## Engage NY Eureka Math 6th Grade Module 2 Lesson 7 Answer Key

### Eureka Math Grade 6 Module 2 Lesson 7 Example Answer Key

Example 1.
Model the following using a partitive interpretation.
$$\frac{3}{4} \div \frac{2}{5}$$
$$\frac{2}{5}$$ of what number is $$\frac{3}{4}$$? Shade 2 of the 5 sections $$\left(\frac{2}{5}\right)$$.
Label the part that is known $$\left(\frac{3}{4}\right)$$.
Make notes below on the math sentences needed to solve the problem.
→ Let’s relate what we just did to multiplication.
Look back at the model. What was the first thing you did? What was the next thing you did?
We found half of $$\frac{3}{4}$$. Then we took the result and multiplied by 5.

→ We can record this process using multiplication:
$$\frac{3}{4} \div \frac{2}{5}=\left(\frac{1}{2} \cdot \frac{3}{4}\right) \cdot 5$$

→ How can you show that $$\left(\frac{1}{2} \cdot \frac{3}{4}\right)$$ . 5 is equivalent to $$\frac{3}{4} \cdot \frac{5}{2}$$? What does that tell you about $$\frac{3}{4} \div \frac{2}{5}$$ and $$\frac{3}{4} \times \frac{5}{2}$$?
Since we are multiplying, we can rearrange the order of our factors:
$$\frac{1}{2} \cdot \frac{3}{4} \cdot 5=\frac{3}{4} \cdot\left(\frac{1}{2} \cdot 5\right)=\frac{3}{4} \cdot \frac{5}{2}$$
Since $$\frac{3}{4} \div \frac{2}{5}$$ is equal to $$\left(\frac{1}{2} \cdot \frac{3}{4}\right)$$ . 5, and that’s equal to $$\frac{3}{4} \cdot \frac{5}{2}$$, we can say that $$\frac{3}{4} \div \frac{2}{5}=\frac{3}{4} \cdot \frac{5}{2}$$.

→ To solve this division problem, we can invert the divisor and multiply. This is called the invert and multiply
method.

Example 2.
Model the following using a measurement interpretation.
$$\frac{3}{5} \div \frac{1}{4}$$
$$\frac{3}{5}$$ is how many fourths? Convert the whole and the divisor to the same fractional units first. Then divide the numerators.
$$\frac{3}{5} \div \frac{1}{4}=\frac{12}{20} \div \frac{5}{20}$$ = 12 twentieths ÷ 5 twentieths $$\frac{12}{5}=2 \frac{2}{5}$$

Example 3.
$$\frac{2}{3} \div \frac{3}{4}$$  Show the number sentences below.
$$\frac{2}{3} \div \frac{3}{4}=\frac{8}{12} \div \frac{9}{12}=\frac{8}{9}$$
$$\frac{1}{3} \cdot \frac{2}{3} \cdot 4=\frac{8}{9}$$
$$\frac{2}{3} \div \frac{3}{4}=\frac{2}{3} \cdot \frac{4}{3}=\frac{8}{9}$$

### Eureka Math Grade 6 Module 2 Lesson 7 Problem Set Answer Key

Invert and multiply to divide.

Question 1.
a. $$\frac{2}{3} \div \frac{1}{4}$$
= $$\frac{2}{3} \times \frac{4}{1}=\frac{8}{3}$$

b. $$\frac{2}{3}$$ ÷ 4
= $$\frac{2}{3} \times \frac{1}{4}=\frac{1}{6}$$

c. 4 ÷ $$\frac{2}{3}$$
= 4 × $$\frac{3}{2}$$ = 6

Question 2.
a. $$\frac{1}{3} \div \frac{1}{4}$$
= $$\frac{1}{3} \times \frac{4}{1}=\frac{4}{3}$$

b. $$\frac{1}{8} \div \frac{3}{4}$$
= $$\frac{1}{8} \times \frac{4}{3}=\frac{1}{6}$$

c. $$\frac{9}{4} \div \frac{6}{5}$$
= $$\frac{9}{4} \times \frac{5}{6}=\frac{15}{8}$$

Question 3.
a. $$\frac{2}{3} \div \frac{3}{4}$$
= $$\frac{2}{3} \times \frac{4}{3}=\frac{8}{9}$$

b. $$\frac{3}{5} \div \frac{3}{2}$$
= $$\frac{3}{5} \times \frac{2}{3}=\frac{2}{5}$$

c. $$\frac{22}{4} \div \frac{2}{5}$$
= $$\frac{22}{4} \times \frac{5}{2}=\frac{55}{4}$$

Question 4.
Summer used $$\frac{2}{5}$$ of her ground beef to make burgers. If she used $$\frac{3}{4}$$ pounds of beef, how much beef did she have at first?
$$\frac{3}{4}$$ is $$\frac{2}{5}$$ of what? So, $$\frac{3}{4} \div \frac{2}{5}=\frac{3}{4} \times \frac{5}{2}=\frac{15}{8}=1 \frac{7}{8}$$

Question 5.
Alistair has 5 half-pound chocolate bars. It takes 1$$\frac{1}{2}$$ pounds of chocolate, broken into chunks, to make a batch of cookies. How many batches can Alistair make with the chocolate he has on hand?
$$1 \frac{1}{2}=\frac{3}{2}$$
$$\frac{5}{2}$$ is how many $$\frac{3}{2}$$
$$\frac{5}{2} \div \frac{3}{2}=\frac{5}{2} \times \frac{2}{3}=\frac{5}{3}$$
Alistair can only make 1 full batch, but he has enough to make another $$\frac{2}{3}$$ batch.

Question 6.
Draw a model that shows $$\frac{2}{5} \div \frac{1}{3}$$. Find the answer as well. $$\frac{2}{5} \div \frac{1}{3}=\frac{2}{5} \cdot \frac{3}{1}=\frac{6}{5}$$ or 1$$\frac{1}{5}$$

Question 7.
Draw a model that shows $$\frac{3}{4} \div \frac{1}{2}$$. Find the answer as well. $$\frac{3}{4} \div \frac{1}{2}=\frac{3}{4} \cdot \frac{2}{1}=\frac{6}{4}$$ or 1$$\frac{1}{2}$$

### Eureka Math Grade 6 Module 2 Lesson 7 Exit Ticket Answer Key

Question 1.
Write the reciprocal of the following numbers.  Question 2.
Rewrite this division expression as an equivalent multiplication expression: $$\frac{5}{8} \div \frac{2}{3}$$
$$\frac{5}{8} \cdot \frac{3}{2} \text { or } \frac{1}{2} \cdot \frac{5}{8} \cdot 3$$ $$\frac{5}{8} \div \frac{2}{3}=\frac{5}{8} \cdot \frac{3}{2}=\frac{15}{16}$$