Eureka Math Grade 5 Module 4 Lesson 32 Answer Key

Engage ny eureka math 5th grade module 4 lesson 32 answer key, eureka math grade 5 module 4 lesson 32 problem set answer key.

Question 1. Circle the expression equivalent to the sum of 3 and 2 divided by \(\frac{1}{3}\). \(\frac{1}{2}\) 3 + (2 ÷ \(\frac{1}{3}\)) (3 + 2) ÷ \(\frac{1}{3}\) \(\frac{1}{3}\) ÷ (3 + 2) Answer:

Question 2. Circle the expression(s) equivalent to 28 divided by the difference between \(\frac{4}{5}\) and \(\frac{7}{10}\). 28 ÷ (\(\frac{4}{5}\) – \(\frac{7}{10}\)) \(\frac{28}{\frac{4}{5}-\frac{7}{10}}\) (\(\frac{4}{5}\) – \(\frac{7}{10}\)) ÷ 28 28 ÷ (\(\frac{7}{10}\) – \(\frac{4}{5}\)) Answer:

Question 3. Fill in the chart by writing an equivalent numerical expression.

a. Half as much as the difference between 2\(\frac{1}{4}\) and \(\frac{3}{8}\).
b. The difference between 2\(\frac{1}{4}\) and \(\frac{3}{8}\) divided by 4.
c. A third of the sum of \(\frac{7}{8}\) and 22 tenths.
d. Add 2.2 and \(\frac{7}{8}\), and then triple the sum.

Question 4. Compare expressions 3(a) and 3(b). Without evaluating, identify the expression that is greater. Explain how you know. Answer:

Question 5. Fill in the chart by writing an equivalent expression in word form.

a. \(\frac{3}{4}\) × (1.75 + \(\frac{3}{5}\))
b. \(\frac{1}{2}\) – (\(\frac{1}{8}\) × 0.2)
c. (1.75 + \(\frac{3}{5}\)) × \(\frac{4}{3}\)
d. 2 ÷ (\(\frac{1}{2}\) × \(\frac{4}{5}\) )

Question 6. Compare the expressions in 5(a) and 5(c). Without evaluating, identify the expression that is less. Explain how you know. Answer:

Question 7. Evaluate the following expressions. a. (9 – 5) ÷ \(\frac{1}{3}\) b. \(\frac{5}{3}\) × (2 × \(\frac{1}{4}\)) c. \(\frac{1}{3}\) ÷ (1 ÷ \(\frac{1}{4}\)) d. \(\frac{1}{2}\) × \(\frac{3}{5}\) × \(\frac{5}{3}\) e. Half as much as (\(\frac{3}{4}\) × 0.2) f. 3 times as much as the quotient of 2.4 and 0.6 Answer:

Question 8. Choose an expression below that matches the story problem, and write it in the blank. \(\frac{2}{3}\) × (20 – 5) (\(\frac{2}{3}\) × 20) – (\(\frac{2}{3}\) × 5) \(\frac{2}{3}\) × 20 – 5 (20 – \(\frac{2}{3}\)) – 5 a. Farmer Green picked 20 carrots. He cooked \(\frac{2}{3}\) of them, and then gave 5 to his rabbits. Write the expression that tells how many carrots he had left. Expression: ___________________________ b. Farmer Green picked 20 carrots. He cooked 5 of them, and then gave \(\frac{2}{3}\) of the remaining carrots to his rabbits. Write the expression that tells how many carrots the rabbits will get. Expression: ___________________________ Answer:

Eureka Math Grade 5 Module 4 Lesson 32 Exit Ticket Answer Key

Question 1. Write an equivalent expression in numerical form. A fourth as much as the product of two-thirds and 0.8 Answer:

Question 2. Write an equivalent expression in word form. a. \(\frac{3}{8}\) × (1 – \(\frac{1}{3}\)) b. (1 – \(\frac{1}{3}\)) ÷ 2 Answer:

