Section C Practice Problems

Problem 1

Solve each problem. Write an equation.

The container holds $\frac{1}{2}$ gallon of water. It is $\frac{3}{4}$ full. How many gallons of water are in the container?
The container has $\frac{1}{2}$ gallon of water. Six friends split the water equally. How many gallons of water does each friend get?
The container holds 1 gallon of water. Each bottle holds $\frac{1}{8}$ of a gallon. How many bottles of water does the container hold?

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Solution

$\frac{3}{8}$ gallon. Sample response: $\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$
$\frac{1}{12}$ gallon. Sample response: $\frac{1}{2} \div 6 = \frac{1}{12}$
8 bottles. Sample response: $1 \div \frac{1}{8} = 8$

Problem 2

Clare has 5 yards of ribbon. It takes $\frac{1}{2}$ yard to make a bow. How many bows can Clare make with the ribbon? Write a multiplication and division equation.

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Solution

10 bows. Sample response:

5 \times 2 = 10

5 \div \frac{1}{2} = 10

Problem 3

What is the greatest product you can make using the numbers 4, 5, 6, 7, 8, or 9?

$\displaystyle \frac{\boxed{\phantom{\frac{000}{0}}}}{\boxed{\phantom{\frac{000}{0}}}} \times \frac{\boxed{\phantom{\frac{000}{0}}}}{\boxed{\phantom{\frac{000}{0}}}}$

You can use each number only once. Explain or show your reasoning.

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Solution

\frac{9}{4} \times \frac{8}{5} = \frac{72}{20}

. Sample response: This is the largest product because I used the largest 2 numbers for the numerators and the smallest 2 numbers for the denominators.

Problem 4

Each millimeter is $\frac{1}{1,000}$ of a meter. There are 1,000 micrometers in a millimeter. How many meters is a micrometer? Explain or show your reasoning.
There are 1,000 nanometers in a micrometer. How many meters is a nanometer? (A single human hair is about 50 micrometers thick. Nanometers are used to describe the size of atoms.)

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Solution

$\frac{1}{1,000,000}$ . Sample response: $\frac{1}{1,000} \div 1,000 = \frac{1}{1,000 \times 1,000}$
$\frac{1}{1,000,000,000}$ . Sample response: $\frac{1}{1,000,000} \div 1,000 = \frac{1}{1,000,000 \times 1,000}$

Problem 5

Jada wants to make a playpen for her dog with at least 70 square feet of space. She has 35 feet of fencing for the frame. Can Jada make a big enough playpen? Explain your reasoning.

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Solution

Yes. Sample responses:

She can make a pen that is $8 \frac{1}{2}$ feet by 9 feet since $8\frac{1}{2} + 9 = 17\frac{1}{2}$ and $2 \times 17 \frac{1}{2} = 35$ . Then $8\frac{1}{2} \times 9$ is $76\frac{1}{2}$ which is more than 70.
She can make a square pen. Each side will have length $35 \div 4$ or $\frac{35}{4}$ feet. Then the area is $\frac{35}{4} \times \frac{35}{4}$ or $\frac{1225}{16}$ square feet which is more than 70 square feet.