831.
f.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 258,983 and 121,897.
first adding the ones place = 3 + 7 = 10 = 10 ones + 0 ones . 10 ones make 1 tens . So 1 is carried to the tens place and added to the tens place values and 0 is represented in ones place
ten place : 8 + 9+ 1(carried number) = 18. 10 tens make 1 hundred . So 1 is carried to the hundreds place and added to the hundreds place values and 8 is represented in tens place
hundreds place = 9 + 8 + 1(carried number)= 18. 10 hundreds make 1 thousands . So 1 is carried to the thousands place and added to the thousands place values and 8 is represented in hundreds place
thousands place = 8 + 1 +1(carried number) = 10 =10 thousand + 0 thousand. 10   thousands make 1 ten thousands . So 1 is carried to the ten thousands place and added to the ten thousands place values and 0 is represented in  thousands place
ten thousands =5 + 2 + 1(carried number) = 8.
Hundred thousands = 2 + 1 = 3.
Sum = 380,880.
g.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 83,906 and 35,808
first adding the ones place = 6 + 8  = 14 = 10 ones + 4 ones . 10 ones make 1 tens . So 1 is carried to the tens place and added to the tens place values and 4 is represented in ones place
ten place : 0 + 0 + 1(carried number) = 1.
hundreds place = 9 + 8 = 17. 10 hundreds make 1 thousands . So 1 is carried to the thousands place and added to the thousands place values and 7 is represented in hundreds place
thousands place = 3 + 5 +1(carried number) = 9.
ten thousands =8 + 3 = 11. 10 ten thousands make 1 hundred thousands . So 1 is carried to the hundred thousands place and added to the hundred thousands place values and 1 is represented in  ten thousands place
Hundred thousands = 1(carried number) = 1.
Sum = 119,714.
h.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 289,999 and 91,849
first adding the ones place = 9 + 9  = 18 = 10 ones + 8 ones . 10 ones make 1 tens . So 1 is carried to the tens place and added to the tens place values and 8 is represented in ones place
ten place : 9 + 4 + 1(carried number) = 14. 10 tens make 1 hundreds . So 1 is carried to the hundreds place and added to the hundreds place values and 4 is represented in tens place
hundreds place = 9 + 8 +1(carried number)= 18 . 10 hundreds make 1 thousands . So 1 is carried to the thousands place and added to the thousands place values and 8 is represented in hundreds place
thousands place = 9 + 1 +1(carried number) = 11. 10  thousands make 1 ten thousands . So 1 is carried to the ten thousands place and added to the ten thousands place values and 1 is represented in  thousands place.
ten thousands =8 + 9 +1(carried number) = 18. 10 ten thousands make 1 hundred thousands . So 1 is carried to the hundred thousands place and added to the hundred thousands place values and 8 is represented in  ten thousands place
Hundred thousands = 2 +1(carried number) = 3.
Sum = 381,848
i.
Answer:

Explanation:
While adding two numbers we add the numbers according to the place values individually. We add number from ones place to the largest place value.
given number 289,999 and 91,849
first adding the ones place = 0 + 0  = 0.
ten place : 0 + 0 = 0.
hundreds place = 9+1= 10 . 10 hundreds make 1 thousands . So 1 is carried to the thousands place and added to the thousands place values and 0 is represented in hundreds place
thousands place = 4 + 5  +1(carried number) = 10. 10  thousands make 1 ten thousands . So 1 is carried to the ten thousands place and added to the ten thousands place values and 0 is represented in  thousands place.
ten thousands =5 + 4 +1(carried number) = 10. 10 ten thousands make 1 hundred thousands . So 1 is carried to the hundred thousands place and added to the hundred thousands place values and 0 is represented in  ten thousands place
Hundred thousands = 7 + 2 +1(carried number) = 1. 10 hundred thousands make 1 million . So 1 is carried to the millions place and added to the millions place values and 0 is represented in  hundred thousands place.
Millions = 1 (carried over number) = 1.
Sum = 1,000,000.

Draw a tape diagram to represent each problem. Use numbers to solve, and write your answer as a statement.

Question 2.
At the zoo, Brooke learned that one of the rhinos weighs 4,897 pounds, one of the giraffes weighs 2,667 pounds, one of the African elephants weighs 12,456 pounds, and one of the Komodo dragons weighs 123 pounds.
Answer:
Given
One of the rhinos weights at the zoo = 4,897 pounds.
One of the giraffes weights at the zoo  = 2,667 pounds
One of the African elephants weights at the zoo = 12, 456 pounds.
One of the Komodo dragons at the zoo weighs = 123 pounds.
a. What is the combined weight of the zoo’s African elephant and the giraffe?
Answer:

b. What is the combined weight of the zoo’s African elephant and the rhino?
Answer:

c. What is the combined weight of the zoo’s African elephant, the rhino, and the giraffe?
Answer:

d. What is the combined weight of the zoo’s Komodo dragon and the rhino?
Answer:

Engage NY Eureka Math 4th Grade Module 7 End of Module Assessment Answer Key

Eureka Math Grade 4 Module 7 End of Module Assessment Task Answer Key

Question 1.
Solve for the following conversions. Draw tape diagrams to model the equivalency.
a. 1 gal = ______ qt
b. 3 qt 1 pt = ______ pt
Answer:

a. 1 gal =  4 qt

b. 3 qt 1 pt = 7 pt

Question 2.
Complete the following tables:
a.

The rule for converting pounds to ounces is _____________.

To convert pounds into ounces, multiply pounds x 16

b.

The rule for converting hours to minutes is _____________.
Answer:

To convert hours into minutes, multiply hours x 60

Question 3.
Answer true or false for the following statements. Explain how you know using pictures, numbers, or words.
a. 68 ounces < 4 pounds _____________ b. 920 minutes > 17 hours _____________
c. 38 inches = 3 feet 2 inches _____________
Answer:

a. False, 4 pounds = 16 x 4 = 64 ounces

So, 68 ounces > 4 pounds

b. False, 17 hours = 17 x 60 = 1,020 minutes

So, 920 minutes < 1,020 minutes

c. True.

3 feet = 36 inches  and 2 inches

Total : 36 + 2 = 38 inches

So, 38 inches = 3 feet 2 inches.