Question 3. Compare the expressions in 2(a) and 2(b). Without evaluating, determine which expression is greater, and explain how you know. Answer:

Eureka Math Grade 5 Module 4 Lesson 32 Homework Answer Key

Question 1. Circle the expression equivalent to the difference between 7 and 4, divided by a fifth. 7 + (4 ÷ \(\frac{1}{5}\)) \(\frac{7-4}{5}\) (7 – 4) ÷ \(\frac{1}{5}\) \(\frac{1}{5}\) ÷ (7 – 4) Answer:

Question 2. Circle the expression(s) equivalent to 42 divided by the sum of \(\frac{2}{3}\) and \(\frac{3}{4}\). (\(\frac{2}{3}\) + \(\frac{3}{4}\)) ÷ 42 (42 ÷ \(\frac{2}{3}\)) + \(\frac{3}{4}\) 42 ÷ (\(\frac{2}{3}\) + \(\frac{3}{4}\)) \(\frac{42}{\frac{2}{8}+\frac{3}{4}}\) Answer:

Question 3. Fill in the chart by writing the equivalent numerical expression or expression in word form.

a. A fourth as much as the sum of 3  and 4.5
b. (3\(\frac{1}{8}\) + 4.5) ÷ 5
c. Multiply  by 5.8; then halve the product
d. \(\frac{1}{6}\) × (4.8 – \(\frac{1}{2}\))
e. 8 – (\(\frac{1}{2}\) ÷ 9)

Question 4. Compare the expressions in 3(a) and 3(b). Without evaluating, identify the expression that is greater. Explain how you know. Answer:

Question 5. Evaluate the following expressions. a. (11 – 6) ÷ \(\frac{1}{6}\) b. \(\frac{9}{5}\) × (4 × \(\frac{1}{6}\)) c. \(\frac{1}{10}\) ÷ (5 ÷ \(\frac{1}{2}\)) d. \(\frac{3}{4}\) × \(\frac{2}{5}\) × \(\frac{4}{3}\) e. 50 divided by the difference between \(\frac{3}{4}\) and \(\frac{5}{8}\) Answer:

Question 6. Lee is sending out 32 birthday party invitations. She gives 5 invitations to her mom to give to family members. Lee mails a third of the rest, and then she takes a break to walk her dog. a. Write a numerical expression to describe how many invitations Lee has already mailed. b. Which expression matches how many invitations still need to be sent out? 32 – 5 – \(\frac{1}{3}\)(32 – 5) \(\frac{2}{3}\) × 32 – 5 (32 – 5) ÷ \(\frac{1}{3}\) \(\frac{1}{3}\) × (32 – 5) Answer:

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Leninsky District, Moscow Oblast

Leninsky District is an administrative and municipal district, one of the thirty-six in Moscow Oblast, Russia. It is located in the center of the oblast just south of the federal city of Moscow. The area of the district is 202.83 square kilometers. Its administrative center is the town of Vidnoye. Population: 172,171; 145,251; 74,490. The population of Vidnoye accounts for 33.0% of the district's total population.

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Eureka Math Grade 4 Module 5 Lesson 41 Answer Key

Engage ny eureka math 4th grade module 5 lesson 41 answer key, eureka math grade 4 module 5 lesson 41 problem set answer key.

Question 1. Find the sums. a. \(\frac{0}{3}+\frac{1}{3}+\frac{2}{3}+\frac{3}{3}\)

Answer: 0/3 + 1/3 + 2/3 + 3/3 = 1.9.

Explanation: In the above-given question, given that, Find the sums. 0/3 + 1/3 + 2/3 + 3/3. 0/3 = 0. 1/3 = 0.3. 2/3 = 0.6. 3/3 = 1. 0 + 0.3 + 0.6 + 1 = 1.9.

b. \(\frac{0}{4}+\frac{1}{4}+\frac{2}{4}+\frac{3}{4}+\frac{4}{4}\)

Answer: 0/4 + 1/4 + 2/4 + 3/4 + 4/4 = 2.5.

