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Eureka Math Grade 5 Module 4 Lesson 29 Answer Key

Engage ny eureka math 5th grade module 4 lesson 29 answer key, eureka math grade 5 module 4 lesson 29 problem set answer key.

Question 1. Divide. Rewrite each expression as a division sentence with a fraction divisor, and fill in the blanks. The first one is done for you.

Example: 2 ÷ 0.1 = 2 ÷ \(\frac{1}{10}\) = 20 There are 10 tenths in 1 whole. There are 20 tenths in 2 wholes.

a. 5 ÷ 0.1 There are ____ tenths in 1 whole. There are ____ tenths in 5 wholes.

Answer: There are 10 tenths in 1 whole. There are 50 tenths in 5 wholes.

Explanation: Given that 5 ÷ 0.1 which is 50. In that, there are 10 tenths in 1 whole and there are 50 tenths in 5 wholes.

There are ____ tenths in 1 whole. There are ____ tenths in 8 wholes.

Answer: There are 10 tenths in 1 whole. There are 8 tenths in 5 wholes.

Explanation: Given that 8 ÷ 0.1 which is 80. In that, there are 10 tenths in 1 whole and there are 80 tenths in 8 wholes.

c. 5.2 ÷ 0.1

There are tenths in 5 wholes. There are ____ tenths in 2 tenths. There are ____ tenths in 5.2.

Answer: There are 2 tenths in 2 tenths. There are 52 tenths in 5.2.

d. 8.7 ÷ 0.1 There are ____ tenths in 8 wholes. There are ____ tenths in 7 tenths. There are ____ tenths in 8.7.

Answer: There are 80 tenths in 8 wholes. There are 7 tenths in 7 tenths. There are 87 tenths in 8.7.

Explanation: Given that 8.7 ÷ 0.1 which is 87. In that, there are 80 tenths in 8 whole and there are 7 tenths in 7 tenths and there are 87 tenths in 8.7.

e. 5 ÷ 0.01 There are 100 hundredths in 1 whole. There are 500 hundredths in 5 wholes.

Answer: There are ____ hundredths in 1 whole. There are ____ hundredths in 5 wholes.

Explanation: Given that 5 ÷ 0.01 which is 500. In that, there are 100 hundredths in 1 whole and there are 500 hundredths in 5 wholes.

f. 8 ÷ 0.01 There are ____ hundredths in 1 whole. There are ____ hundredths in 8 wholes.

Answer: There are 100 hundredths in 1 whole. There are 800 hundredths in 8 wholes.

Explanation: Given that 8 ÷ 0.01 which is 800. In that, there are 100 hundredths in 1 whole and there are 800 hundredths in 8 wholes.

g. 5.2 ÷ 0.01 There are ____ hundredths in 5 wholes. There are ____ hundredths in 2 tenths. There are ____ hundredths in 5.2.

Answer: There are 500 hundredths in 1 whole. There are 20 hundredths in 5 tenths. There are 520 hundredths in 5.2.

Explanation: Given that 5.2 ÷ 0.01 which is 520. In that, there are 500 hundredths in 1 whole and there are 20 hundredths in 5 tenths and there are 520 hundredths in 5.2.

h. 8.7 ÷ 0.01 There are ____ hundredths in 8 wholes. There are ____ hundredths in 7 tenths. There are ____ hundredths in 8.7.

Answer: There are 800 hundredths in 8 whole. There are 70 hundredths in 7 tenths. There are 870 hundredths in 8.7.

Explanation: Given that 8.7 ÷ 0.01 which is 870. In that, there are 800 hundredths in 8 whole and there are 70 hundredths in 7 tenths and there are 870 hundredths in 8.7.

Question 2. Divide. a. 6 ÷ 0.1

Answer: 6 ÷ 0.1 = 60.

Explanation: The division of 6 ÷ 0.1 is 60.

b. 18 ÷ 0.1

Answer: 18 ÷ 0.1 = 180.

