grade 4 module 5 lesson 5 homework

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4th grade (Eureka Math/EngageNY)

Unit 1: module 1: place value, rounding, and algorithms for addition and subtraction, unit 2: module 2: unit conversions and problem solving with metric measurement, unit 3: module 3: multi-digit multiplication and division, unit 4: module 4: angle measure and plane figures, unit 5: module 5: fraction equivalence, ordering, and operations, unit 6: module 6: decimal fractions, unit 7: module 7: exploring measurement with multiplication.

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Eureka Math Grade 4 Module 5 Lesson 16 Answer Key

Engage ny eureka math 4th grade module 5 lesson 16 answer key, eureka math grade 4 module 5 lesson 16 problem set answer key.

Question 1. Solve. a. 3 fifths – 1 fifth = _____2 __fifths_____

Answer: 3 fifths – 1 fifth = 2 fifths.

Explanation: In the above-given question, given that, 3 fifths = 3/5. 3/5 = 0.6. 1 fifth = 1/5. 1/5 = 0.2. 0.6 – 0.2 = 0.4. 2/5 = 0.4. 3 fifths – 1 fifth = 2 fifths.

b. 5 fifths – 3 fifths = _____2_fifths._________

Answer: 5 fifths – 3 fifth = 2 fifths.

Explanation: In the above-given question, given that, 5 fifths = 5/5. 5/5 = 1. 3 fifth = 3/5. 3/5 = 0.6. 1 – 0.6 = 0.4. 2/5 = 0.4. 3 fifths – 1 fifth = 2 fifths.

c. 3 halves – 2 halves = _____1_ halves._____

Answer: 3 halves – 2 halves = 1 halves

Explanation: In the above-given question, given that, 3 halves = 3/2. 3/2 = 1.5. 2 halves = 2/2. 2/2 = 1. 1.5 – 1 = 0.5. 1/2 = 0.5. 3 halves – 2 halves = 1 half.

d. 6 fourths – 3 fourths = ____3__fourths._______

Answer: 6 fourths – 3 fourths = 3 fourths.

Explanation: In the above-given question, given that, 6 fourths = 6/4. 6/4 = 1.5. 3 fourths = 3/4. 3/4 = 0.75. 1.5 – 0.75 = 0.75. 3/4 = 0.75. 6 fourths – 3 fourths = 3 fourths.

Question 2. Solve.

a. \(\frac{5}{6}\) – \(\frac{3}{6}\)

Answer: \(\frac{5}{6}\) – \(\frac{3}{6}\) = \(\frac{2}{6}\)

Explanation: In the above-given question, given that, 5 sixths = 5/6. 5/6 = 0.83. 3 sixths = 3/6. 3/6 = 0.5. 0.83 – 0.5 = 0.33. 2/6 = 0.33. \(\frac{5}{6}\) – \(\frac{3}{6}\) = \(\frac{2}{6}\)

b. \(\frac{6}{8}\) – \(\frac{4}{8}\)

Answer: \(\frac{6}{8}\) – \(\frac{4}{8}\) = \(\frac{2}{8}\)

Explanation: In the above-given question, given that, 6 eights = 6/8. 6/8 = 0.75. 4 eights = 4/8. 4/8 = 0.5. 0.75 – 0.5 = 0.25. 2/8 = 0.25. \(\frac{6}{8}\) – \(\frac{4}{8}\) = \(\frac{2}{8}\)

c. \(\frac{3}{10}\) – \(\frac{3}{10}\)

Answer: \(\frac{3}{10}\) – \(\frac{3}{10}\) = \(\frac{0}{0}\)

Explanation: In the above-given question, given that, 3 tens = 3/10. 3/10 = 0.3. 3 tens = 3/10. 3/10 = 0.3. 0.3 – 0.3 = 0. 0/6 = 0. \(\frac{3}{10}\) – \(\frac{3}{10}\) = \(\frac{0}{0}\)

d. \(\frac{5}{5}\) – \(\frac{4}{5}\)

Answer: \(\frac{5}{5}\) – \(\frac{4}{5}\) = \(\frac{1}{5}\)