Question 4.
Convert the following measurements.
a. Express the length of a 9 kilometre trip in meters. _______________
b. Express the capacity of a 3 liter 240 millilitre container in millilitres. ______________
c. Express the length of a 3 foot 5 inch fish in inches. _______________
d. Express the length of a 2\(\frac{1}{4}\) hour movie in minutes. _______________
e. Express the weight of a 24\(\frac{3}{8}\) pound wolverine in ounces. _______________
Answer:

a. Express the length of a 9 kilometre trip in meters. 9000 meters
b. Express the capacity of a 3 liter 240 millilitre container in millilitres. 3240 millilitres
c. Express the length of a 3 foot 5 inch fish in inches. 41 inches
d. Express the length of a 2\(\frac{1}{4}\) hour movie in minutes. 135 minutes
e. Express the weight of a 24\(\frac{3}{8}\) pound wolverine in ounces. 390 ounces

Question 5.
Find the following sums and differences. Show your work.
a. 4 gal 2 qt + 5 gal 3 qt = _______ gal _______ qt
b. 6 ft 2 in – 9 inches = _______ ft _______ in
c 3 min 34 sec + 7 min 46 sec = _______ min _______ sec
d. 24 lb 9 oz – 3 lb 11 oz = _______ lb _______ oz
Answer:

a. 4 gal 2 qt + 5 gal 3 qt = 10 gal 1 qt
b. 6 ft 2 in – 9 inches = 5 ft 5 in
c 3 min 34 sec + 7 min 46 sec = 11 min 20 sec
d. 24 lb 9 oz – 3 lb 11 oz = 20 lb 14 oz

Question 6.
a. Complete the table.

b. Describe the rule for converting yards to inches.
c. How many inches are in 15 yards?
d. Jacob says that he can find the number of inches in 15 yards by tripling the number of inches in 5 yards. Does his strategy work? Why or why not?
e. A blue rope in Garret’s camping backpack is 6 yards long. The blue rope is 3 times as long as a red rope. A yellow rope is 2 feet 7 inches shorter than the red rope. What is the difference in length between the blue rope and the yellow rope?
Answer:

B.

To convert yards into inches

Multiply the number of yards x 36

c.

1 yard = 36 inches

15 yards = 15 x 36 = 540

Therefore, 15 yards = 540 inches.

d.

Yes, Jacob strategy is right.

15 yards can be shown as 5 yards x 3

1 yard = 36 inches

15 yards = 540 inches

5 yards tripling by 3 =

5 yards = 5 x 36 = 180

5 yards = 180 inches

180 inches x 3 = 540

e.

Given, the length of blue rope = 6 yards long

6 yards = 18 feet

Also given, the blue rope is 3 times as long as a red rope

so, length of red rope = 2 yards = 6 feet

A yellow rope is 2 feet 7 inches shorter than red rope

So, 6 feet – 2 feet 7 inches

= 3 feet 5 inches

Now,

18 feet – 3 feet 5 inches = 14 feet 7 inches.

Therefore, the length difference between the blue rope and the yellow rope is 14 feet 7 inches.

Engage NY Eureka Math 4th Grade Module 7 Lesson 18 Answer Key

Eureka Math Grade 4 Module 7 Lesson 18 Reflection Answer Key

Question 1.
Why do you think vocabulary was such an important part of fourth-grade math? How does vocabulary help you in math?
Answer:

Yes, Vocabulary is important in mathematics.

Vocabulary helps in understanding and communication. It helps to solve complex and real problems.

Question 2.
Which vocabulary terms do you know well, and which would you like to improve upon?
Answer:

I came across several vocabulary words like Area, data, absolute value, ratio etc…. I would like improve more on vocabulary terms by practicing.

Engage NY Eureka Math 4th Grade Module 7 Lesson 17 Answer Key

Eureka Math Grade 4 Module 7 Lesson 17 Reflection Answer Key

Question 1.
What are you able to do now in math that you were not able to do at the beginning of Grade 4?
Answer:

I am able to solve some critical problems related to areas and calculations which I am not able to do before

Question 2.
Which activities would you like to practice this summer in order to keep fluent or become more fluent?
Answer:

The activities I would like to practice are reading some books, I think they  will keep me more productive and useful for my studies too

Question 3.
What type of practice would help you build your fluency with these concepts?
Answer:

I think practicing some more critical problems and reasoning will help me to build fluency.

Eureka Math Grade 4 Module 7 Lesson 17 Homework Answer Key

Question 1.
Decimal Fraction Review: Plot and label each point on the number line below, and complete the chart. Only solve the portion above the dotted line.

Answer:

Question 2.
Complete the chart. Create your own problem for B, and plot the point.

Answer:

Question 3.
Complete the chart. The first one has been done for you. Only solve the top portion above the dotted line.

Answer:

Question 4.
Complete the chart. Create your own problem in the last row.

Answer:

Engage NY Eureka Math 4th Grade Module 7 Lesson 16 Answer Key

Eureka Math Grade 4 Module 7 Lesson 16 Problem Set Answer Key

Work with your partner to create each floor plan on a separate piece of paper, as described below.
You should use a protractor and a ruler to create each floor plan and be sure each rectangle you create has two sets of parallel lines and four right angles.
Be sure to label each part of your model with the correct measurement.
Question 1.
The bedroom in Samantha’s dollhouse is a rectangle 26 centimetres long and 15 centimetres wide. It has a rectangular bed that is 9 centimetres long and 6 centimetres wide. The two dressers in the room are each 2 centimetres wide. One measures 7 centimetres long, and the other measures 4 centimetres long. Create a floor plan of the bedroom containing the bed and dressers. Find the area of the open floor space in the bedroom after the furniture is in place.
Answer:

Total area = length x width

= 26 x 15

= 390 sq. cm.

Bedroom + dresser + dresser =

54 + 14 +14 = 76 sq. cm.

Now, Room furniture =

390 – 76 = 314 sq. cm.

Therefore, The area of the open floor space in the bedroom after furniture is placed = 314 sq. cm.

Question 2.
A model of a rectangular pool is 15 centimeters long and 10 centimeters wide. The walkway around the pool is 5 centimeters wider than the pool on each of the four sides. In one section of the walkway, there is a flowerbed that is 3 centimeters by 5 centimeters. Create a diagram of the pool area with the surrounding walkway and flowerbed. Find the area of the open walkway around the pool.
Answer:

Total area = 25 x 20 = 500 sq. cm

Pool + flower bed =

150 + 15 = 165 sq. cm.