Explanation: The division of 18 ÷ 0.1 is 180.

c. 6 ÷ 0.01

Answer: 6 ÷ 0.01 = 600.

Explanation: The division of 6 ÷ 0.01 is 600.

d. 1.7 ÷ 0.1

Answer: 1.7 ÷ 0.1 = 17.

Explanation: The division of 1.7 ÷ 0.1 is 17.

e. 31 ÷ 0.01

Answer: 31 ÷ 0.01 = 3,100.

Explanation: The division of 31 ÷ 0.01 is 3,100.

f. 11 ÷ 0.01

Answer: 11 ÷ 0.01 = 1,100.

Explanation: The division of 11 ÷ 0.01 is 1,100.

g. 125 ÷ 0.1

Answer: 125 ÷ 0.1 = 1,250.

Explanation: The division of 125 ÷ 0.1 is 1,250.

h. 3.74 ÷ 0.01

Answer: 3.74 ÷ 0.01 = 374.

Explanation: The division of 3.74 ÷ 0.01 is 374.

i. 12.5 ÷ 0.01

Answer: 12.5 ÷ 0.01 = 1,250.

Explanation: The division of 12.5 ÷ 0.01 is 1,250.

Question 3. Yung bought $4.60 worth of bubble gum. Each piece of gum cost $0.10. How many pieces of bubble gum did Yung buy?

Answer: Yung bought 46 pieces of gum.

Explanation: Here, Yung bought $4.60 worth of bubble gum, and each piece of gum cost $0.10. So the number of pieces of bubble gum did Yung bought is $4.60 ÷ $0.10 = $46. So Yung bought 46 pieces of gum.

Question 4. Cheryl solved a problem: 84 ÷ 0.01 = 8,400. Jane said, “Your answer is wrong because when you divide, the quotient is always smaller than the whole amount you start with, for example, 6 ÷ 2 = 3 and 100 ÷ 4 = 25.” Who is correct? Explain your thinking.

Answer: Some examples are, 84 ÷ 1 = 84, 84 ÷ 10 = 8.4, 84 ÷ 0.1 = 840.

Explanation: Cheryl is correct and Jane is correct only some of the time and Cheryl can help Jane understand by showing some examples like, 84 ÷ 1 = 84, 84 ÷ 10 = 8.4, 84 ÷ 0.1 = 840.

Question 5. The U.S. Mint sells 2 ounces of American Eagle gold coins to a collector. Each coin weighs one-tenth of an ounce. How many gold coins were sold to the collector? Answer: The number of gold coins was sold to the collector is 20 gold coins.

Explanation: Here, U.S. Mint sells 2 ounces of American Eagle gold coins to a collector and each coin weighs one-tenth of an ounce, so the number of gold coins were sold to the collector is 2 ÷ 1/10 which is 2 ÷ 0.1 = 20 gold coins.

Eureka Math Grade 5 Module 4 Lesson 29 Exit Ticket Answer Key

Question 1. 8.3 is equal to _______ tenths _______ hundredths Answer: 83 tenths 830 hundredths.

Explanation: Given that the number is 8.3 which is equal to 83 tenths and 830 hundred.

Question 2. 28 is equal to _______ hundredths _______ tenths Answer: 2800 tenths 830 hundredths.

Question 3. 15.09 ÷ 0.01 = _______ Answer: 15.09 ÷ 0.01 = 1,509.

Explanation: Given that the equation is 15.09 ÷ 0.01 which is equal to 1,509.

Question 4. 267.4 ÷ \(\frac{1}{10}\) = _______ Answer: 267.4 ÷ \(\frac{1}{10}\) = 2,674

Explanation: Given that the equation is 267.4 ÷ \(\frac{1}{10}\) which is equal to 2,674.

Question 5. 632.98 ÷ \(\frac{1}{100}\) = _______ Answer: 632.98 ÷ \(\frac{1}{100}\) = 63,298

Explanation: Given that the equation is 632.98 ÷ \(\frac{1}{100}\) which is equal to 63,298.