Explanation: In the above-given question, given that, 5 fifths = 5/5. 5/5 = 1. 4 fifths = 4/5. 4/5 = 0.8. 1 – 0.8 = 0.2. 1/5 = 0.2. \(\frac{5}{5}\) – \(\frac{4}{5}\) = \(\frac{1}{5}\)

e. \(\frac{5}{4}\) – \(\frac{4}{4}\)

Answer: \(\frac{5}{4}\) – \(\frac{4}{4}\) = \(\frac{1}{4}\)

Explanation: In the above-given question, given that, 5 fours = 5/4. 5/4 = 1.25. 4 fours = 4/4. 4/4 = 1. 1.25 – 1 = 0.25. 1/4 = 0.25. \(\frac{5}{4}\) – \(\frac{4}{4}\) = \(\frac{1}{4}\)

f. \(\frac{5}{4}\) – \(\frac{3}{4}\)

Answer: \(\frac{5}{4}\) – \(\frac{3}{4}\) = \(\frac{2}{4}\)

Explanation: In the above-given question, given that, 5 fours = 5/4. 5/4 = 1.25. 3 fours = 3/4. 3/4 = 0.75. 1.25 – 0.75 = 0.5. 2/4 = 0.5. \(\frac{5}{4}\) – \(\frac{3}{4}\) = \(\frac{2}{4}\)

Answer: 12/8 – 3/8 = 9/8.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 12/8 – 3/8. 9/8. 9/8 = 8/8 + 1/8.

b. \(\frac{12}{6}\) – \(\frac{5}{6}\)

Answer: 12/6 – 5/6 = 7/6.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 12/6 – 5/6. 7/6. 7/6 = 6/6 + 1/6.

c. \(\frac{9}{5}\) – \(\frac{3}{5}\)

Answer: 9/5 – 3/5 = 6/5.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 9/5 – 3/5. 6/5. 6/5 = 5/5 + 1/5.

d. \(\frac{14}{8}\) – \(\frac{3}{8}\)

Answer: 14/8 – 3/8 = 11/8.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 14/8 – 3/8. 11/8. 11/8 = 8/8 + 3/8.

e. \(\frac{8}{4}\) – \(\frac{2}{4}\)

Answer: 8/4 – 2/4 = 6/4.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 8/4 – 2/4. 6/4. 6/4 = 4/4 + 2/4.

f. \(\frac{15}{10}\) – \(\frac{3}{10}\)

Answer: 15/10 – 3/10 = 7/10.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 15/10 – 3/10. 7/10. 7/10 = 10/10 + 1/6.

Question 4. Solve. Write the sum in unit form.

a. 2 fourths + 1 fourth = _3 fourths._

Answer: 2 fourths + 1 fourth = 3 fourths.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 2 fourths = 1/4 + 1/4. 2 fourths + 1 fourth = 3 fourths. 1/4 + 1/4 + 1/4 = 3/4.

b. 4 fifths + 3 fifths = ____7__fifths.___

Answer: 4 fifths + 3 fifths = 7 fifths.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 4 fifths = 1/5 + 1/5 + 1/5 + 1/5. 3 fifths = 1/5 + 1/5 + 1/5. 4 fifths + 3 fifths = 7 fifths. 1/5 + 1/5 + 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 7/5.

Question 5. Solve. a. \(\frac{2}{8}\) + \(\frac{5}{8}\)

Answer: \(\frac{2}{8}\) + \(\frac{5}{8}\) = \(\frac{7}{8}\)

Explanation: In the above-given question, given that, 2 eights = 2/8. 2/8 = 0.25. 5 eights = 5/8. 5/8 = 0.625. 0.25 + 0.625 = 0.875. 7/8 = 0.875. \(\frac{2}{8}\) + \(\frac{5}{8}\) = \(\frac{7}{8}\)

b. \(\frac{4}{12}\) + \(\frac{5}{12}\)

Answer: \(\frac{4}{12}\) + \(\frac{5}{12}\) = \(\frac{9}{12}\)

Explanation: In the above-given question, given that, 4 twelfths = 4/12. 4/12 = 0.33. 5 twelfths = 5/12. 5/12 = 0.41. 0.33 + 0.41 = 0.74. 9/12 = 0.74. \(\frac{4}{12}\) + \(\frac{5}{12}\) = \(\frac{9}{12}\)

Question 6. Solve. Use a number bond to decompose the sum. Record your final answer as a mixed number. Problem (a) has been completed for you.

