Section B Practice Problems

Problem 1

Decide which expression is greater in each pair. Explain your choice without calculating the value of the expressions.

$210 \div 3$

$210 \div 5$
$210 \div 3$

$75 \div 3$

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Solution

$210 \div 3$ is greater. Sample response: There are more groups of 3 in 210 than there are groups of 5.
$210 \div 3$ is greater. Sample response: There are more groups of 3 in 210 than there are in 75.

Problem 2

A pan of macaroni and cheese is $\frac{1}{3}$ full. A group of 4 friends splits the remaining macaroni and cheese equally.

Make a drawing that represents the situation.
Write a division expression representing how much of a pan each friend gets.
Explain how the drawing shows the division expression.

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Solution

Sample response:

$\frac{1}{3} \div 4$
The left column is $\frac{1}{3}$ of the pan and I divided it into 4 equal pieces and shaded one of them.

Problem 3

Use this diagram to represent the expression $\frac{1}{5} \div 2$ .
Explain how the diagram shows $\frac{1}{5} \div 2$ .
What is the value of $\frac{1}{5} \div2$ ?

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Solution

Sample response:
Sample response: I first divided the tape into 5 equal parts and then I divided one of those pieces, which is $\frac{1}{5}$ , into two equal parts and shaded one of them.
$\frac{1}{10}$

Problem 4

Mai has a strip of paper that is 3 feet long. She cuts it into $\frac{1}{4}$ foot strips.

How many $\frac{1}{4}$ foot strips did Mai make? Explain or show your reasoning.
Write a division equation to represent your answer.

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Solution

12. Sample response. There are twelve $\frac{1}{4}$ s in 3.
$3 \div \frac{1}{4} = 12$ .

Problem 5

Find the value of each expression.

$5 \div \frac{1}{4}$
$6 \div \frac{1}{4}$
$3 \div \frac{1}{6}$
$3 \div \frac{1}{7}$

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Solution

Problem 6

Solve each problem. Write an equation.

There are 4 liters of water. How many $\frac{1}{2}$ liter bottles of water can you fill?
4 friends split $\frac{1}{2}$ pound of dried fruit equally. How many pounds of fruit does each friend get?

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Solution

Sample responses:

8, $4 \div \frac{1}{2} = 8$
$\frac{1}{8}$ , $\frac{1}{2} \div 4 = \frac{1}{8}$

Problem 7

Find the value of each expression. Explain or show your reasoning.

$3 \div \frac{1}{4}$
$\frac{1}{5} \div 8$

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Solution

12. Sample response: There are 4 $\frac{1}{4}$ s in 1 and so there are $3 \times 4$ or 12 $\frac{1}{4}$ s in 3.
$\frac{1}{40}$ . Sample response: There are 5 $\frac{1}{5}$ s in a whole and so if I divide each one into 8 equal pieces there are 40 of those smaller pieces in a whole.

Problem 8

For each diagram, write a story problem that the tape diagram represents. Then use the diagram to solve the problem.

Diagram. 4 equal parts, each labeled question mark. Total length, 1. — A

Diagram. 3 equal parts. 1 part divided into 4 equal parts, 1 shaded. Total length, 1. — B

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Solution

Sample responses:

Four students equally split a liter of milk. How many liters of milk did each student drink? $\frac{1}{4}$ liter
Noah has $\frac{1}{3}$ bag of dog treats left for his puppy for the next 4 days. Noah will give the puppy the same amount of treats each day. How much of a bag will the puppy get each day? $\frac{1}{12}$ bag

Problem 9

It takes Earth 1 year to go around the Sun.

During the time it takes Earth to go around the Sun, Mercury goes around the Sun about 4 times. How many years does it take Mercury to make 1 full orbit of the Sun?
During the time it takes Earth to go around the Sun, Saturn goes $\frac{1}{29}$ of the way around the Sun. How many years does it take Saturn to go around the Sun?

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Solution

Sample responses:

$\frac{1}{4}$ year because $1 \div 4 = \frac{1}{4}$
29 years because $1 \div \frac{1}{29} = 29$ .