Eureka Math Grade 5 Module 4 Lesson 29 Homework Answer Key

Question 1. Divide. Rewrite each expression as a division sentence with a fraction divisor, and fill in the blanks. The first one is done for you. a. 9 ÷ 0.1 There are ______ tenths in 1 whole. There are ______ tenths in 9 wholes.

Answer: There are 10 tenths in 1 whole. There are 90 tenths in 9 wholes.

Explanation: Given that 9 ÷ 0.1 which is 90. In that, there are 10 tenths in 1 whole and there are 90 tenths in 9 wholes.

b. 6 ÷ 0.1 There are ______ tenths in 1 whole. There are ______ tenths in 6 wholes.

Answer: There are 10 tenths in 1 whole. There are 60 tenths in 6 wholes.

Explanation: Given that 6 ÷ 0.1 which is 60. In that, there are 10 tenths in 1 whole and there are 60 tenths in 6 wholes.

c. 3.6 ÷ 0.1 There are ______ tenths in 3 wholes. There are ______ tenths in 6 tenths. There are ______ tenths in 3.6.

Answer: There are 30 tenths in 3 wholes. There are 6 tenths in 6 tenths. There are 36 tenths in 3.6.

Explanation: Given that 3.6 ÷ 0.1 which is 36. In that, there are 30 tenths in 3 wholes and there are 6 tenths in 6 tenths and there are 36 tenths in 3.6.

d. 12.8 ÷ 0.1 There are ______ tenths in 12 wholes. There are ______ tenths in 8 tenths. There are ______ tenths in 12.8.

Answer: There are 120 tenths in 12 wholes. There are 8 tenths in 8 tenths. There are 128 tenths in 12.8.

Explanation: Given that 12.8 ÷ 0.1 which is 128. In that, there are 120 tenths in 12 wholes and there are 8 tenths in 8 tenths and there are 128 tenths in 12.8.

e. 3 ÷ 0.1 There are ______ tenths in 1 whole. There are ______ tenths in 3 wholes.

Answer: There are 100 tenths in 1 whole. There are 300 tenths in 3 wholes.

Explanation: Given that 3 ÷ 0.1 which is 30. In that, there are 100 tenths in 1 whole and there are 300 tenths in 3 wholes.

f. 7 ÷ 0.1 There are ______ tenths in 1 whole. There are ______ tenths in 7 wholes.

Answer: There are 100 tenths in 1 whole. There are 700 tenths in 7 wholes.

Explanation: Given that 7 ÷ 0.1 which is 70. In that, there are 100 tenths in 1 whole and there are 700 tenths in 7 wholes.

g. 4.7 ÷ 0.01 There are ______ tenths in 4 wholes. There are ______ tenths in 7 tenths. There are ______ tenths in 4.7.

Answer: There are 400 tenths in 4 wholes. There are 70 tenths in 7 tenths. There are 470 tenths in 4.7.

Explanation: Given that 4.7 ÷ 0.01 which is 470. In that, there are 400 tenths in 4 wholes and there are 70 tenths in 7 tenths and there are 470 tenths in 4.7.

h. 11.3 ÷ 0.01 There are ______ tenths in 11 wholes. There are ______ tenths in 3 tenths. There are ______ tenths in 11.3.

Answer: There are 1100 tenths in 11 wholes. There are 30 tenths in 3 tenths. There are 1130 tenths in 11.3.

Explanation: Given that 11.3 ÷ 0.01 which is 1,130. In that, there are 1100 tenths in 11 wholes and there are 30 tenths in 3 tenths and there are 1130 tenths in 11.3.

Question 2. Divide. a. 2 ÷ 0.1

Answer: 2 ÷ 0.1 = 20.

Explanation: The division of 2 ÷ 0.1 is 20.

b. 23 ÷ 0.1

Answer: 23 ÷ 0.1 = 230.

Explanation: The division of 23 ÷ 0.1 is 230.

c. 5 ÷ 0.01

Answer: 5 ÷ 0.01 = 500.