Answer: 3/5 + 4/5 = 7/5.

Explanation: In the above-given question, given that, Use a number bond to decompose the sum. 3/5 + 4/5. 7/5. 7/5 = 5/5 + 2/5.

b. \(\frac{4}{4}\) + \(\frac{3}{4}\)

Answer: 4/4 + 3/4 = 7/4.

Explanation: In the above-given question, given that, Use a number bond to decompose the sum. 4/4 + 3/4. 7/4. 7/4 = 4/4 + 3/4.

c. \(\frac{6}{9}\) + \(\frac{6}{9}\)

Answer: 6/9 + 6/9 = 12/9.

Explanation: In the above-given question, given that, Use a number bond to decompose the sum. 6/9 + 6/9. 12/9. 12/9 = 9/9 + 3/9.

d. \(\frac{7}{10}\) + \(\frac{6}{10}\)

Answer: 7/10 + 6/10 = 13/10.

Explanation: In the above-given question, given that, Use a number bond to decompose the sum. 7/10 + 6/10. 13/10. 13/10 = 10/10 + 3/10.

e. \(\frac{5}{6}\) + \(\frac{7}{6}\)

Answer: 5/6 + 7/6 = 12/6.

Explanation: In the above-given question, given that, Use a number bond to decompose the sum. 5/6 + 7/6. 12/6. 12/6 = 6/6 + 7/6.

f. \(\frac{9}{8}\) + \(\frac{5}{8}\)

Answer: 9/8 + 5/8 = 14/8.

Explanation: In the above-given question, given that, Use a number bond to decompose the sum. 9/8 + 5/8. 14/8. 14/8 = 8/8 + 6/8.

Question 7. Solve. Use a number line to model your answer. a. \(\frac{7}{4}\) – \(\frac{5}{4}\)

Answer: \(\frac{7}{4}\) – \(\frac{5}{4}\) = \(\frac{2}{4}\)

Explanation: In the above-given question, given that, 7 fours = 7/4. 7/4 = 1.75. 5 fours = 5/4. 5/4 = 1.25. 1.75 – 1.25 = 0.5. 2/4 = 0.5. \(\frac{7}{4}\) – \(\frac{5}{4}\) = \(\frac{2}{4}\)

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

Answer: 5/4 + 2/4 = 7/4.

Explanation: In the above-given question, given that, Use a number bond to decompose the sum. 5/4 + 2/4. 7/4. 7/4 = 4/4 + 3/4.

Eureka Math Grade 4 Module 5 Lesson 16 Exit Ticket Answer Key

Question 1. Solve. Use a number bond to decompose the difference. Record your final answer as a mixed number. \(\frac{16}{9}\) – \(\frac{5}{9}\)

Answer: 16/9 – 5/9 = 11/9.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 16/9 – 5/9. 11/9. 11/9 = 9/9 + 2/9.

Question 2. Solve. Use a number bond to decompose the sum. Record your final answer as a mixed number. \(\frac{5}{12}\) + \(\frac{10}{12}\)

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

Explanation: In the above-given question, given that, Use a number bond to decompose the sum. 5/12 + 10/12. 15/12. 15/12 = 12/12 + 3/12.

Eureka Math Grade 4 Module 5 Lesson 16 Homework Answer Key

Question 1. Solve. a. 3 sixths – 2 sixths = __1__sixths___________

Answer: 3 sixths – 2 sixths = 1 sixths.

Explanation: In the above-given question, given that, 3 sixths = 3/6. 3/6 = 0.5. 2 sixths = 2/6. 2/6 = 0.33. 0.5 – 0.3 = 0.1. 1/6 = 0.1.

b. 5 tenths – 3 tenths = ___2 tenths._____

Answer: 5 tenths – 3 tenths = 2 tenths.

