Dividing Fractions: Word Problems worksheet with real-life scenarios and a playful design.

Problem: Dividing Fractions: Word Problems

The task involves solving word problems that require dividing fractions. Let's solve each problem step by step.

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#### Problem 1:
Tessa wants to make pillows for her couch. She has 6 pards of fabric. Each pillow uses $\frac{3}{4}$ of a yard of fabric. How many pillows can she make?

Solution:
To find out how many pillows Tessa can make, we need to divide the total amount of fabric by the amount of fabric required for one pillow.

- Total fabric: $6$ yards
- Fabric per pillow: $\frac{3}{4}$ yard

We calculate:
$$
\text{Number of pillows} = \frac{\text{Total fabric}}{\text{Fabric per pillow}} = \frac{6}{\frac{3}{4}}
$$

Dividing by a fraction is equivalent to multiplying by its reciprocal:
$$
\frac{6}{\frac{3}{4}} = 6 \times \frac{4}{3} = \frac{6 \times 4}{3} = \frac{24}{3} = 8
$$

Answer: Tessa can make $\boxed{8}$ pillows.

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#### Problem 2:
Zander is making individual desserts for a dinner party. He has $\frac{5}{6}$ of a cup of whipped cream, and he wants to put $\frac{1}{3}$ of a cup of whipped cream on each dessert. How many desserts can he make?

Solution:
To find out how many desserts Zander can make, we need to divide the total amount of whipped cream by the amount used per dessert.

- Total whipped cream: $\frac{5}{6}$ cup
- Whipped cream per dessert: $\frac{1}{3}$ cup

We calculate:
$$
\text{Number of desserts} = \frac{\text{Total whipped cream}}{\text{Whipped cream per dessert}} = \frac{\frac{5}{6}}{\frac{1}{3}}
$$

Dividing by a fraction is equivalent to multiplying by its reciprocal:
$$
\frac{\frac{5}{6}}{\frac{1}{3}} = \frac{5}{6} \times \frac{3}{1} = \frac{5 \times 3}{6 \times 1} = \frac{15}{6} = \frac{5}{2} = 2.5
$$

Since Zander cannot make half a dessert, he can make $2$ full desserts.

Answer: Zander can make $\boxed{2}$ desserts.

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#### Problem 3:
Daniel is using apple juice to make juice pops. He has 2 cups of juice, and each juice pop uses $\frac{2}{5}$ of a cup of juice. How many juice pops can he make?

Solution:
To find out how many juice pops Daniel can make, we need to divide the total amount of juice by the amount used per juice pop.

- Total juice: $2$ cups
- Juice per juice pop: $\frac{2}{5}$ cup

We calculate:
$$
\text{Number of juice pops} = \frac{\text{Total juice}}{\text{Juice per juice pop}} = \frac{2}{\frac{2}{5}}
$$

Dividing by a fraction is equivalent to multiplying by its reciprocal:
$$
\frac{2}{\frac{2}{5}} = 2 \times \frac{5}{2} = \frac{2 \times 5}{2} = \frac{10}{2} = 5
$$

Answer: Daniel can make $\boxed{5}$ juice pops.

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#### Problem 4:
Katie feeds her cat, Elvis, $\frac{3}{4}$ 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 it take Elvis to finish the bag of cat food?

Solution:
To find out how many days it will take Elvis to finish the bag of cat food, we need to divide the total amount of food by the amount of food consumed per day.

- Total food: $18$ cups
- Food per day: $\frac{3}{4}$ cup

We calculate:
$$
\text{Number of days} = \frac{\text{Total food}}{\text{Food per day}} = \frac{18}{\frac{3}{4}}
$$

Dividing by a fraction is equivalent to multiplying by its reciprocal:
$$
\frac{18}{\frac{3}{4}} = 18 \times \frac{4}{3} = \frac{18 \times 4}{3} = \frac{72}{3} = 24
$$

Answer: It will take Elvis $\boxed{24}$ days to finish the bag of cat food.

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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 $\frac{1}{8}$ of a foot long. The original wire is $\frac{3}{4}$ of a foot long. How many pieces will Lucas have?

Solution:
To find out how many pieces Lucas can cut from the wire, we need to divide the total length of the wire by the length of each piece.

- Total wire length: $\frac{3}{4}$ foot
- Length per piece: $\frac{1}{8}$ foot

We calculate:
$$
\text{Number of pieces} = \frac{\text{Total wire length}}{\text{Length per piece}} = \frac{\frac{3}{4}}{\frac{1}{8}}
$$

Dividing by a fraction is equivalent to multiplying by its reciprocal:
$$
\frac{\frac{3}{4}}{\frac{1}{8}} = \frac{3}{4} \times \frac{8}{1} = \frac{3 \times 8}{4 \times 1} = \frac{24}{4} = 6
$$

Answer: Lucas will have $\boxed{6}$ pieces.

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#### Problem 6:
Nina 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 3 cups of crushed ice in the ice maker. How many smoothies can she make with that ice?

Solution:
To find out how many smoothies Nina can make, we need to divide the total amount of crushed ice by the amount used per smoothie.

- Total crushed ice: $3$ cups
- Crushed ice per smoothie: $\frac{1}{4}$ cup

We calculate:
$$
\text{Number of smoothies} = \frac{\text{Total crushed ice}}{\text{Crushed ice per smoothie}} = \frac{3}{\frac{1}{4}}
$$

Dividing by a fraction is equivalent to multiplying by its reciprocal:
$$
\frac{3}{\frac{1}{4}} = 3 \times \frac{4}{1} = \frac{3 \times 4}{1} = \frac{12}{1} = 12
$$

Answer: Nina can make $\boxed{12}$ smoothies.

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#### Problem 7:
Oylan bought $\frac{1}{2}$ a pound of sunflower seeds. If one serving of sunflower seeds is $\frac{1}{16}$ of a pound, how many servings are in the bag?

Solution:
To find out how many servings Oylan has, we need to divide the total weight of the sunflower seeds by the weight of one serving.

- Total weight: $\frac{1}{2}$ pound
- Weight per serving: $\frac{1}{16}$ pound

We calculate:
$$
\text{Number of servings} = \frac{\text{Total weight}}{\text{Weight per serving}} = \frac{\frac{1}{2}}{\frac{1}{16}}
$$

Dividing by a fraction is equivalent to multiplying by its reciprocal:
$$
\frac{\frac{1}{2}}{\frac{1}{16}} = \frac{1}{2} \times \frac{16}{1} = \frac{1 \times 16}{2 \times 1} = \frac{16}{2} = 8
$$

Answer: There are $\boxed{8}$ servings in the bag.

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Final Answers:

1. $\boxed{8}$
2. $\boxed{2}$
3. $\boxed{5}$
4. $\boxed{24}$
5. $\boxed{6}$
6. $\boxed{12}$
7. $\boxed{8}$