Explanation: The division of 5 ÷ 0.01 is 500.

d. 7.2 ÷ 0.1

Answer: 7.2 ÷ 0.1 = 72.

Explanation: The division of 7.2 ÷ 0.1 is 72.

e. 51 ÷ 0.01

Answer: 51 ÷ 0.01 = 5,100.

Explanation: The division of 51 ÷ 0.01 is 5,100.

f. 31 ÷ 0.1

Answer: 31 ÷ 0.1 = 310.

Explanation: The division of 31 ÷ 0.1 is 310.

g. 231 ÷ 0.1

Answer: 231 ÷ 0.1 = 2,310.

Explanation: The division of 231 ÷ 0.1 is 2,310.

h. 4.37 ÷ 0.01

Answer: 4.37 ÷ 0.01 = 437.

Explanation: The division of 4.37 ÷ 0.01 is 437.

i. 24.5 ÷ 0.01

Answer: 24.5 ÷ 0.01 = 2,450.

Explanation: The division of 24.5 ÷ 0.01 is 2,450.

Question 3. Giovanna is charged $0.01 for each text message she sends. Last month, her cell phone bill included a $12.60 charge for text messages. How many text messages did Giovanna send? Answer: The number of text messages did Giovanna send is 1,260.

Explanation: Here, Giovanna is charged $0.01 for each text message she sends, and in last month, her cell phone bill included a $12.60 charge for text messages. So the number of text messages did Giovanna send is $12.60 ÷ $0.01 which is 1,260.

Question 4. Geraldine solved a problem: 68.5 ÷ 0.01 = 6,850. Ralph said, “This is wrong because a quotient can’t be greater than the whole you start with. For example, 8 ÷ 2 = 4 and 250 ÷ 5 = 50.” Who is correct? Explain your thinking. Answer: Geraldine was correct.

Explanation: Geraldine was correct. As quotient can be greater than the whole start. So Geraldine was correct.

Question 5. The price for an ounce of gold on September 23, 2013, was $1,326.40. A group of 10 friends decide to equally share the cost of 1 ounce of gold. How much money will each friend pay? Answer: Each friend pays $1326.40 ÷ 10 which is $132.64.

Explanation: Here, the price for an ounce of gold on September 23, 2013, was $1,326.40 and a group of 10 friends decide to equally share the cost of 1 ounce of gold. So each friend pays $1326.40 ÷ 10 which is $132.64.

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Eureka Math Grade 5 Module 4 Lesson 24 Answer Key

Engage ny eureka math 5th grade module 4 lesson 24 answer key, eureka math grade 5 module 4 lesson 24 problem set answer key.

Question 1. A vial contains 20 mL of medicine. If each dose is \(\frac{1}{8}\) of the vial, how many mL is each dose? Express your answer as a decimal.

Answer: Each dose has a 2.5 ml dose.

Explanation: Here, a vial contains 20 mL of medicine, and if each dose is \(\frac{1}{8}\) of the vial, so each dose has \(\frac{1}{8}\) × 20 ml which is \(\frac{5}{2}\). So each dose has a 2.5 ml dose.

Question 2. A container holds 0.7 liters of oil and vinegar. \(\frac{3}{4}\) of the mixture is vinegar. How many liters of vinegar are in the container? Express your answer as both a fraction and a decimal.

Answer: The number of liters of vinegar is in the container is \(\frac{21}{40}\) liters. And in decimals it is 0.75 × 0.7 = 0.525 liters.

Explanation: Here, a container holds 0.7 liters of oil and vinegar and \(\frac{3}{4}\) of the mixture is vinegar, so the number of liters of vinegar is in the container is \(\frac{3}{4}\) × 0.7 = \(\frac{3}{4}\) × \(\frac{7}{10}\) = \(\frac{21}{40}\) liters. and in decimals it is 0.75 × 0.7 = 0.525 liters.