Explanation: In the above-given question, given that, Find the sums. 0/4 + 1/4 + 2/4 + 3/4 + 4/4. 0/4 = 0. 1/4 = 0.25. 2/4 = 0.5. 3/4 = 0.75 4/4 = 1. 0 + 0.25 + 0.5 + 0.75 + 1 = 2.5.

c. \(\frac{0}{5}+\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}+\frac{5}{5}\)

Answer: 0/5 + 1/5 + 2/5 + 3/5 + 4/5 + 5/5 = 3.

Explanation: In the above-given question, given that, Find the sums. 0/5 + 1/5 + 2/5 + 3/5 + 4/5 + 5/5. 0/5 = 0. 1/5 = 0.2. 2/5 = 0.4. 3/5 = 0.6. 4/5 = 0.8. 5/5 = 1. 0 + 0.2 + 0.4 + 0.6 + 0.8 + 1 = 3.

d. \(\frac{0}{6}+\frac{1}{6}+\frac{2}{6}+\frac{3}{6}+\frac{4}{6}+\frac{5}{6}+\frac{6}{6}\)

Answer: 0/6 + 1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6 = 3.3.

Explanation: In the above-given question, given that, Find the sums. 0/6 + 1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6. 0/6 = 0. 1/6 = 0.1. 2/6 = 0.3. 3/6 = 0.5. 4/6 = 0.6. 5/6 = 0.8. 6/6 = 1 0 + 0.1 + 0.3 + 0.5 + 0.6 + 0.8 + 1 = 3.3.

e. \(\frac{0}{7}+\frac{1}{7}+\frac{2}{7}+\frac{3}{7}+\frac{4}{7}+\frac{5}{7}+\frac{6}{7}+\frac{7}{7}\)

Answer: 0/7 + 1/7 + 2/7 + 3/7 + 4/7 + 5/7 + 6/7  + 7/7 = 3.7.

Explanation: In the above-given question, given that, Find the sums. 0/7 + 1/7 + 2/7 + 3/7 + 4/7 + 5/7 + 6/7 + 7/7. 0/7 = 0. 1/7 = 0.1. 2/7 = 0.2. 3/7 = 0.4. 4/7 = 0.5. 5/7 = 0.7. 6/7 = 0.8. 7/7 = 1. 0 + 0.1 + 0.3  + 0.4 + 0.5 + 0.6 + 0.8 + 1 = 3.7.

f. \(\frac{0}{8}+\frac{1}{8}+\frac{2}{8}+\frac{3}{8}+\frac{4}{8}+\frac{5}{8}+\frac{6}{8}+\frac{7}{8}+\frac{8}{8}\)

Answer: 0/8 + 1/8 + 2/8 + 3/8 + 4/8 + 5/8 + 6/8  + 7/8 = 4.2.

Explanation: In the above-given question, given that, Find the sums. 0/8 + 1/8 + 2/8 + 3/8 + 4/8 + 5/8 + 6/8 + 7/8 + 8/8. 0/8 = 0. 1/8 = 0.125. 2/8 = 0.25. 3/8 = 0.37. 4/8 = 0.5. 5/8 = 0.6. 6/8 = 0.7. 7/8 = 0.8. 8/8 = 1. 0 + 0.1 + 0.3  + 0.4 + 0.5 + 0.6 + 0.8 + 1 = 4.2.

Question 2. Describe a pattern you notice when adding the sums of fractions with even denominators as opposed to those with odd denominators.

Answer: The sum of fractions with even denominators increases. the sum of fractions with odd denominators decreases.

Explanation: In the above-given question, given that, when adding the sums of fractions with even denominators increases. when adding the sums of fractions with odd denominators decreases. 0/3 = 1.9. 0/4 = 2.5. 0/5 = 3. 0/6 = 3.3. 0/7 = 3.7. 0/8 = 4.2.