Explanation: In the above-given question, given that, 5 tenths = 5/10. 5/10 = 0.5. 3 tenths = 3/10. 3/10 = 0.3. 0.5 – 0.3 = 0.2. 2/10 = 0.2.

c. 3 fourths – 2 fourths = ____1__fourth._________

Answer: 3 fourths – 2 fourths = 1 fourth.

Explanation: In the above-given question, given that, 3 fourths = 3/4. 3/4 = 0.75. 2 fourths = 2/4. 2/4 = 0.5. 0.75 – 0.5 = 0.25. 1/4 = 0.25.

d. 5 thirds – 2 thirds = ___3__thirds._____

Answer: 5 thirds – 2 thirds = 3 thirds.

Explanation: In the above-given question, given that, 5 thirds = 5/3. 3/5 = 1.6. 2 thirds = 2/3. 2/3 = 0.6. 1.6 – 0.6 = 1. 3/3 = 1.

a. \(\frac{3}{5}\) – \(\frac{2}{5}\)

Answer: \(\frac{3}{5}\) – \(\frac{2}{5}\) = \(\frac{1}{5}\)

Explanation: In the above-given question, given that, 3 fives = 3/5. 3/5 = 0.6. 2 fives = 2/5. 2/5 = 0.4. 0.6 – 0.4 = 0.2. 1/5 = 0.2. \(\frac{3}{5}\) – \(\frac{2}{5}\) = \(\frac{1}{5}\)

b. \(\frac{7}{9}\) – \(\frac{3}{9}\)

Answer: \(\frac{7}{9}\) – \(\frac{3}{9}\) = \(\frac{4}{9}\)

Explanation: In the above-given question, given that, 7 nines = 7/9. 7/9 = 0.7. 3 nines = 3/9. 3/9 = 0.3. 0.7 – 0.3 = 0.4. 4/9 = 0.4. \(\frac{7}{9}\) – \(\frac{3}{9}\) = \(\frac{4}{9}\)

c. \(\frac{7}{12}\) – \(\frac{3}{12}\)

Answer: \(\frac{7}{12}\) – \(\frac{3}{12}\) = \(\frac{4}{12}\)

Explanation: In the above-given question, given that, 7 twelfths = 7/12. 7/12 = 0.58. 3 twelfths = 3/12. 3/12 = 0.25. 0.58 – 0.25 = 0.33. 4/12 = 0.33. \(\frac{7}{12}\) – \(\frac{3}{12}\) = \(\frac{4}{12}\)

d. \(\frac{6}{6}\) – \(\frac{4}{6}\)

Answer: \(\frac{6}{6}\) – \(\frac{4}{6}\) = \(\frac{2}{6}\)

Explanation: In the above-given question, given that, 6 sixs = 6/6. 6/6 = 1. 4 sixs = 4/6. 4/6 = 0.6. 1 – 0.6 = 0.4. 2/6 = 0.4. \(\frac{6}{6}\) – \(\frac{4}{6}\) = \(\frac{2}{6}\)

e. \(\frac{5}{3}\) – \(\frac{2}{3}\)

Answer: \(\frac{5}{3}\) – \(\frac{2}{3}\) = \(\frac{3}{3}\)

Explanation: In the above-given question, given that, 5 threes = 5/3. 5/3 = 1.6. 2 threes = 2/3. 2/3 = 0.6. 1.25 – 1 = 0.25. 3/3 = 1. \(\frac{5}{3}\) – \(\frac{2}{3}\) = \(\frac{3}{3}\)

f. \(\frac{7}{4}\) – \(\frac{5}{4}\)

Answer: \(\frac{7}{4}\) – \(\frac{5}{4}\) = \(\frac{3}{4}\)

Explanation: In the above-given question, given that, 7 fours = 7/4. 7/4 = 1.75. 5 fours = 4/4. 5/4 = 1.25. 1.75 – 1.25 = 0.75. 3/4 = 0.75. \(\frac{7}{4}\) – \(\frac{5}{4}\) = \(\frac{3}{4}\)

Answer: 12/6 – 3/6 = 9/6.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 12/6 – 3/4. 9/6. 9/6 = 6/6 + 3/6.

b. \(\frac{17}{8}\) – \(\frac{6}{8}\)