Total area = 500 – 165 = 335 sq. cm.

Therefore, The area of the open walkway around the pool = 335 sq. cm.

Eureka Math Grade 4 Module 7 Lesson 16 Reflection Answer Key

In the table below are skills that you learned in Grade 4 and that you used to complete today’s lesson. These skills were originally introduced in earlier grades, and you will continue to work on them as you go on to later grades. Choose three topics from the chart, and explain how you think you might build on and use them in Grade 5.

Eureka Math Grade 4 Module 7 Lesson 16 Homework Answer Key

For homework, complete the top portion of each page. This will become an answer key for you to refer to when completing the bottom portion as a mini-personal white board activity during the summer.

Use a ruler and protractor to create and shade a figure according to the directions. Then, find the area of the unshaded part of the figure.
Question 1.
Draw a rectangle that is 18 cm long and 6 cm wide. Inside the rectangle, draw a smaller rectangle that is 8 cm long and 4 cm wide. Inside the smaller rectangle, draw a square that has a side length of 3 cm. Shade in the smaller rectangle, but leave the square unshaded. Find the area of the unshaded space.
Answer:

The area of unshaded part =

( 4 x 8 ) – ( 3 x 3 )

32 – 9

= 23 sq. cm

Therefore, the area of unshaded part = 23 sq. cm.

Question 2.
Emanuel’s science project display board is 42 inches long and 48 inches wide. He put a 6-inch border around the edge inside the board and placed a title in the center of the board that is 22 inches long and 6 inches wide. How many square inches of open space does Emanuel have left on his board?
Answer:

The square inches of open space Emanuel have left on his board.

(42 x 48)-{(6 x 42)+(6 x 42)+(6 x 32 )+( 6 x 32 ) + (6 x 22)}

= 2016 – { 252 + 252 + 216 + 216+ 132 }

= 2016 – 1068

= 948 sq. inches.

Challenge: Replace the given dimensions with different measurements, and solve again.

Engage NY Eureka Math 4th Grade Module 7 Lesson 15 Answer Key

Eureka Math Grade 4 Module 7 Lesson 15 Problem Set Answer Key

Question 1.
Emma’s rectangular bedroom is 11 ft long and 12 ft wide with an attached closet that is 4 ft by 5 ft. How many square feet of carpet does Emma need to cover both the bedroom and closet?
Answer:

Given,

Emma’s rectangular bedroom measurements :

length = 11 ft

and width = 12 ft

Area = length x width

A = 11 x 12 = 132 sq. ft.

Also given the measurement of attached closet :

length = 4 ft

and width = 5 ft

Area = 4 x 5 = 20 sq. ft.

Total square feet of carpet Emma need to cover both the bedroom and closet =

132+ 20 = 152 square feet.

Therefore, Emma needs 152 sq. ft to cover bedroom and closet.

Question 2.
To save money, Emma is no longer going to carpet her closet. In addition, she wants one 3 ft by 6 ft corner of her bedroom to be wood floor. How many square feet of carpet will she need for the bedroom now?
Answer:

The area of Emma’s bedroom = 132 sq. ft.

Given that,

Emma wants to cover her 3 ft by 6 ft corner with wood floor

Now, Area = length x width

A = 3 x 6 = 18 sq. ft.

Now, the square feet of carpet Emma need for her bedroom =

132 – 18 = 114

Therefore, Emma need 114 sq. ft. of carper for her bedroom.

Question 3.
Find the area of the figure pictured to the right.

Answer:

Area of rectangle = length x width

a. Area = length x width

A = 15 x 8 = 120 sq. ft

b. Area = length x width

A= 12 x 5 = 60 sq. ft.

c. Area = length x width

A = 12 x 5 = 60 sq. ft.

Total area = 120 + 60 +60 = 240

Therefore, total area = 240 sq. ft.

Question 4.
Label the sides of the figure below with measurements that make sense. Find the area of the figure.

Answer:-

Area = length x width

a. 3 x 2 = 6 sq. inches

b. 3 x 1 = 3 sq. inches

c. 3 x 2 = 6 sq.inches

Total : 6 sq.in + 3 sq.in + 6 sq. in.

= 15 sq. inches

Question 5.
Peterkin Park has a square fountain with a walkway around it. The fountain measures 12 feet on each side. The walkway is 3\(\frac{1}{2}\) feet wide. Find the area of the walkway.
Answer: 217 sq. ft.

Explanation :

Given that,

The measurement of fountain on each side = 12 sq. ft.

Area = length x width

A = 12 x 12 = 144 sq. ft.

The measurement of walkway = 3 1/2 feet wide

Total measurement = 144 + 3 1/2 +3  1/2 = 19

Area = length x width

A = 19 x 19

= 361 sq. ft

Now, the area of walkway =

361 – 144 = 217

Therefore, the area of walkway = 217 sq. ft.

Question 6.
If 1 bag of gravel covers 9 square feet, how many bags of gravel will be needed to cover the entire walkway around the fountain in Peterkin Park?
Answer:

Given that,

1 bag of gravels covers 9 sq. ft.

Total area of walkway = 217 sq.ft.

Now,

217 / 9 = 24

24 and remaining of 1

Therefore, 25 bags of graved will be required to cover the walkway.

Eureka Math Grade 4 Module 7 Lesson 15 Reflection Answer Key

In the table below are topics that you learned in Grade 4 and that were used in today’s lesson. Choose 1 topic, and describe how you were successful in using it today.

Eureka Math Grade 4 Module 7 Lesson 15 Homework Answer Key

For homework, complete the top portion of each page. This will become an answer key for you to refer to when completing the bottom portion as a mini-personal white board activity during the summer.
Find the area of the figure that is shaded.
Question 1.

Answer:

a. Area of rectangle = length x width

Area = 4 x 16 = 64 sq. ft.

b. area = length x breadth

Area = 16 x 8 = 128

Total area =

64 + 128 = 192 sq.ft.

2.

Area of rectangle = length x breadth

The area of shaded part =

16 x 24 – {( 9 x 7 ) + ( 5 x 4 )}

= 384 – [63 + 20 ]

= 384 – 83

= 301 sq. ft.

Find the area of the figure that is shaded.
Question 1.