Question 3. How would the sums change if the addition started with the unit fraction rather than with 0?

Answer: The sum does not change.

Explanation: In the above-given question, given that, How would the sums change if the addition started with the unit fraction? 0 plus anything is anything. 0 + 1 = 1. so the sum does not change.

Question 4. Find the sums. a. \(\frac{0}{10}+\frac{1}{10}+\frac{2}{10}+\cdots+\frac{10}{10}\)

Answer: 0/10 + 1/10 + 2/10 + 10/10 = 1.3.

Explanation: In the above-given question, given that, Find the sums. 0/10 + 1/10 + 2/10 + 10/10. 0/10 = 0. 1/10 = 0.1. 2/10 = 0.2. 10/10 = 1. 0 + 0.1 + 0.2 + 1 = 1.3.

b. \(\frac{0}{12}+\frac{1}{12}+\frac{2}{12}+\cdots+\frac{12}{12}\)

Answer: 0/12 + 1/12 + 2/12 + 12/12 = 1.18.

Explanation: In the above-given question, given that, Find the sums. 0/12 + 1/12 + 2/12 + 12/12. 0/12 = 0. 1/12 = 0.08. 2/12 = 0.1. 12/12 = 1. 0 + 0.08 + 0.1 + 1 = 1.18.

c. \(\frac{0}{15}+\frac{1}{15}+\frac{2}{15}+\cdots+\frac{15}{15}\)

Answer: 0/15 + 1/15 + 2/15 + 15/15 = 1.16.

Explanation: In the above-given question, given that, Find the sums. 0/15 + 1/15 + 2/15 + 15/15. 0/15 = 0. 1/15 = 0.06. 2/15 = 0.1. 15/15 = 1. 0 + 0.06 + 0.1 + 1 = 1.16.

d. \(\frac{0}{25}+\frac{1}{25}+\frac{2}{25}+\cdots+\frac{25}{25}\)

Answer: 0/25 + 1/25 + 2/25 + 25/25 = 1.12.

Explanation: In the above-given question, given that, Find the sums. 0/25 + 1/25 + 2/25 + 25/25. 0/25 = 0. 1/25 = 0.04. 2/25 = 0.08. 25/25 = 1. 0 + 0.04 + 0.08 + 1 = 1.12.

e. \(\frac{0}{50}+\frac{1}{50}+\frac{2}{50}+\cdots+\frac{50}{50}\)

Answer: 0/50 + 1/50 + 2/50 + 50/50 = 1.06.

Explanation: In the above-given question, given that, Find the sums. 0/50 + 1/50 + 2/50 + 50/50. 0/50 = 0. 1/50 = 0.02. 2/50 = 0.04. 50/50 = 1. 0 + 0.02 + 0.04 + 1 = 1.06.

f. \(\frac{0}{100}+\frac{1}{100}+\frac{2}{100}+\cdots+\frac{100}{100}\)

Answer: 0/100 + 1/100 + 2/100 + 100/100 = 1.03.

Explanation: In the above-given question, given that, Find the sums. 0/100 + 1/100 + 2/100 + 100/100. 0/100 = 0. 1/100 = 0.01. 2/100 = 0.02. 100/100 = 1. 0 + 0.01 + 0.02 + 1 = 1.03.

Question 5. Compare your strategy for finding the sums in Problems 4(d), 4(e), and 4(f) with a partner.

Answer: The sum is the same.

Explanation: In the above-given question, given that, my partner found also the same. the sum is the same.

Question 6. How can you apply this strategy to find the sum of all the whole numbers from 0 to 100?

Answer: The sum of all the whole numbers is the same.

Explanation: In the above-given question, given that, we can find the sum of all the whole numbers from 0 to 100. if we find the whole numbers from 0 to 100. the sum increases.

Eureka Math Grade 4 Module 5 Lesson 41 Exit Ticket Answer Key

Find the sums. Question 1. \(\frac{0}{20}+\frac{1}{20}+\frac{2}{20}+\cdots+\frac{20}{20}\)

Answer: 0/20 + 1/20 + 2/20 + 20/20 = 1.15.