Question 3. Andres completed a 5-km race in 13.5 minutes. His sister’s time was 1\(\frac{1}{2}\) times longer than his time. How long, in minutes, did it take his sister to run the race?

Answer: His sister to run the race in 20.25 minutes.

Explanation: Here, Andres completed a 5-km race in 13.5 minutes, and his sister’s time was 1\(\frac{1}{2}\) times longer than his time. So his sister run the race in \(\frac{1}{2}\) of 13.5 which is 0.5 × 13.5 = 6.75. And his sister to run the race in 13.5 + 6.75 which is 20.25 minutes.

Question 4. A clothing factory uses 1,275.2 meters of cloth a week to make shirts. How much cloth is needed to make 3\(\frac{3}{5}\) times as many shirts?

Answer: The cloth needed is 4,509.72 meters.

Explanation: Here, a clothing factory uses 1,275.2 meters of cloth a week to make shirts which is, and the cloth needed to make shirts are 1,275.2 of 3\(\frac{3}{5}\) which is 1,275.2 × \(\frac{18}{5}\) = 4,509.72 meters.

Question 5. There are \(\frac{3}{4}\) as many boys as girls in a class of fifth-graders. If there are 35 students in the class, how many are girls?

Answer: The number of girls is 20 students.

Explanation: Given that there are \(\frac{3}{4}\) as many boys as girls in a class of fifth-graders and there are 35 students in the class, so the number of girls is, as the total of 7 units are the same as 35 students and for 1 unit it will be 35 ÷ 7 which is 5 students. So the number of girls is 4 × 5 = 20 students and the number of boys is 3 × 5 = 15 students.

Question 6. Ciro purchased a concert ticket for $56. The cost of the ticket was \(\frac{4}{5}\) the cost of his dinner. The cost of his hotel was 2\(\frac{1}{2}\) times as much as his ticket. How much did Ciro spend altogether for the concert ticket, hotel, and dinner?

Answer: Ciro spends altogether for the concert ticket, hotel, and dinner is $266.

Explanation: Given that Ciro purchased a concert ticket for $56 and the cost of the ticket was \(\frac{4}{5}\) the cost of his dinner is, for 4 units it is 56, so for 1 unit it will be \(\frac{56}{4}\) which is 14, and for dinner, it is 5 × 14 = 70. The cost of his hotel was 2\(\frac{1}{2}\) times as much as his ticket, so 2.5 × 56 which is 140. So altogether it will be 140 + 70 + 56 which is 266. Ciro spends altogether for the concert ticket, hotel, and dinner is $266.

Eureka Math Grade 5 Module 4 Lesson 24 Exit Ticket Answer Key

Question 1. An artist builds a sculpture out of metal and wood that weighs 14.9 kilograms. \(\frac{3}{4}\) of this weight is metal, and the rest is wood. How much does the wood part of the sculpture weigh?

Answer: The wooden part is 3.725 kilograms.

Explanation: Given that an artist builds a sculpture out of metal and wood that weighs 14.9 kilograms and \(\frac{3}{4}\) of this weight is metal, and the rest is wood. So the weight of the sculpture is, as metal part is \(\frac{3}{4}\) × 14.9 which is 11.175 kilograms and the wooden part is 14.9 – 11.175 = 3.725 kilograms.

Question 2. On a boat tour, there are half as many children as there are adults. There are 30 people on the tour. How many children are there?

Answer: The number of children is 10 children.

Explanation: The total number of people is 30 and a half as many children as there are adults which means the number of children is \(\frac{1}{2}\). Let the number of adults be X and the equation is X + X \(\frac{1}{2}\) = 30, now we will multiply both side by 2. So 2X + X = 60, 3X = 60 X = 20. So the number of children is \(\frac{1}{2}\) × 20 = 10 children.

Eureka Math Grade 5 Module 4 Lesson 24 Homework Answer Key

Question 1. Jesse takes his dog and cat for their annual vet visit. Jesse’s dog weighs 23 pounds. The vet tells him his cat’s weight is \(\frac{5}{8}\) as much as his dog’s weight. How much does his cat weigh?

