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 provide the solution.

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Problem 1:

Tina wants to make three 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 are given:
- Total fabric = 6 yards
- Fabric per pillow = $ \frac{3}{4} $ yard

To find how many pillows she can make, divide total fabric by fabric per pillow:

$$
\text{Number of pillows} = \frac{6}{\frac{3}{4}} = 6 \div \frac{3}{4}
$$

Dividing by a fraction is the same as multiplying by its reciprocal:

$$
= 6 \times \frac{4}{3} = \frac{24}{3} = 8
$$

✔ Answer: 8 pillows

> ✔ She can make 8 pillows (even though she only wanted 3, she has enough for more).

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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:
Total whipped cream = $ \frac{3}{4} $ cup
Per dessert = $ \frac{1}{8} $ cup

$$
\text{Number of desserts} = \frac{3/4}{1/8} = \frac{3}{4} \div \frac{1}{8}
$$

Multiply by reciprocal:

$$
= \frac{3}{4} \times \frac{8}{1} = \frac{24}{4} = 6
$$

✔ Answer: 6 desserts

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Problem 3:

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

#### Step-by-step:
Total juice = 3 cups
Each popsicle = $ \frac{1}{4} $ cup

$$
\text{Number of popsicles} = 3 \div \frac{1}{4} = 3 \times 4 = 12
$$

✔ Answer: 12 popsicles

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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:
Total food = 18 cups
Daily use = $ \frac{3}{4} $ cup

$$
\text{Number of days} = 18 \div \frac{3}{4} = 18 \times \frac{4}{3} = \frac{72}{3} = 24
$$

✔ Answer: 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}{6} $ 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:
Original wire length = $ \frac{3}{4} $ ft
Each piece = $ \frac{1}{6} $ ft

$$
\text{Number of pieces} = \frac{3/4}{1/6} = \frac{3}{4} \div \frac{1}{6} = \frac{3}{4} \times \frac{6}{1} = \frac{18}{4} = 4.5
$$

But we can't have half a piece — we need whole pieces, so we take the whole number part.

✔ Answer: 4 pieces

> 🚫 Note: The remainder is $ \frac{1}{4} $ ft, which is not enough for another $ \frac{1}{6} $ ft piece.

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Problem 6:

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

#### Step-by-step:
Total ice = 6 cups
Per smoothie = $ \frac{1}{6} $ cup

$$
\text{Number of smoothies} = 6 \div \frac{1}{6} = 6 \times 6 = 36
$$

✔ Answer: 36 smoothies

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Problem 7:

Glyn bought a $ \frac{1}{2} $-pound bag of sunflower seeds. If one serving of sunflower seeds is $ \frac{1}{16} $ of a pound, how many servings are in the bag?

#### Step-by-step:
Total weight = $ \frac{1}{2} $ lb
Serving size = $ \frac{1}{16} $ lb

$$
\text{Number of servings} = \frac{1/2}{1/16} = \frac{1}{2} \div \frac{1}{16} = \frac{1}{2} \times \frac{16}{1} = \frac{16}{2} = 8
$$

✔ Answer: 8 servings

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | 8 pillows |
| 2 | 6 desserts |
| 3 | 12 popsicles |
| 4 | 24 days |
| 5 | 4 pieces |
| 6 | 36 smoothies |
| 7 | 8 servings |

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🔍 Key Concept:

All these problems involve dividing fractions. The general rule is:

> To divide by a fraction, multiply by its reciprocal.

For example:
$$
a \div \frac{b}{c} = a \times \frac{c}{b}
$$

This method helps determine how many smaller parts fit into a larger quantity.

Let me know if you'd like this turned into a printable worksheet or want visual models!