Explanation: In the above-given question, given that, Find the sums. 0/20 + 1/20 + 2/20 + 20/20. 0/20 = 0. 1/20 = 0.05. 2/20 = 0.1. 20/20 = 1. 0 + 0.05 + 0.1 + 1 = 1.15.

Question 2. \(\frac{0}{200}+\frac{1}{200}+\frac{2}{200}+\cdots+\frac{200}{200}\)

Answer: 0/200 + 1/200 + 2/200 + 200/200 = 1.015.

Explanation: In the above-given question, given that, Find the sums. 0/200 + 1/200 + 2/200 + 200/200. 0/200 = 0. 1/200 = 0.005. 2/200 = 0.01. 200/200 = 1. 0 + 0.005 + 0.01 + 1 = 1.015.

Eureka Math Grade 4 Module 5 Lesson 41 Homework Answer Key

Question 1. Find the sums. a. \(\frac{0}{5}+\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}+\frac{5}{5}\)

b. \(\frac{0}{6}+\frac{1}{6}+\frac{2}{6}+\frac{3}{6}+\frac{4}{6}+\frac{5}{6}+\frac{6}{6}\)

c. \(\frac{0}{7}+\frac{1}{7}+\frac{2}{7}+\frac{3}{7}+\frac{4}{7}+\frac{5}{7}+\frac{6}{7}+\frac{7}{7}\)

Explanation: In the above-given question, given that, Find the sums. 0/7 + 1/7 + 2/7 + 3/7 + 4/7 + 5/7 + 6/7 + 7/7. 0/7 = 0. 1/7 = 0.1. 2/7 = 0.2. 3/7 = 0.4. 4/7 = 0.5. 5/7 = 0.7. 6/7 = 0.8. 7/7 = 1.

d. \(\frac{0}{8}+\frac{1}{8}+\frac{2}{8}+\frac{3}{8}+\frac{4}{8}+\frac{5}{8}+\frac{6}{8}+\frac{7}{8}+\frac{8}{8}\)

e. \(\frac{0}{9}+\frac{1}{9}+\frac{2}{9}+\frac{3}{9}+\frac{4}{9}+\frac{5}{9}+\frac{6}{9}+\frac{7}{9}+\frac{8}{9}+\frac{9}{9}\)

Answer: 0/9 + 1/9 + 2/9 + 3/9 + 4/9 + 5/9 + 6/9  + 7/9 + 8/9 + 9/9 = 4.6.

Explanation: In the above-given question, given that, Find the sums. 0/9 + 1/9 + 2/9 + 3/9 + 4/9 + 5/9 + 6/9 + 7/9 + 8/9 + 9/9. 0/9 = 0. 1/9 = 0.1. 2/9 = 0.2. 3/9 = 0.3. 4/9 = 0.4. 5/9 = 0.5. 6/9 = 0.6. 7/9 = 0.7. 8/9 = 0.8. 9/9 = 1 0 + 0.1 + 0.2 + 0.3  + 0.4 + 0.5 + 0.6  + 0.7+ 0.8 + 1 = 4.6.

f. \(\frac{0}{10}+\frac{1}{10}+\frac{2}{10}+\frac{3}{10}+\frac{4}{10}+\frac{5}{10}+\frac{6}{10}+\frac{7}{10}+\frac{8}{10}+\frac{9}{10}+\frac{10}{10}\)

Answer: 0/10 + 1/10 + 2/10 + 3/10 + 4/10 + 5/10 + 6/10  + 7/10 + 8/10 + 9/10 + 10/10 = 5.5.