Answer: The weight of the cat is 14.375 pounds.

Explanation: Given that Jesse takes his dog and cat for their annual vet visit and Jesse’s dog weighs 23 pounds and the vet tells him his cat’s weight is \(\frac{5}{8}\) as much as his dog’s weight. So the weight of the cat is 23 × \(\frac{5}{8}\) which is 23 × 0.625 = 14.375 pounds.

Question 2. An image of a snowflake is 1.8 centimeters wide. If the actual snowflake is \(\frac{1}{8}\) the size of the image, what is the width of the actual snowflake? Express your answer as a decimal.

Answer: The width of the actual snowflake is 0.225 cm.

Explanation: Given that the image of a snowflake is 1.8 centimeters wide and the actual snowflake is \(\frac{1}{8}\) the size of the image, and the width of the actual snowflake is 1.8 × \(\frac{1}{8}\) which is 0.225 cm.

Question 3. A community bike ride offers a short 5.7-mile ride for children and families. The short ride is followed by a long ride, 5\(\frac{2}{3}\) times as long as the short ride, for adults. If a woman bikes the short ride with her children and then the long ride with her friends, how many miles does she ride altogether?

Answer: The adult ride and children ride altogether 38.019 miles.

Explanation: As a community bike ride offers a short 5.7-mile ride for children and families and the short ride is followed by a long ride, 5\(\frac{2}{3}\) times as long as the short ride, for adults. So if a woman bikes the short ride with her children and then the long ride with her friends, so the adult ride is  5.7 ×  5\(\frac{2}{3}\) which is 5.7 × 5.67 = 32.319. Now we will add the adult ride and children ride altogether, which is 5.7 + 32.319 = 38.019 miles.

Question 4. Sal bought a house for $78,524.60. Twelve years later he sold the house for 2\(\frac{3}{4}\) times as much. What was the sale price of the house?

Answer: The sale price of the house is $ 215,942.65.

Explanation: Here, Sal bought a house for $78,524.60 and twelve years later he sold the house for 2\(\frac{3}{4}\) times as much. So the sale price of the house is 2\(\frac{3}{4}\) × 78,524.60 which is 2.75 × 78,524.60 = $ 215,942.65.

Question 5. In the fifth grade at Lenape Elementary School, there are \(\frac{4}{5}\) as many students who do not wear glasses as those who do wear glasses. If there are 60 students who wear glasses, how many students are in the fifth grade?

Answer: The number of students are in fifth grade is 300 students.

Explanation: Given that there are \(\frac{4}{5}\) as many students who do not wear glasses as those who do wear glasses and the total number of students are equal with one or \(\frac{5}{5}\) which means the proportion of user who wear glasses is \(\frac{5}{5}\) – \(\frac{4}{5}\) which is \(\frac{1}{5}\) and from the information we can process (\(\frac{4}{5}\) ÷ \(\frac{5}{5}\)) × 60 on solving we will get the result as 240. So it means the total number of students in the class is accumulation between students without glasses is 240 + 60 = 300 students.

Question 6. At a factory, a mechanic earns $17.25 an hour. The president of the company earns 6\(\frac{2}{3}\) times as much for each hour he works. The janitor at the same company earns \(\frac{3}{5}\) as much as the mechanic. How much does the company pay for all three employees’ wages for one hour of work?

Answer: The company pay for all three employees wages for one hour of work is $142.60.

Explanation: Given that a factory, a mechanic earns $17.25 an hour and the president of the company earns 6\(\frac{2}{3}\) times as much for each hour he works, so presidents wage is 6\(\frac{2}{3}\) × $17.25 which is $115. And the janitor at the same company earns \(\frac{3}{5}\) as much as the mechanic, so janitor wage is \(\frac{3}{5}\) × $17.25 which is $10.35. So the company pay for all three employees wages for one hour of work is $17.25 + $115 + $10.35 which is $142.60.

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