5th Grade Math - Interpret the Product (a/b) × q as a Part of a Partition of q into b Equal Parts: CCSS.Math.Content.5.NF.B.4a

Katie made gallons of punch. $\frac{1}{6}$ of the punch was water. How much water did she use to make the punch?

$\frac{3}{6}$

$\frac{1}{6}$

$\frac{4}{6}$

Explanation

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{6}$ of the punch is water.

We know that we have gallons of punch so we can set up our multiplication problem.

$\frac{1}{6}\times3$

3 6

$\frac{1}{6}\times3$ which means $\frac{1}{6}$ of each group of $3=\frac{3}{6}$

Lauren made gallons of punch. $\frac{1}{9}$ of the punch was water. How much water did she use to make the punch?

$\frac{5}{9}$

$\frac{6}{9}$

$\frac{7}{9}$

Explanation

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{9}$ of the punch is water.

We know that we have gallons of punch so we can set up our multiplication problem.

$\frac{1}{9}\times5$

5 9

$\frac{1}{9}\times5$ which means $\frac{1}{9}$ of each group of $5=\frac{5}{9}$

Lindsey made gallons of punch. $\frac{1}{10}$ of the punch was water. How much water did she use to make the punch?

$\frac{8}{10}$

$\frac{9}{10}$

$\frac{7}{10}$

Explanation

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{10}$ of the punch is water.

We know that we have gallons of punch so we can set up our multiplication problem.

$\frac{1}{10}\times8$

8 10

$\frac{1}{10}\times8$ which means $\frac{1}{10}$ of each group of $8=\frac{8}{10}$

Beatrice has six cats. Each cat eats $\frac{2}{3}$ of a can of cat food each day. Set up a mathematical equation to find the number of cans of cat food that Beatrice goes through each day to feed all six of her cats.

$6\ cats\times \frac{2}{3}\ can\ per\ cat=6\times \frac{2}{3}=\frac{12}{3}=4\ cans\ per\ day$

$6\ cats\times \frac{2}{3}\ can\ per\ cat=6\times \frac{2}{3}=\frac{12}{3}=9\ cans\ per\ day$

$6\ cats\times \frac{3}{2}\ can\ per\ cat=6\times \frac{3}{2}=\frac{18}{2}=9\ cans\ per\ day$

$6\ cats\times \frac{2}{3}\ can\ per\ cat=6\times \frac{2}{3}=\frac{18}{3}=6\ cans\ per\ day$

$6\ cats+ \frac{2}{3}\ can\ per\ cat=6+ \frac{2}{3}=\frac{20}{3}\ cans\ per\ day$

Explanation

Kenzie lives $\frac{5}{9}$ of a mile away from her friend's house. She walked $\frac{1}{3}$ of the way there and then stopped to get ice cream from an ice cream truck driving by. How far did she travel before she stopped to get ice cream?

$\frac{5}{27}\text{ of a mile}$

$\frac{6}{27}\text{ of a mile}$

$\frac{6}{26}\text{ of a mile}$

$\frac{7}{26}\text{ of a mile}$

$\frac{4}{26}\text{ of a mile}$

Explanation

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{3}$ of the way to her friends house she stopped.

We know that her friend lives $\frac{5}{9}$ of a mile away from her so we can set up our multiplication problem.

$\frac{1}{3}\times\frac{5}{9}$

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

5 27

We make the area model by because those are the denominators of our fractions. We shade up and over , because those are the numerators of our fractions. Our answer is a fraction made up of the boxes that are shaded (the numerator) and the total tiles in the area model (the denominator).

$\frac{1}{3}\times\frac{5}{9}=\frac{5}{27}$

Brooke made gallons of punch. $\frac{1}{7}$ of the punch was water. How much water did she use to make the punch?

$\frac{2}{7}$

$\frac{3}{7}$

$\frac{4}{7}$

Explanation

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{7}$ of the punch is water.

We know that we have gallons of punch so we can set up our multiplication problem.

$\frac{1}{7}\times2$

2 7

$\frac{1}{7}\times2$ which means $\frac{1}{7}$ of each group of $2=\frac{2}{7}$

Emily made gallons of punch. $\frac{1}{8}$ of the punch was water. How much water did she use to make the punch?

$\frac{6}{8}$

$\frac{5}{8}$

$\frac{3}{8}$

Explanation

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{8}$ of the punch is water.

We know that we have gallons of punch so we can set up our multiplication problem.

$\frac{1}{8}\times6$

6 8

$\frac{1}{8}\times6$ which means $\frac{1}{8}$ of each group of $6=\frac{6}{8}$

Kate made gallons of punch. $\frac{1}{9}$ of the punch was water. How much water did she use to make the punch?

$\frac{7}{9}$

$\frac{8}{9}$

$\frac{5}{9}$

Explanation

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{9}$ of the punch is water.

We know that we have gallons of punch so we can set up our multiplication problem.

$\frac{1}{9}\times7$

7 9

$\frac{1}{9}\times7$ which means $\frac{1}{9}$ of each group of $7=\frac{7}{9}$

Ronda made gallons of punch. $\frac{1}{5}$ of the punch was water. How much water did she use to make the punch?

$\frac{3}{5}$

$\frac{2}{5}$

$\frac{1}{5}$

Explanation

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{5}$ of the punch is water.

We know that we have gallons of punch so we can set up our multiplication problem.

$\frac{1}{5}\times3$

3 5

$\frac{1}{5}\times3$ which means $\frac{1}{5}$ of each group of $3=\frac{3}{5}$

Lisa made gallons of punch. $\frac{1}{8}$ of the punch was water. How much water did she use to make the punch?

$\frac{2}{8}$

$\frac{3}{8}$

$\frac{6}{8}$

Explanation

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{8}$ of the punch is water.