Engage NY Eureka Math 6th Grade Module 2 Lesson 3 Answer Key

Example 1.
$$\frac{8}{9} \div \frac{2}{9}$$
Write the expression in unit form, and then draw a model to solve.

Here we have 4 groups of $$\frac{2}{9}$$. Therefore, the quotient is 4.

Example 2.
$$\frac{9}{12} \div \frac{3}{12}$$
Write the expression in unit form, and then draw a model to solve.

9 twelfths ÷ 3 twelfths = 9 ÷ 3 = 3

Example 3.
$$\frac{7}{9} \div \frac{3}{9}$$

→ Look at your model. How many units of $$\frac{3}{9}$$ can you see in $$\frac{3}{9}$$?
→2 complete units and then part of another

→ How can we name the part of the incomplete unit?
→There is one out of the three needed pieces to make another whole. So, it is $$\frac{1}{3}$$
→This means that $$\frac{7}{9} \div \frac{3}{9}$$ = 2$$\frac{1}{3}$$.
→This is the same as 7 ÷ 3.

→Do we get the same result solving $$\frac{7}{9} \div \frac{3}{9}$$ as we do when solving $$\frac{7}{9} \times \frac{9}{3}$$ ?

Write an expression to represent each problem. Then, draw a model to solve.

Exercise 1.
How many fourths are In 3 fourths?
I need to divide three fourths by one fourth, which is 3.
$$\frac{3}{4} \div \frac{1}{4}$$ = 3 fourth = 3 ÷ 1

There are 3 one-fourths in three-fourths.

Exercise 2.
$$\frac{4}{5} \div \frac{2}{5}$$

This is really 4 fifths ÷ 2 fifths, which is 2.

Exercise 3.
$$\frac{9}{4} \div \frac{3}{4}$$

This is really 9 fourths ÷ 3 fourths, which is 3.

Exercise 4.
$$\frac{7}{8} \div \frac{2}{8}$$

This is really 7 eighths ÷ 2 eighths, which is $$\frac{7}{8}$$ or 3$$\frac{1}{2}$$

Exercise 5.
$$\frac{13}{10} \div \frac{2}{10}$$

This is really 13 tenths ÷ 2 tenths, which is $$\frac{13}{2}$$ or 6$$\frac{1}{2}$$

Exercise 6.
$$\frac{11}{9} \div \frac{3}{9}$$

This is really 11 ninths ÷ 3 ninths, which is $$\frac{11}{3}$$ or 3$$\frac{2}{3}$$.

Eureka Math Grade 6 Module 2 Lesson 3 Problem Set Answer Key

For the following exercises, rewrite the division expression in unit form. Then, find the quotient. Draw a model to support your answer.

Question 1.
$$\frac{4}{5} \div \frac{1}{5}$$
4 fifths ÷ 1 fifth = 4

Question 2.
$$\frac{8}{9} \div \frac{4}{9}$$
8 ninths ÷ 4 ninths = 2

Question 3.
$$\frac{15}{4} \div \frac{3}{4}$$
15 fourths ÷ 3 fourths = 5

Question 4.
$$\frac{13}{5} \div \frac{4}{5}$$
13 fifths ÷ 4fifths = ÷=3

Rewrite the expression In unit form, and find the quotient.

Question 5.
$$\frac{10}{3} \div \frac{2}{3}$$
10 thirds ÷ 2 thirds = 5

Question 6.
$$\frac{8}{5} \div \frac{3}{5}$$
8 fifths ÷ 3 fifths = = 2

Question 7.
$$\frac{12}{7} \div \frac{12}{7}$$
12 sevenths ÷ 12 sevenths = 1

Represent the division expression using unit form. Find the quotient. Show all necessary work.

Question 8.
A runner is  mile from the finish line. If she can travel  mile per minute, how long will it take her to finish the race?
7 eighths ÷ 3 eighths = $$\frac{7}{3}=2 \frac{1}{3}$$
It will take her 2$$\frac{1}{3}$$ minutes to finish the race.

Question 9.
An electrician has 4. 1 meters of wire.
a. How many strips m long can he cut?
41 tenths ÷ 7 tenths = $$\frac{41}{7}$$ = 5$$\frac{6}{7}$$
He can cut 5 complete strips.

b. How much wire will he have left over?
He will have $$\frac{6}{10}$$m left over.

Question 10.
Saeed bought 21$$\frac{1}{2}$$ lb. of ground beef. He used $$\frac{1}{4}$$ of the beef to make tacos and $$\frac{2}{3}$$ of the remainder to make quarter-pound burgers. How many burgers did he make?
$$\frac{1}{2}$$ of 21$$\frac{1}{2}$$ = 10$$\frac{3}{4}$$ → 10$$\frac{3}{4}$$ Ib. of beef is used for burgers.
43 fourths ÷ 1 fourth = 43

Question 11.
A baker bought some flour. He used $$\frac{2}{5}$$ of the flour to make bread and used the rest to make batches of muffins. If he used 16 lb. of flour making bread and $$\frac{2}{3}$$ lb. for each batch of muffins, how many batches of muffins did he make?
16 is $$\frac{2}{5}$$ group of what size?
2 units = 16
1 unit = 16 ÷ 2 = 8
3 units = 3 × 8 = 24
The baker used 24 ib. of flour for muffins.

24 ÷ $$\frac{2}{3}$$
72 thirds ÷ 2 thirds = 36
The baker made 36 batches of muffins.

Eureka Math Grade 6 Module 2 Lesson 3 Exit Ticket Answer Key

Find the quotient. Draw a model to support your solution.

Question 1.
$$\frac{9}{4} \div \frac{3}{4}$$
This is really 9 fourths ÷ 3 fourths, which is 3.

Question 2.
$$\frac{7}{3} \div \frac{2}{3}$$
This is really 7 thirds ÷ 2 thirds, which is $$\frac{7}{2}$$ or 3$$\frac{1}{2}$$.

Eureka Math Grade 6 Module 2 Lesson 3 Opening Exercise Answer Key

Question 1.
Draw a model to represent 12 ÷ 3.
There are two interpretations:
Partitive Division

Measurement Division

Question 2.
Create a question or word problem that matches your model.