Dividing Fractions: Word Problems | Interactive Worksheet ... - Free Printable

Let's solve each of the "Dividing Fractions: Word Problems" step by step. I'll go through each problem, explain the reasoning, and show the math.

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Problem 1:

Tina wants to make throw pillows for her couch. She has 6 yards of fabric. Each pillow uses $ \frac{3}{4} $ of a yard of fabric. How many pillows can she make?

#### Step-by-step:
We need to divide the total fabric by the amount used per pillow:
$$
6 \div \frac{3}{4}
$$

To divide by a fraction, multiply by its reciprocal:
$$
6 \times \frac{4}{3} = \frac{24}{3} = 8
$$

✔ Answer: Tina can make 8 pillows.

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Problem 2:

Joseph is making individual desserts for a dinner party. He has $ \frac{3}{4} $ of a cup of whipped cream, and he wants to put $ \frac{1}{8} $ of a cup of whipped cream on each dessert. How many desserts can he make?

#### Step-by-step:
$$
\frac{3}{4} \div \frac{1}{8}
$$

Multiply by the reciprocal:
$$
\frac{3}{4} \times \frac{8}{1} = \frac{24}{4} = 6
$$

✔ Answer: Joseph can make 6 desserts.

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Problem 3:

Darrel is using apple juice to make juice pops. He has 3 cups of juice, and each juice pop uses $ \frac{1}{4} $ of a cup of juice. How many juice pops can he make?

#### Step-by-step:
$$
3 \div \frac{1}{4} = 3 \times \frac{4}{1} = 12
$$

✔ Answer: Darrel can make 12 juice pops.

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Problem 4:

Yvette feeds her cat, Simon, $ \frac{3}{4} $ of a cup of food each day. She buys a bag of cat food that contains 18 cups of dry food. How many days will the bag of food last?

#### Step-by-step:
$$
18 \div \frac{3}{4} = 18 \times \frac{4}{3} = \frac{72}{3} = 24
$$

✔ Answer: The bag will last 24 days.

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Problem 5:

Lucas is making a wire sculpture for art class. For the sculpture, he needs to cut a wire into pieces that are each $ \frac{1}{4} $ of a foot long. If the original wire is $ \frac{3}{4} $ of a foot long, how many pieces can Lucas have?

#### Step-by-step:
$$
\frac{3}{4} \div \frac{1}{4} = \frac{3}{4} \times \frac{4}{1} = 3
$$

✔ Answer: Lucas can make 3 pieces.

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Problem 6:

Willa works at Sweet Smoothies. She uses $ \frac{1}{4} $ of a cup of crushed ice in each smoothie. When Nina starts her shift, there are 6 cups of crushed ice in the ice maker. How many smoothies can she make until the ice runs out?

#### Step-by-step:
$$
6 \div \frac{1}{4} = 6 \times \frac{4}{1} = 24
$$

✔ Answer: She can make 24 smoothies.

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Problem 7:

Dylan bought a $ \frac{3}{4} $-pound bag of sunflower seeds. If one serving of sunflower seeds is $ \frac{1}{8} $ of a pound, how many servings are in the bag?

#### Step-by-step:
$$
\frac{3}{4} \div \frac{1}{8} = \frac{3}{4} \times \frac{8}{1} = \frac{24}{4} = 6
$$

✔ Answer: There are 6 servings in the bag.

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✔ Final Answers:

1. 8 pillows
2. 6 desserts
3. 12 juice pops
4. 24 days
5. 3 pieces
6. 24 smoothies
7. 6 servings

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🔍 Key Concept:

When dividing fractions, you multiply by the reciprocal:
$$
a \div \frac{b}{c} = a \times \frac{c}{b}
$$

Also, remember: "How many groups of $ \frac{1}{4} $ are in $ \frac{3}{4} $" → this is division!

Let me know if you'd like a visual explanation or a printable version! 😊