Complex Fraction: Unit Rate online exercise for - Free Printable

Let's solve each problem step by step, following the instructions: set up the ratio, simplify (using division of fractions), and label with appropriate units. We'll also write a complete sentence for each answer.

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Problem 1: Joe painted $ \frac{1}{4} $ of a bedroom in $ \frac{1}{2} $ a day. How many days will it take for Joe to paint one bedroom?

#### Step 1: Set up the ratio
We want to find how many days it takes to paint 1 whole bedroom, given that $ \frac{1}{4} $ bedroom is painted in $ \frac{1}{2} $ day.

So, the rate is:
$$
\frac{\frac{1}{4} \text{ bedroom}}{\frac{1}{2} \text{ day}}
$$

This represents bedrooms per day, but we need to find how many days per bedroom.

To find days per bedroom, we can invert the rate or divide:

$$
\frac{1 \text{ bedroom}}{\frac{1}{4} \text{ bedroom}} \div \frac{1}{2} \text{ day}
\quad \Rightarrow \quad \frac{1}{\frac{1}{4}} \times \frac{1}{\frac{1}{2}} = ?
$$

But better to do:

We want:
$$
\text{Days per bedroom} = \frac{\frac{1}{2} \text{ day}}{\frac{1}{4} \text{ bedroom}} = \frac{1/2}{1/4} \text{ days per bedroom}
$$

So, set up the ratio:
$$
\frac{1/2}{1/4}
$$

#### Step 2: Simplify
Divide fractions:
$$
\frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times \frac{4}{1} = \frac{4}{2} = 2
$$

#### Step 3: Label with appropriate units
Answer: 2 days per bedroom

#### Sentence:
It will take Joe 2 days to paint one bedroom.

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Problem 2: A turtle walked $ \frac{1}{8} $ of a mile in $ \frac{1}{2} $ of an hour. How many miles will the turtle walk in one hour?

#### Step 1: Set up the ratio
Rate of walking:
$$
\frac{\frac{1}{8} \text{ mile}}{\frac{1}{2} \text{ hour}} = \frac{1/8}{1/2} \text{ miles per hour}
$$

We want miles per hour, so this is already in the right form.

#### Step 2: Simplify
$$
\frac{1}{8} \div \frac{1}{2} = \frac{1}{8} \times \frac{2}{1} = \frac{2}{8} = \frac{1}{4}
$$

#### Step 3: Label with appropriate units
Answer: $ \frac{1}{4} $ miles per hour

#### Sentence:
The turtle will walk $ \frac{1}{4} $ of a mile in one hour.

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Problem 3: Abby read $ \frac{1}{10} $ of a novel in $ \frac{1}{2} $ an hour. How long will it take her to read one novel?

#### Step 1: Set up the ratio
We want to know how many hours it takes to read 1 novel, given she reads $ \frac{1}{10} $ novel in $ \frac{1}{2} $ hour.

So:
$$
\frac{\frac{1}{2} \text{ hour}}{\frac{1}{10} \text{ novel}} = \frac{1/2}{1/10} \text{ hours per novel}
$$

#### Step 2: Simplify
$$
\frac{1}{2} \div \frac{1}{10} = \frac{1}{2} \times \frac{10}{1} = \frac{10}{2} = 5
$$

#### Step 3: Label with appropriate units
Answer: 5 hours per novel

#### Sentence:
It will take Abby 5 hours to read one novel.

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✔ Final Answers Filled In:

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#### Problem 1:
1. Set up the ratio:
$$
\frac{1/2}{1/4}
$$

2. Simplify:
$$
\frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times \frac{4}{1} = \frac{4}{2} = 2
$$

3. Label:
2 per day → 2 days per bedroom

Sentence: It will take Joe 2 days to paint one bedroom.

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#### Problem 2:
1. Set up the ratio:
$$
\frac{1/8}{1/2}
$$

2. Simplify:
$$
\frac{1}{8} \div \frac{1}{2} = \frac{1}{8} \times \frac{2}{1} = \frac{2}{8} = \frac{1}{4}
$$

3. Label:
$ \frac{1}{4} $ per hour → $ \frac{1}{4} $ miles per hour

Sentence: The turtle will walk $ \frac{1}{4} $ of a mile in one hour.

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#### Problem 3:
1. Set up the ratio:
$$
\frac{1/2}{1/10}
$$

2. Simplify:
$$
\frac{1}{2} \div \frac{1}{10} = \frac{1}{2} \times \frac{10}{1} = \frac{10}{2} = 5
$$

3. Label:
5 per hour → 5 hours per novel

Sentence: It will take Abby 5 hours to read one novel.

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✔ All problems solved using unit rates with complex fractions. Remember: when dividing fractions, multiply by the reciprocal!