Answer: 17/8 – 6/8 = 11/8.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 17/8 – 6/8. 11/8. 11/8 = 8/8 + 2/8.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 9/5 – 3/5. 6/5. 6/5 = 5/5 + 1/6.

d. \(\frac{11}{4}\) – \(\frac{6}{4}\)

Answer: 11/4 – 6/4 = 5/4.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 11/4 – 6/4. 5/4. 5/4 = 4/4 + 1/4.

e. \(\frac{10}{7}\) – \(\frac{2}{7}\)

Answer: 10/7 – 2/7 = 8/7.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 10/7 – 2/7. 8/7. 8/7 = 7/7 + 1/7.

f. \(\frac{21}{10}\) – \(\frac{9}{10}\)

Answer: 21/10 – 9/10 = 11/10.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 21/10 – 9/10. 11/10. 11/10 = 10/10 + 1/10.

Question 4. Solve. Write the sum in unit form. a. 4 fifths + 2 fifths = ____6__fifths.____

Answer: 4 fifths + 2 fifths = 6 fifths.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 4 fifths = 1/5 + 1/5 + 1/5 + 1/5. 2 fifths = 1/5 + 1/5. 4 fifths + 2 fifth = 6 fifths. 1/5 + 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 6/5.

b. 5 eighths + 2 eighths = __7___eights.______

Answer: 5 eights + 2 eighths = 7 eights.

Explanation: In the above-given question, given that, Use a number bond to show how to convert the difference to a mixed number. 5 eights = 1/8 + 1/8 + 1/8 + 1/8 + 1/8. 2 eights = 1/8 + 1/8. 5 eights + 2 eights = 7 eights. 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 = 7/8.

Question 5. Solve. a. \(\frac{3}{11}\) + \(\frac{6}{11}\)

Answer: 3/11 + 6/11 = 9/11.

Explanation: In the above-given question, given that, Use a number bond to decompose the sum. 3/11 + 6/11. 9/11. 9/11 = 3/11 + 9/11.

b. \(\frac{3}{10}\) + \(\frac{6}{10}\)

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

Explanation: In the above-given question, given that, Use a number bond to decompose the sum. 3/10 + 6/10. 9/10. 9/10 = 3/10 + 6/10.

Question 6. Solve. Use a number bond to decompose the sum. Record your final answer as a mixed number. a. \(\frac{3}{4}\) + \(\frac{3}{4}\)

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

Explanation: In the above-given question, given that, Use a number bond to decompose the sum. 3/4 + 3/4. 6/4. 6/4 = 4/4 + 5/4.

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

Answer: 8/12 + 6/12 = 14/12.

Explanation: In the above-given question, given that, Use a number bond to decompose the sum. 8/12 + 6/12. 14/12. 14/12 = 12/12 + 2/12.

c. \(\frac{5}{8}\) + \(\frac{7}{8}\)

Answer: 5/8 + 7/8 = 12/8.

Explanation: In the above-given question, given that, Use a number bond to decompose the sum. 5/8 + 7/8. 12/8. 12/8 = 8/8 + 4/8.

d. \(\frac{8}{10}\) + \(\frac{5}{10}\)

Answer: 8/10 + 5/10 = 13/10.

Explanation: In the above-given question, given that, Use a number bond to decompose the sum. 8/10 + 5/10. 13/10. 13/10 = 10/10 + 3/10.

e. \(\frac{3}{5}\) + \(\frac{6}{5}\)

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

Explanation: In the above-given question, given that, Use a number bond to decompose the sum. 3/5 + 6/5. 9/5. 9/5 = 5/5 + 4/5.

Question 7. Solve. Use a number line to model your answer.

a. \(\frac{11}{9}\) – \(\frac{5}{9}\)

Answer: \(\frac{11}{9}\) – \(\frac{5}{9}\) = \(\frac{6}{9}\)

Explanation: In the above-given question, given that, 11 nines = 11/9. 11/9 = 0.58. 5 nines = 5/9. 5/9 = 0.25. 0.58 – 0.25 = 0.33. 6/9 = 0.33. \(\frac{11}{9}\) – \(\frac{5}{9}\) = \(\frac{6}{1}\)

b. \(\frac{13}{12}\) + \(\frac{4}{12}\)

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