Ratios and Rates Worksheets - Math Monks - Free Printable

Let's solve each problem step by step, using unit rates and ratios of fractions.

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Problem 1:

John writes $\frac{1}{6}$ of a page in $\frac{1}{12}$ of a minute. How much time does it take him to write a full page?

We are given:
- $\frac{1}{6}$ page → $\frac{1}{12}$ minutes

We want to find how long it takes to write 1 full page.

So we set up a proportion:

$$
\frac{\frac{1}{6} \text{ page}}{\frac{1}{12} \text{ min}} = \frac{1 \text{ page}}{x \text{ min}}
$$

Cross-multiply:

$$
\frac{1}{6} \cdot x = 1 \cdot \frac{1}{12}
\Rightarrow x = \frac{1}{12} \div \frac{1}{6} = \frac{1}{12} \times \frac{6}{1} = \frac{6}{12} = \frac{1}{2}
$$

✔ Answer: It takes John $\frac{1}{2}$ minute (or 30 seconds) to write a full page.

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Problem 2:

David fills $\frac{1}{5}$ of a water bottle in $\frac{1}{25}$ of a minute. How much time will it take to fill the full water bottle?

Given:
- $\frac{1}{5}$ bottle → $\frac{1}{25}$ minutes

Find time for 1 full bottle.

Set up ratio:

$$
\frac{\frac{1}{5}}{\frac{1}{25}} = \frac{1}{x}
\Rightarrow \frac{1}{5} \cdot x = 1 \cdot \frac{1}{25}
\Rightarrow x = \frac{1}{25} \div \frac{1}{5} = \frac{1}{25} \times \frac{5}{1} = \frac{5}{25} = \frac{1}{5}
$$

✔ Answer: It takes David $\frac{1}{5}$ minute (or 12 seconds) to fill the full bottle.

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Problem 3:

Jen writes $\frac{1}{7}$ of a page in $\frac{1}{15}$ of a minute. How many minutes does it take her to write a full page?

Given:
- $\frac{1}{7}$ page → $\frac{1}{15}$ min

Find time for 1 page.

$$
x = \frac{1}{15} \div \frac{1}{7} = \frac{1}{15} \times \frac{7}{1} = \frac{7}{15}
$$

✔ Answer: It takes Jen $\frac{7}{15}$ minutes to write a full page.

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Problem 4:

Chris walked $\frac{1}{8}$ of a mile in $\frac{1}{16}$ of an hour. Compute the unit rate in simplified form.

Unit rate = miles per hour.

$$
\text{Rate} = \frac{\frac{1}{8} \text{ mile}}{\frac{1}{16} \text{ hour}} = \frac{1}{8} \div \frac{1}{16} = \frac{1}{8} \times \frac{16}{1} = \frac{16}{8} = 2
$$

✔ Answer: The unit rate is 2 miles per hour.

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Problem 5:

Gabriel drinks $\frac{1}{5}$ of milk in a glass in $\frac{1}{15}$ of a minute. How long will it take to complete the entire glass of milk?

Given:
- $\frac{1}{5}$ glass → $\frac{1}{15}$ min

Find time for 1 full glass.

$$
x = \frac{1}{15} \div \frac{1}{5} = \frac{1}{15} \times \frac{5}{1} = \frac{5}{15} = \frac{1}{3}
$$

✔ Answer: It takes Gabriel $\frac{1}{3}$ minute (or 20 seconds) to drink the entire glass.

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✔ Final Answers:

1. $\boxed{\frac{1}{2}}$ minute
2. $\boxed{\frac{1}{5}}$ minute
3. $\boxed{\frac{7}{15}}$ minutes
4. $\boxed{2}$ miles per hour
5. $\boxed{\frac{1}{3}}$ minute

Let me know if you'd like these explained visually or with diagrams!