Answer:

a. Area of rectangle = length x width

Area = 2 x 8 = 16 sq. ft.

b. area = length x breadth

Area = 8 x 4 = 32

Total area =

16 + 32 = 48 sq.ft.

2.

Area of rectangle = length x breadth

The area of shaded part =

16 x 24 – {( 9 x 7 ) + ( 5 x 4 )}

= 384 – [63 + 20 ]

= 384 – 83

= 301 sq. ft.

Find the area of the figure that is shaded.
Question 1.

Challenge: Replace the given dimensions with different measurements, and solve again.

Question 3.
A wall is 8 feet tall and 19 feet wide. An opening 7 feet tall and 8 feet wide was cut into the wall for a doorway. Find the area of the remaining portion of the wall.
Answer:

The area of remaining portion of wall =

( 8 x 19 ) – ( 7 x 8 )

= 152 – 56

= 96

Therefore, the area of the remaining portion of the wall = 96 sq. ft.

Engage NY Eureka Math 4th Grade Module 7 Lesson 14 Answer Key

Eureka Math Grade 4 Module 7 Lesson 14 Problem Set Answer Key

Use RDW to solve the following problems.
Question 1.
A cartoon lasts \(\frac{1}{2}\) hour. A movie is 6 times as long as the cartoon. How many minutes does it take to watch both the cartoon and the movie?
Answer:

Given that,

The time taken by cartoon to last = 1/2 hour = 30 minutes

Also given, a movie is 6 times as long as the cartoon

30 x 6 = 180 minutes

Now, 180 +30 = 210 minutes

Therefore, The number of minutes required to watch both the cartoon and movie = 210 minutes.

Question 2.
A large bench is 7 \(\frac{1}{6}\) feet long. It is 17 inches longer than a shorter bench. How many inches long is the shorter bench?
Answer:

Given,

The length of large bench = 7 1/6 feet

7 1/6 feet =

1 feet = 12 inches

So, 7 feet = 7 x 12 = 84 inches

1/6 feet = 2 inches

Total : 84 + 2 = 86

Also given,

Longer bench is 17 inches longer than a shorter bench

So, 86 – 17 = 69

Therefore, the length of shorter bench is 69 inches.

Question 3.
The first container holds 4 gallons 2 quarts of juice. The second container can hold 1\(\frac{3}{4}\) gallons more than the first container. Altogether, how much juice can the two containers hold?
Answer:

Given that,

The capacity of first container = 4 gallons 2 quarts or 4 1/2

Also given the capacity of second container is 1 3/4 gallons more than first container

Which means, 4 1/2 + 1 3/4 =6 1/4

Total : 4 1/2 gallons + 6 1/4  gallons

10 gallons + 3/4 gal  = 10 gallons 3 quarts

Therefore, two contains can hold 103/4 gallons altogether.

Question 4.
A girl’s height is 3\(\frac{1}{3}\) feet. A giraffe’s height is 3 times that of the girl’s. How many inches taller is the giraffe than the girl?
Answer:

Given,

The height of a girl = 3 1/3 feet

The height of giraffe is 3 times of the girl

We know that 1 feet = 12 inches

3 1/3 +3 1/3 = 6 feet 8 inches

6 feet = 6 x 12 = 72 inches

72 + 8 = 80

Therefore, The girrafe is 80 inches taller than the girl.

Question 5.
Five ounces of pretzels are put into each bag. How many bags can be made from 22\(\frac{3}{4}\) pounds of pretzels?
Answer:

1 pound = 16 ounces

22 3/4 pounds of pretzels =

22 x 16 =352 ounces and

3/4 = 12 ounces

Total : 352 + 12 = 364 ounces

Given that, 5 pounds of pretzels are kept in each bag

Now, 364 / 5 = 72

Therefore, 72 bags can be made from 22 3/4 pounds of pretzels.

Question 6.
Twenty servings of pancakes require 15 ounces of pancake mix.
a. How much pancake mix is needed for 120 servings?
b. Extension: The mix is bought in 2\(\frac{1}{2}\)-pound bags. How many bags will be needed to make 120 servings?
Answer:

Given that,

Twenty servings of pancakes require 15 ounces of pancake mix.

20+20+20+20+20+20 = 120

Now, 6 x 15 = 90 ounces

Therefore, 90 ounces of pancake is needed for 120 servings.

b.

1 pound = 16 ounces

Given that mix is bought 2 1/2 pounds

Which means, 2 1/2 = 2 x 16 = 32 oz + 8 oz = 40 oz

40 oz x 2 = 80 ounces

Therefore, to make 120 servings  3 bags of mix will be need to purchase.

Because, 2 1/2 mix can only make 80 ounces which is nit enough..

Eureka Math Grade 4 Module 7 Lesson 14 Exit Ticket Answer Key

Use RDW to solve the following problem.
It took Gigi 1 hour and 20 minutes to complete a bicycle race. It took Johnny twice as long because he got a flat tire. How many minutes did it take Johnny to finish the race?
Answer:

The time taken by Gigi to complete his bicycle race = 1 hour 20 minutes

The time taken by Johnny is twice as long because he got a flat tire =

Which means,

1 hour 20 minutes + 1 hour 20 minutes = 2 hours 40 minutes

1 hour = 60 minutes

2 hours = 2 x 60 = 120 minutes

120 minutes + 40 minutes = 160 minutes

Therefore, it took Johnny 160 minutes to finish his bicycle race.

Eureka Math Grade 4 Module 7 Lesson 14 Homework Answer Key

Use RDW to solve the following problems.
Question 1.
Molly baked a pie for 1 hour and 45 minutes. Then, she baked banana bread for 35 minutes less than the pie. How many minutes did it take to bake the pie and the bread?
Answer:

The amount of time Molly backed a pie = 1 hour 45 minutes

Given that, the time taken to bake the banana bread is 35 minutes less

Which means, 1 hour 45 minutes – 35 minutes = 1 hour 10 minutes

Total time required to bake both the pie and bread :

1 hour 45 minutes + 1 hour 10 minutes = 2 hours 55 minutes.

Therefore, it took 2 hours 55 minutes to bake pie and banana bread.

Question 2.
A slide on the playground is 12\(\frac{1}{2}\) feet long. It is 3 feet 7 inches longer than the small slide. How long is the small slide?
Answer:

Given that, the length of the longer slide = 12 1/2  = 12 feet 6 inches

The length of smaller slide is 3 feet 7 inches shorter than longer slide.