Explanation: In the above-given question, given that, Find the sums. 0/10 + 1/10 + 2/10 + 3/10 + 4/10 + 5/10 + 6/10 + 7/10 + 8/10 + 9/10 + 10/10. 0/10 = 0. 1/10 = 0.1. 2/10 = 0.2. 3/10 = 0.3. 4/10 = 0.4. 5/10 = 0.5. 6/10 = 0.6. 7/10 = 0.7. 8/10 = 0.8. 9/10 = 0.9. 10/10 = 1. 0 + 0.1 + 0.2 + 0.3  + 0.4 + 0.5 + 0.6  + 0.7+ 0.8  + 0.9 + 1 = 5.5.

Question 4. Find the sums. a. \(\frac{0}{20}+\frac{1}{20}+\frac{2}{20}+\cdots+\frac{20}{20}\)

b. \(\frac{0}{35}+\frac{1}{35}+\frac{2}{35}+\cdots+\frac{35}{35}\)

Answer: 0/35 + 1/35 + 2/35 + 35/35 = 1.07.

Explanation: In the above-given question, given that, Find the sums. 0/35 + 1/35 + 2/35 + 35/35. 0/35 = 0. 1/35 = 0.02. 2/35 = 0.05. 35/35 = 1. 0 + 0.02 + 0.05 + 1 = 1.07.

c. \(\frac{0}{36}+\frac{1}{36}+\frac{2}{36}+\cdots+\frac{36}{36}\)

Answer: 0/36 + 1/36 + 2/36 + 36/36 = 1.25.

Explanation: In the above-given question, given that, Find the sums. 0/36 + 1/36 + 2/36 + 36/36. 0/36 = 0. 1/36 = 1.07. 2/36 = 0.2. 36/36 = 0.05. 0 + 0.05 + 0.2 + 1 = 1.25.

d. \(\frac{0}{75}+\frac{1}{75}+\frac{2}{75}+\cdots+\frac{75}{75}\)

Answer: 0/75 + 1/75 + 2/75 + 75/75 = 1.03.

Explanation: In the above-given question, given that, Find the sums. 0/75 + 1/75 + 2/75 + 75/75. 0/75 = 0. 1/75 = 0.01. 2/75 = 0.02. 75/75 = 1. 0 + 0.01 + 0.02 + 1 = 1.03.

e. \(\frac{0}{100}+\frac{1}{100}+\frac{2}{100}+\cdots+\frac{100}{100}\)

Explanation: In the above-given question, given that, Find the sums. 0/100 + 1/100+ 2/100 + 100/100. 0/100 = 0. 1/100 = 0.01. 2/100 = 0.02. 100/100 = 1. 0 + 0.01 + 0.02 + 1 = 1.03.

f. \(\frac{0}{99}+\frac{1}{99}+\frac{2}{99}+\cdots+\frac{99}{99}\)

Answer: 0/99 + 1/99 + 2/99 + 99/99 = 1.03.

Explanation: In the above-given question, given that, Find the sums. 0/99 + 1/99 + 2/99 + 99/99. 0/99 = 0. 1/99 = 0.01. 2/99 = 0.02. 99/99 = 1. 0 + 0.01 + 0.02 + 1 = 1.03.

Question 5. How can you apply this strategy to find the sum of all the whole numbers from 0 to 50? To 99?

Explanation: In the above-given question, given that, we can find the sum of all the whole numbers from 0 to 50. if we find the whole numbers from 0 to 50. the sum increases.

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    A residential and industrial region in the south-east of Mocsow. It was founded on the spot of two villages: Chagino (what is now the Moscow Oil Refinery) and Ryazantsevo (demolished in 1979). in 1960 the town was incorporated into the City of Moscow as a district. Population - 45,000 people (2002). The district is one of the most polluted residential areas in Moscow, due to the Moscow Oil ...

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    Zhukovsky International Airport, formerly known as Ramenskoye Airport or Zhukovsky Airfield - international airport, located in Moscow Oblast, Russia 36 km southeast of central Moscow, in the town of Zhukovsky, a few kilometers southeast of the old Bykovo Airport. After its reconstruction in 2014-2016, Zhukovsky International Airport was officially opened on 30 May 2016.

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