Math worksheet on word problems with fractions and mixed numbers for students to solve.

Let's solve each of these word problems involving fractions and mixed numbers step by step. I'll show all the work, use labels, and explain the reasoning clearly.

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Problem 1: Sheila’s Cakes

> Sheila is baking a few cakes for the bake sale for her school. Each cake requires 2 1/2 cups of sugar. How many cakes can she bake if she has 7 1/3 cups of sugar?

#### Step 1: Convert mixed numbers to improper fractions
- $ 2 \frac{1}{2} = \frac{5}{2} $
- $ 7 \frac{1}{3} = \frac{22}{3} $

#### Step 2: Divide total sugar by sugar per cake
We want to find how many cakes (each using $ \frac{5}{2} $ cups) can be made from $ \frac{22}{3} $ cups:
$$
\frac{22}{3} \div \frac{5}{2} = \frac{22}{3} \times \frac{2}{5} = \frac{44}{15}
$$

#### Step 3: Convert improper fraction to mixed number
$$
\frac{44}{15} = 2 \frac{14}{15}
$$

Since she can't bake a fraction of a cake, we take the whole number part only.

✔ Answer: She can bake 2 full cakes.

> ✔ Final Answer: 2 cakes

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Problem 2: Sheldon’s Running

> Sheldon is a long-distance runner. He can run a mile at a consistent pace of 6 4/5 minutes. How many miles can he run in 30 minutes, if he keeps that pace?

#### Step 1: Convert mixed number to improper fraction
- $ 6 \frac{4}{5} = \frac{34}{5} $ minutes per mile

#### Step 2: Divide total time by time per mile
$$
30 \div \frac{34}{5} = 30 \times \frac{5}{34} = \frac{150}{34}
$$

Simplify:
$$
\frac{150}{34} = \frac{75}{17} \approx 4.4118
$$

Convert to mixed number:
$$
\frac{75}{17} = 4 \frac{7}{17}
$$

✔ Answer: Sheldon can run 4 7/17 miles in 30 minutes.

> ✔ Final Answer: 4 7/17 miles

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Problem 3: Lourdes’ Plant Growth

> Lourdes got a plant as a birthday gift. Her plant grows an average of 1 2/5 inches every month. How long will it take for the plant to grow a full 10 2/3 inches?

#### Step 1: Convert mixed numbers to improper fractions
- Growth per month: $ 1 \frac{2}{5} = \frac{7}{5} $
- Total growth needed: $ 10 \frac{2}{3} = \frac{32}{3} $

#### Step 2: Divide total growth by monthly growth
$$
\frac{32}{3} \div \frac{7}{5} = \frac{32}{3} \times \frac{5}{7} = \frac{160}{21}
$$

Convert to mixed number:
$$
\frac{160}{21} = 7 \frac{13}{21}
$$

✔ Answer: It will take 7 13/21 months.

> ✔ Final Answer: 7 13/21 months

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#### a) How long will Lourdes have to wait for her plant to grow a total of 14 1/4 inches?

Total growth needed: $ 14 \frac{1}{4} = \frac{57}{4} $

Use same monthly growth: $ \frac{7}{5} $

$$
\frac{57}{4} \div \frac{7}{5} = \frac{57}{4} \times \frac{5}{7} = \frac{285}{28}
$$

Convert to mixed number:
$$
\frac{285}{28} = 10 \frac{5}{28}
$$

✔ Answer: It will take 10 5/28 months.

> ✔ Final Answer: 10 5/28 months

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Problem 4: Elsa’s Bathroom Tiling

> Elsa is remodeling her bathroom floor. She is going to use tile that is 4/9 of a foot long. If her bathroom is 7 1/3 feet long, how many tiles will she need to first cover the length of the bathroom?

#### Step 1: Convert mixed number to improper fraction
- Length of bathroom: $ 7 \frac{1}{3} = \frac{22}{3} $
- Tile length: $ \frac{4}{9} $

#### Step 2: Divide length by tile size
$$
\frac{22}{3} \div \frac{4}{9} = \frac{22}{3} \times \frac{9}{4} = \frac{198}{12}
$$

Simplify:
$$
\frac{198}{12} = \frac{33}{2} = 16 \frac{1}{2}
$$

Since you can’t use half a tile in practice (you must cover the full length), you need to round up.

✔ Answer: She needs 17 tiles to cover the length.

> ✔ Final Answer: 17 tiles

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#### a) Elsa’s tile is a square, so it is also 4/9 of a foot wide. If Elsa’s bathroom is 5 3/4 feet wide, how many tiles will she need to cover the width of her bathroom?

Width of bathroom: $ 5 \frac{3}{4} = \frac{23}{4} $

Tile width: $ \frac{4}{9} $

$$
\frac{23}{4} \div \frac{4}{9} = \frac{23}{4} \times \frac{9}{4} = \frac{207}{16}
$$

Convert to mixed number:
$$
\frac{207}{16} = 12 \frac{15}{16}
$$

Again, round up because you need full tiles.

✔ Answer: She needs 13 tiles to cover the width.

> ✔ Final Answer: 13 tiles

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✔ Summary of Answers:

| Problem | Answer |
|--------|--------|
| 1 | 2 cakes |
| 2 | 4 7/17 miles |
| 3 | 7 13/21 months |
| 3a | 10 5/28 months |
| 4 | 17 tiles (length) |
| 4a | 13 tiles (width) |

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📝 Notes:

- Always convert mixed numbers → improper fractions before dividing.
- When dividing fractions, multiply by the reciprocal.
- For real-world problems (like tiles or cakes), round up when necessary (can't use partial items).
- Use labels like "miles", "tiles", "months" in your answers.

Let me know if you'd like this printed out or formatted for a student!