Now,

12 feet 6 inches – 3 feet 7 inches = 8 feet 11 inches

Therefore, the length of smaller slide is 8 feet 11 inches.

Question 3.
The fish tank holds 8 gallons 2 quarts of water. Jeffrey poured 1\(\frac{3}{4}\) gallons into the empty tank. How much more water does he still need to pour into the tank to fill it?
Answer:

The quantity of water the fish tank can hold = 8 gallons 2 quarts

The quantity of water of Jeffrey poured into empty tank = 1 3/4 gallons or 1 gallon 3 quarts

Now,

8 gallons 2 quarts – 1 gallons 3 quarts = 6 gallons 1 quarts

Therefore, Jeffrey need to pour 6 gallons 1 quarts of water to fill the tank.

Question 4.
The candy shop puts 10 ounces of gummy bears in each box. How many boxes do they need to fill if there are 21\(\frac{1}{4}\) pounds of gummy bears?
Answer:

1 pound = 16 ounces

21 1/4 =

21 pounds x 16 = 336 ounces

1/4 = 4 ounces

Total : 336 + 4 = 340 ounces

Given that,

The number of gummy bears the candy shop puts in each box = 10

Now, 340 / 10 = 34

Therefore, they need to fill 34 boxes.

Question 5.
Mom can make 10 brownies from a 12-ounce package.
a. How many ounces of brownie mix would be needed to make 50 brownies?
b. Extension: The brownie mix is also sold in 1\(\frac{1}{2}\)-pound bags. How many bags would be needed to make 120 brownies?
Answer:

a.

Given that,

Mom can make 10 brownies from a 12- ounce package.

The amount of brownie mix she need to make 50 brownies  =

12 x 5 = 60

Therefore, 60 ounces of brownie mix is needed to make 50 brownies

b.

1 pound = 16 ounces

1 1/2 =

16 ounces + 8 ounces = 24 ounces

Given , 10 brownies are made from 12 ounce brownie mix

Now, 10 x 12 =120

12 x 12 = 144 ounces

Now, 144 ounces / 24 ounces = 6

Therefore, 6 bags are needed to make 120 brownies.

Engage NY Eureka Math 4th Grade Module 7 Lesson 13 Answer Key

Eureka Math Grade 4 Module 7 Lesson 13 Problem Set Answer Key

Question 1.
Solve.

a. \(\frac{1}{16}\) pound = _______ ounce
b. \(\frac{}{16}\) pound = \(\frac{1}{2}\) pound = _______ ounces
c. \(\frac{}{16}\) pound = \(\frac{1}{4}\) pound = _______ ounces
d. \(\frac{}{16}\) pound = \(\frac{3}{4}\) pound = _______ ounces
e. \(\frac{}{16}\) pound = \(\frac{1}{8}\) pound = _______ ounces
f. \(\frac{}{16}\) pound = \(\frac{3}{8}\) pound = _______ ounces
Answer:

a. \(\frac{1}{16}\) pound = 1 ounce
b. \(\frac{8}{16}\) pound = \(\frac{1}{2}\) pound = 8 ounces
c. \(\frac{4}{16}\) pound = \(\frac{1}{4}\) pound = 4 ounces
d. \(\frac{12}{16}\) pound = \(\frac{3}{4}\) pound = 12 ounces
e. \(\frac{2}{16}\) pound = \(\frac{1}{8}\) pound = 2 ounces
f. \(\frac{6}{16}\) pound = \(\frac{3}{8}\) pound = 6 ounces

Question 2.
Draw a tape diagram to show 2\(\frac{1}{2}\) pounds = 40 ounces.
Answer:

1 pound = 16 ounces

2 1/2 = 40 ounces

Question 3.

a. \(\frac{1}{60}\) hour = _______ minute
b. \(\frac{}{60}\) hour = \(\frac{1}{2}\) hour = _______ minutes
c. \(\frac{}{60}\) hour = \(\frac{1}{4}\) hour = _______ minutes
Answer:

a. \(\frac{1}{60}\) hour = 1 minute
b. \(\frac{30}{60}\) hour = \(\frac{1}{2}\) hour = 30 minutes
c. \(\frac{15}{60}\) hour = \(\frac{1}{4}\) hour = 15 minutes

Question 4.
Draw a tape diagram to show that 1\(\frac{1}{2}\) hours = 90 minutes.
Answer:

1 hour = 60 minutes

So, 1 1/2 hours = 60 + 30 = 90 minutes

Question 5.
a. 1\(\frac{1}{8}\)pounds = _____ ounces
Answer:

1\(\frac{1}{8}\)pounds = 18 ounces

b. 3\(\frac{3}{8}\) pounds = _______ ounces
Answer:

3\(\frac{3}{8}\) pounds = 54 ounces

c. 5\(\frac{3}{4}\) lb = _______ oz
Answer:

5\(\frac{3}{4}\) lb = 92 oz

d. 5\(\frac{1}{2}\) lb = ________ oz
Answer:

5\(\frac{1}{2}\) lb = 88 oz

e. 1\(\frac{1}{4}\) hours = _______ minutes
Answer:

1\(\frac{1}{4}\) hours = 75 minutes

f. 3\(\frac{1}{2}\) hours = _______ minutes
Answer:

3\(\frac{1}{2}\) hours = 210 minutes

g. 2\(\frac{1}{4}\) hr = _______ min
Answer:

2\(\frac{1}{4}\) hr = 135 min

h. 5\(\frac{1}{2}\) hr = _______ min
Answer:

5\(\frac{1}{2}\) hr = 330 min

i. 3\(\frac{1}{3}\) yards = ________ feet
Answer:

3\(\frac{1}{3}\) yards = 10 feet

j. 7\(\frac{2}{3}\) yd = ________ ft
Answer:

7\(\frac{2}{3}\) yd = 23 ft

k. 4\(\frac{1}{2}\) gallons = ________ quarts
Answer:

4\(\frac{1}{2}\) gallons = 18 quarts

l. 6\(\frac{3}{4}\) gal = ________ qt
Answer:

6\(\frac{3}{4}\) gal = 27 qt

m. 5\(\frac{3}{4}\) feet = _______ inches
Answer:

5\(\frac{3}{4}\) feet = 69 inches

n. 8\(\frac{1}{3}\) ft = _______ in
Answer:

8\(\frac{1}{3}\) ft =  100 in

Eureka Math Grade 4 Module 7 Lesson 13 Exit Ticket Answer Key

Question 1.
Draw a tape diagram to show that 4\(\frac{3}{4}\) gallons = 19 quarts.
Answer:

1 gallon = 4 quarts

So, 4 3/4 gallons = 19 quarts

Question 2.
Solve.
a. 1\(\frac{1}{4}\) pounds = _______ ounces
Answer:

1\(\frac{1}{4}\) pounds = 20 ounces

b. 2\(\frac{3}{4}\) hr = _____ min
Answer:

2\(\frac{3}{4}\) hr = 165 min

c. 5\(\frac{1}{2}\) feet = ________ inches
Answer:

5\(\frac{1}{2}\) feet = 66 inches

d. 3\(\frac{5}{6}\) ft = _________ in
Answer:

3\(\frac{5}{6}\) ft =  46 in

Eureka Math Grade 4 Module 7 Lesson 13 Homework Answer Key

Question 1.
Solve.

a. \(\frac{1}{16}\) pound = _______ ounce
b. \(\frac{}{16}\) pound = \(\frac{1}{2}\) pound = _______ ounces
c. \(\frac{}{16}\) pound = \(\frac{1}{4}\) pound = _______ ounces
d. \(\frac{}{16}\) pound = \(\frac{3}{4}\) pound = _______ ounces
e. \(\frac{}{16}\) pound = \(\frac{1}{8}\) pound = _______ ounces
f. \(\frac{}{16}\) pound = \(\frac{5}{8}\) pound = _______ ounces
Answer:

a. \(\frac{1}{16}\) pound = 1 ounce
b. \(\frac{8}{16}\) pound = \(\frac{1}{2}\) pound = 8 ounces
c. \(\frac{4}{16}\) pound = \(\frac{1}{4}\) pound = 4 ounces
d. \(\frac{12}{16}\) pound = \(\frac{3}{4}\) pound = 12 ounces
e. \(\frac{2}{16}\) pound = \(\frac{1}{8}\) pound = 2 ounces
f. \(\frac{10}{16}\) pound = \(\frac{5}{8}\) pound = 10 ounces

Question 2.
Draw a tape diagram to show 1\(\frac{1}{4}\) pounds = 20 ounces.
Answer:

1 pound = 16 ounces

So, 1 1/4 = 20 ounces.

Question 3.
Solve.

a. \(\frac{1}{60}\) hour = _______ minute
b. \(\frac{}{60}\) hour = \(\frac{1}{2}\) hour = _______ minutes
c. \(\frac{}{60}\) hour = \(\frac{1}{4}\) hour = _______ minutes
d. \(\frac{}{60}\) hour = \(\frac{1}{3}\) hour = _______ minutes
Answer:

a. \(\frac{1}{60}\) hour = 1 minute
b. \(\frac{30}{60}\) hour = \(\frac{1}{2}\) hour = 30 minutes
c. \(\frac{15}{60}\) hour = \(\frac{1}{4}\) hour = 15 minutes
d. \(\frac{20}{60}\) hour = \(\frac{1}{3}\) hour = 20 minutes

Question 4.
Draw a tape diagram to show that 2\(\frac{1}{4}\) hours = 135 minutes.
Answer:

1 hour = 60 minutes

So, 2 1/4 = 135 minutes

Question 5.
Solve.
a. 2\(\frac{1}{2}\) pounds = _______ounces
Answer:

2\(\frac{1}{2}\) pounds = 36 ounces

b. 4\(\frac{7}{8}\) pounds = _________ ounces
Answer:

4\(\frac{7}{8}\) pounds = 78 ounces

c. 6\(\frac{3}{4}\) lb = ________ oz
Answer:

6\(\frac{3}{4}\) lb = 108 oz

d. 4\(\frac{1}{8}\) lb = ________ oz
Answer:

4\(\frac{1}{8}\) lb = 66 oz

e. 1\(\frac{3}{4}\) hours = ________ minutes
Answer:

1\(\frac{3}{4}\) hours = 105 minutes

f. 4\(\frac{1}{2}\) hours = ________ minutes
Answer:

4\(\frac{1}{2}\) hours = 270 minutes

g. 3\(\frac{3}{4}\) hr = _______ min
Answer:

3\(\frac{3}{4}\) hr = 225 min

h. 5\(\frac{1}{3}\) hr = _________ min
Answer:

5\(\frac{1}{3}\) hr = 320 min

i. 4\(\frac{2}{3}\) yards = ______ feet
Answer:

4\(\frac{2}{3}\) yards = 14 feet

j. 6\(\frac{1}{3}\) yd = _______ ft
Answer:

6\(\frac{1}{3}\) yd = 19 ft

k. 4\(\frac{1}{4}\) gallons = ________ quarts
Answer:

4\(\frac{1}{4}\) gallons = 17 quarts

l. 2\(\frac{3}{4}\) gal = ________ qt
Answer:

2\(\frac{3}{4}\) gal = 11 qt

m. 6\(\frac{1}{4}\) feet = ________ inches
Answer:

6\(\frac{1}{4}\) feet = 75 inches

n. 9\(\frac{5}{6}\) ft = ________ in
Answer:

9\(\frac{5}{6}\) ft = 118 in

Engage NY Eureka Math 4th Grade Module 7 Lesson 12 Answer Key

Eureka Math Grade 4 Module 7 Lesson 12 Problem Set Answer Key

Question 1.
Draw a tape diagram to show 1 yard divided into 3 equal parts.
a. \(\frac{1}{3}\) yd = _________ ft
b. \(\frac{2}{3}\) yd = _________ ft
c. \(\frac{3}{3}\) yd = _________ ft
Answer:

a. \(\frac{1}{3}\) yd = 1 ft
b. \(\frac{2}{3}\) yd = 2 ft
c. \(\frac{3}{3}\) yd = 3 ft

Question 2.
Draw a tape diagram to show 2\(\frac{2}{3}\) yards = 8 feet.
Answer:

1 yard = 3 feet

2 2/3 yard = 8 feet

Question 3.
Draw a tape diagram to show \(\frac{3}{4}\) gallon = 3 quarts.
Answer:

1 gallon = 4 quarts

So, 3/4 gallons = 3 quarts

Question 4.
Draw a tape diagram to show 3\(\frac{3}{4}\) gallons = 15 quarts.
Answer:

1 gallon = 4 quarts

So, 3 3/4 gallons = 15 quarts

Question 5.
Solve the problems using whatever tool works best for you.

a. \(\frac{1}{12}\) ft = _______ in
b. \(\frac{}{12}\) ft = \(\frac{1}{2}\) ft = _______ in
c. \(\frac{}{12}\) ft = \(\frac{1}{4}\) ft = _______ in
d. \(\frac{}{12}\) ft = \(\frac{3}{4}\) ft = _______ in
e. \(\frac{}{12}\) ft = \(\frac{1}{3}\) ft = _______ in
f. \(\frac{}{12}\) ft = \(\frac{2}{3}\) ft = _______ in
Answer:

a. \(\frac{1}{12}\) ft = 1 in
b. \(\frac{6}{12}\) ft = \(\frac{1}{2}\) ft = 6 in
c. \(\frac{3}{12}\) ft = \(\frac{1}{4}\) ft = 3 in
d. \(\frac{9}{12}\) ft = \(\frac{3}{4}\) ft = 9 in
e. \(\frac{4}{12}\) ft = \(\frac{1}{3}\) ft = 4 in
f. \(\frac{8}{12}\) ft = \(\frac{2}{3}\) ft = 8 in

Question 6.
Solve.
a. 1\(\frac{1}{3}\) yd = _______ ft
Answer:

1\(\frac{1}{3}\) yd = 4 ft

b. 4\(\frac{2}{3}\) yd = _______ ft
Answer:

4\(\frac{2}{3}\) yd = 14 ft

c. 2\(\frac{1}{2}\) gal = ______ qt
Answer:

2\(\frac{1}{2}\) gal = 10 qt

d. 7\(\frac{3}{4}\) gal = _______ qt
Answer:

7\(\frac{3}{4}\) gal = 31 qt

e. 1\(\frac{1}{2}\) ft = ______ in
Answer:

1\(\frac{1}{2}\) ft = 18 in

f. 6\(\frac{1}{2}\) ft = ______ in
Answer:

6\(\frac{1}{2}\) ft = 78 in

g. 1\(\frac{1}{4}\) ft = ______ in
Answer:

1\(\frac{1}{4}\) ft = 15 in

h. 6\(\frac{1}{4}\) ft = _______ in
Answer:

6\(\frac{1}{4}\) ft = 75 in

Eureka Math Grade 4 Module 7 Lesson 12 Exit Ticket Answer Key

Question 1.
Solve the problems using whatever tool works best for you.

a. \(\frac{}{12}\) ft = \(\frac{1}{2}\) ft = _______in
b. \(\frac{}{12}\) ft = \(\frac{3}{4}\) ft = _______in
Answer:

a. \(\frac{6}{12}\) ft = \(\frac{1}{2}\) ft = 6 in
b. \(\frac{9}{12}\) ft = \(\frac{3}{4}\) ft = 9 in

Question 2.
Solve.
a. 1\(\frac{1}{3}\) yd = ______ ft
Answer:

1\(\frac{1}{3}\) yd = 4  ft

b. 5\(\frac{3}{4}\) gal = ________ qt
Answer:

5\(\frac{3}{4}\) gal = 23 qt

Eureka Math Grade 4 Module 7 Lesson 12 Homework Answer Key

Question 1.
Draw a tape diagram to show 1\(\frac{1}{3}\) yards = 4 feet.
Answer:

1 yard = 3 feet

3 feet + 1 foot = 4 feet

So, 1 1/3 yards = 4 feet

Question 2.
Draw a tape diagram to show \(\frac{1}{2}\) gallon = 2 quarts.
Answer:

1 gallon = 4 quarts

So, 1/2 gallon = 2 quarts

Question 3.
Draw a tape diagram to show 1\(\frac{3}{4}\) gallons = 7 quarts.
Answer:

1 gallon = 4 quarts

3/4 gallon = 3 quarts

So, 1 3/4 gallons = 7 quarts.

Question 4.
Solve the problems using whatever tool works best for you.

a. \(\frac{1}{2}\) foot = _______inches
b. \(\frac{}{12}\)foot = \(\frac{1}{4}\) foot = _______inches
c. \(\frac{}{12}\) foot = \(\frac{1}{6}\) foot = _______inches
d. \(\frac{}{12}\) foot = \(\frac{1}{3}\) foot = _______inches
e. \(\frac{}{12}\) foot = \(\frac{2}{3}\) foot = _______inches
f. \(\frac{}{12}\) foot = \(\frac{5}{6}\) foot = _______inches
Answer:

a. \(\frac{1}{2}\) foot = 6 inches
b. \(\frac{3}{12}\)foot = \(\frac{1}{4}\) foot = 3 inches
c. \(\frac{2}{12}\) foot = \(\frac{1}{6}\) foot = 2 inches
d. \(\frac{4}{12}\) foot = \(\frac{1}{3}\) foot = 4 inches
e. \(\frac{8}{12}\) foot = \(\frac{2}{3}\) foot = 8 inches
f. \(\frac{10}{12}\) foot = \(\frac{5}{6}\) foot = 10  inches

Question 5.
Solve.
a. 2\(\frac{2}{3}\) yd = _____ ft
Answer:

2\(\frac{2}{3}\) yd = 8 ft

b. 3\(\frac{1}{3}\) yd = ______ ft
Answer:

3\(\frac{1}{3}\) yd = 10 ft

c. 3\(\frac{1}{2}\)gal = _______ qt
Answer:

3\(\frac{1}{2}\)gal = 14 qt

d. 5\(\frac{1}{4}\)gal = _______ qt
Answer:

5\(\frac{1}{4}\)gal = 21 qt

e. 6\(\frac{1}{4}\)ft = ________ in
Answer:

6\(\frac{1}{4}\)ft = 75 in

f. 7\(\frac{1}{3}\)ft = ______ in
Answer:

7\(\frac{1}{3}\)ft = 88 in

g. 2\(\frac{1}{2}\)ft = _____ in
Answer:

2\(\frac{1}{2}\)ft = 30 in

h. 5\(\frac{3}{4}\)ft = _______ in
Answer:

5\(\frac{3}{4}\)ft = 69 in

i. 9\(\frac{2}{3}\)ft = _______ in
Answer:

9\(\frac{2}{3}\)ft = 116 in

j. 7\(\frac{5}{6}\)ft = ______ in
Answer:

7\(\frac{5}{6}\)ft = 94 in

Engage NY Eureka Math 4th Grade Module 7 Lesson 11 Answer Key

Eureka Math Grade 4 Module 7 Lesson 11 Problem Set Answer Key

Use RDW to solve the following problems.
Question 1.
Lauren ran a marathon and finished 1 hour 15 minutes after Amy, who had a time of 2 hours 20 minutes. Cassie finished 35 minutes after Lauren. How long did it take Cassie to run the marathon?
Answer:

The time taken by Amy to complete the run = 2 hours 20 minutes

The time taken by Lauren is 1 hour 15 minutes more

Which means, 2 hours 20 minutes + 1 hour 15 minutes = 3 hours 35 minutes

The time taken by Cassie to finish the run is 35 minutes more than Lauren

Which means, 3 hours 35 minutes + 35 minutes

= 3 hours 70 minutes

It is also written as 4 hours 10 minutes

Therefore, Cassie took 4 hours 10 minutes to run the marathon.

Question 2.
Chef Joe has 8 lb 4 oz of ground beef in his freezer. This is \(\frac{1}{3}\) of the amount needed to make the number of burgers he planned for a party. If he uses 4 oz of beef for each burger, how many burgers is he planning to make?
Answer:

The amount of beef Chef Joe has in his freezer = 8 lb 4 oz

Given that, 1/3 of the amount is needed to make the number of burgers

Now, 3 x ( 8 lb 4 oz )

= 24 lb 12 oz

24 lb is also written as 384 ounces

So, 384 ounces + 12 ounces = 396 ounces

If he uses 4 oz of beef for each burger

The number of burgers he is planning to make =

396 /4  = 99

Therefore, chef Joe is planning to make 99 burgers.

Question 3.
Sarah read for 1 hour 17 minutes each day for 6 days. If she took 3 minutes to read each page, how many pages did she read in 6 days?
Answer:

Given,

The time each day Sarah read for 6 days = 1 hour 17 minutes

1 hour 17 minutes = 77 minutes

77 minutes  x 6 days = 462 minutes

If she took 3 minutes to read each page , the number of pages she can read in 6 days =

462 / 3 = 154

In 6 days she can read 154 pages.

Question 4.
Grades 3, 4, and 5 have their annual field day together. Each grade level is given 16 gallons of water. If there are a total of 350 students, will there be enough water for each student to have 2 cups?
Answer:

We know that, 1 gallon = 16 cups

16 x 3 = 48 gallons

Now, 48 gallons in cups =

48 x 16 = 768 cups

We have 768 cups of water

Total number of students = 350

Now, 350 x 2 = 700 cups

Therefore, therefore is enough water for each student to have 2 cups.

Eureka Math Grade 4 Module 7 Lesson 11 Exit Ticket Answer Key

Use RDW to solve the following problem.
Judy spent 1 hour 15 minutes less than Sandy exercising last week. Sandy spent 50 minutes less than Mary, who spent 3 hours at the gym. How long did Judy spend exercising?
Answer:

Given,

The time spend by Mary at the gym = 3 hours

The time Sandy spend at the gym is 50 minutes less than Mary

Which means,

3 hours – 50 minutes

= 2 hours 10 minutes

The time Judy spent at the gym is 1 hour 15 minutes less than Sandy

Which means, 2 hours 10 minutes – 1 hour 15 minutes

= 55 minutes

Therefore, Judy spent 55 minutes for exercising.

Eureka Math Grade 4 Module 7 Lesson 11 Homework Answer Key

Use RDW to solve the following problems.
Question 1.
Ashley ran a marathon and finished 1 hour 40 minutes after P.J., who had a time of 2 hours 15 minutes. Kerry finished 12 minutes before Ashley. How long did it take Kerry to run the marathon?
Answer:

The time taken for p.j. to complete his run = 2 hours 15 minutes

The time taken for Ashley to finish his run is 1 hour 40 minutes after p.j.

Which means, 2 hours 15 minutes + 1 hour 40 minutes = 3 hours 55 minutes

The time taken for Kerry to finish his run is 12 minutes before Ashley

Which means,

3 hours 55 minutes – 12 minutes = 3 hours 43 minutes

Therefore, Kerry took 3 hours 43 minutes to run the marathon.

Question 2.
Mr. Foote’s deck is 12 ft 6 in wide. Its length is twice the width plus 3 more inches. How long is the deck?
Answer:

Given,

The wide of deck = 12 feet 6 in

Also given, The length is twice the width plus 3 more inches

So, 12 feet 6 inches + 12 feet 6 inches + 3 inches

= 24 feet 15 inches

We, know that, 1 feet = 12 inches

Therefore, the deck is 25 feet 3 inches long.

Question 3.
Mrs. Lorentz bought 12 pounds 8 ounces of sugar. This is \(\frac{1}{4}\) of the sugar she will use to make sugar cookies in her bakery this week. If she uses 10 ounces of sugar for each batch of sugar cookies, how many batches of sugar cookies will she make in a week?
Answer:

Given,

The amount of sugar Mrs. Lorentz bought = 12 pounds 8 ounces

We know that, 1 pound = 16 ounces

12 pounds 8 ounces = 200 ounces

If she uses 10 ounces of sugar

The number of batches of sugar cookies she will make in a week

= 200 / 10 = 20

Therefore, she will make 20 batches of cookies.

Question 4.
Beth Ann practiced piano for 1 hour 5 minutes each day for 1 week. She had 5 songs to practice and spent the same amount of time practicing each song. How long did she practice each song during the week?
Answer:

Given that,

The time Beth Ann spent to practice piano for 1 week = 1 hour 5 minutes

Total number of songs = 5

1 hour 5 minutes = 65 minutes

65 minutes x 7 days = 455 minutes

Now, 455 / 5 = 91

Therefore, Beth Ann practiced each song for 91 minutes.

Question 5.
The concession stand has 18 gallons of punch. If there are a total of 240 students who want to purchase 1 cup of punch each, will there be enough punch for everyone?
Answer:

Total number of students = 240

We know that,

1 gallon = 4 quart = 8 pints = 16 cups

1 pint = 2 cups

Now,

240 x 2 = 480 cups

Therefore, There will be enough punch for everyone.