## Math Expressions Common Core Grade 4 Unit 6 Lesson 4 Answer Key Mixed Numbers and Fractions Greater Than 1

**Math Expressions Grade 4 Unit 6 Lesson 4 Homework**

**Write the equivalent fraction.**

Question 1.

6\(\frac{2}{5}\) = _____________

Answer:

6\(\frac{2}{5}\) = \(\frac{30}{5}\) + \(\frac{2}{5}\)

= \(\frac{32}{5}\)

Question 2.

2\(\frac{3}{8}\) = _____________

Answer:

2\(\frac{3}{8}\) = \(\frac{16}{8}\) + \(\frac{3}{8}\)

= \(\frac{19}{8}\)

Question 3.

4\(\frac{6}{7}\) = _____________

Answer:

4\(\frac{6}{7}\) = \(\frac{28}{7}\) + \(\frac{6}{7}\)

= \(\frac{34}{7}\)

Question 4.

8\(\frac{1}{3}\) = _____________

Answer:

8\(\frac{1}{3}\) = \(\frac{24}{3}\) + \(\frac{1}{3}\)

= \(\frac{25}{3}\)

Question 5.

3\(\frac{7}{10}\) = ____________

Answer:

3\(\frac{7}{10}\) = \(\frac{30}{10}\) + \(\frac{7}{10}\)

= \(\frac{37}{10}\)

Question 6.

5\(\frac{5}{6}\) = ______________

Answer:

5\(\frac{5}{6}\) = \(\frac{30}{6}\) + \(\frac{5}{6}\)

= \(\frac{35}{6}\)

Question 7.

7\(\frac{3}{4}\) = _____________

Answer:

7\(\frac{3}{4}\) = \(\frac{28}{4}\) + \(\frac{3}{4}\)

= \(\frac{31}{4}\)

Question 8.

1\(\frac{4}{9}\) = ______________

Answer:

1\(\frac{4}{9}\) = \(\frac{9}{9}\) + \(\frac{4}{9}\)

= \(\frac{13}{9}\)

**Write the equivalent mixed number.**

Question 9.

\(\frac{50}{7}\) = ______________

Answer:

\(\frac{50}{7}\) = 7\(\frac{1}{7}\)

Question 10.

\(\frac{16}{10}\) = ______________

Answer:

\(\frac{16}{10}\) = 1\(\frac{6}{10}\)

Question 11.

\(\frac{23}{4}\) = ______________

Answer:

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

Question 12.

\(\frac{50}{5}\) = ______________

Answer:

\(\frac{50}{5}\) = 9\(\frac{5}{5}\)

Question 13.

\(\frac{21}{8}\) = ______________

Answer:

\(\frac{21}{8}\) = 2\(\frac{5}{8}\)

Question 14.

\(\frac{11}{3}\) = ______________

Answer:

\(\frac{11}{3}\) = 3\(\frac{2}{3}\)

Question 15.

\(\frac{60}{9}\) = ______________

Answer:

\(\frac{60}{9}\) = 6\(\frac{6}{9}\)

Question 16.

\(\frac{23}{5}\) = ______________

Answer:

\(\frac{23}{5}\) = 3\(\frac{8}{5}\)

**Solve. Show your work.**

Question 17.

Castor brought 6\(\frac{3}{4}\) small carrot cakes to share with the 26 students in his class. Did Castor bring enough for each student to have \(\frac{1}{4}\) of a cake? Explain your thinking.

Answer:

Yes, Castor brought enough cake for each student to have \(\frac{1}{4}\).

Explanation:

Quantity of cake Castor brought = 6\(\frac{3}{4}\)

Number of students to share the cake = 26.

Quantity of share the cake to each student in the class = \(\frac{1}{4}\)

Total quantity of cake students got = Number of students to share the cake × Quantity of share the cake to each student in the class

= 26 × \(\frac{1}{4}\)

= 6\(\frac{2}{4}\)

Question 18.

Claire cut some apples into eighths. She and her friends ate all but 17 pieces. How many whole apples and parts of apples did she have left over? Tell how you know.

Answer:

Number of apples left over = 7.

Explanation:

Number of apple pieces she and her friend ate = 17.

Number of whole apples = 3.

Total pieces of three apples = 8 × 3 = 24.

Number of apples left over = Total pieces of three apples – Number of apple pieces she and her friend ate

= 24 – 17

= 7.

**Math Expressions Grade 4 Unit 6 Lesson 4 Remembering**

**Write and solve an equation to solve each problem. Draw comparison bars when needed.**

Question 1.

Brigitte fostered 14 dogs this year, which is 5 less than last year. How many dogs did Brigitte foster last year?

Answer:

Number of dogs Brigitte fostered last year = 19.

Explanation:

Number of dogs Brigitte fostered this year = 14.

Brigitte fostered 14 dogs this year, which is 5 less than last year.

=> Number of dogs Brigitte fostered last year = Number of dogs Brigitte fostered this year + 5

= 14 + 5

= 19.

Question 2.

Rema has two jobs. In one year, she worked 276 hours at her first job. In the same year. she worked 3 times the number of hours at her second job. How many hours did Rema work that year at her second job?

Answer:

Number of hours she worked at her second job = 828.

Explanation:

Number of hours she worked at her first job = 276.

In the same year. she worked 3 times the number of hours at her second job.

=> Number of hours she worked at her second job = Number of hours she worked at her first job × 3

= 276 × 3

= 828.

**Complete.**

Question 3.

How many milliliters are equal to 21 L?

Answer:

21 Liters = 21,000 milliliters.

Explanation:

1 Liter = 1000 milliliters.

=> 21 Liters = 1000 × 21 = 21,000 milliliters.

Question 4.

How many milligrams are equal to 9 g?

Answer:

9 g = 9,000 milligrams.

Explanation:

1 gram = 1000 milligrams.

=> 9 grams = 1000 × 9 = 9,000 milligrams.

Question 5.

How many grams are equal to 400 kg?.

Answer:

400 kg = 400,000 grams.

Explanation:

1 kilogram = 1000 grams.

=> 400 kilograms = 1000 × 400 = 400,000 grams.

**Solve.**

Question 6.

\(\frac{3}{4}\) – \(\frac{1}{4}\) = __________

Answer:

\(\frac{3}{4}\) – \(\frac{1}{4}\)

= \(\frac{2}{4}\)

Question 7.

\(\frac{2}{9}\) + \(\frac{3}{9}\) = ___________

Answer:

\(\frac{2}{9}\) + \(\frac{3}{9}\)

= \(\frac{5}{9}\)

Question 8.

\(\frac{7}{8}\) – \(\frac{1}{8}\) = _____________

Answer:

\(\frac{7}{8}\) – \(\frac{1}{8}\)

= \(\frac{6}{8}\)

Question 9.

**Stretch Your Thinking** Harrison says that to convert a mixed number to a fraction greater than 1, he thinks of it this way: 4\(\frac{2}{5}\) = \(\frac{5}{5}\) + \(\frac{5}{5}\) + \(\frac{5}{5}\) + \(\frac{5}{5}\) + \(\frac{2}{5}\) = \(\frac{22}{5}\). Does his strategy work? Explain.

Answer:

His strategy works because to convert a mixed number to a fraction greater than 1, what he writes is correct.

Explanation:

Equation Harrison says that to convert a mixed number to a fraction greater than 1:

4\(\frac{2}{5}\) = \(\frac{5}{5}\) + \(\frac{5}{5}\) + \(\frac{5}{5}\) + \(\frac{5}{5}\) + \(\frac{2}{5}\) = \(\frac{22}{5}\).