Math worksheet with word problems on fractions and mixed numbers for practice.

Problem 1: Sheila is baking cakes

Question: 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?

#### Solution:
1. Convert mixed numbers to improper fractions:
- Each cake requires \( 2 \frac{1}{2} \) cups of sugar.
\[
2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}
\]
- Sheila has \( 7 \frac{1}{3} \) cups of sugar.
\[
7 \frac{1}{3} = \frac{7 \times 3 + 1}{3} = \frac{22}{3}
\]

2. Set up the division problem:
- To find how many cakes Sheila can bake, divide the total sugar by the sugar required per cake:
\[
\text{Number of cakes} = \frac{\text{Total sugar}}{\text{Sugar per cake}} = \frac{\frac{22}{3}}{\frac{5}{2}}
\]

3. Divide fractions by multiplying by the reciprocal:
\[
\frac{\frac{22}{3}}{\frac{5}{2}} = \frac{22}{3} \times \frac{2}{5} = \frac{22 \times 2}{3 \times 5} = \frac{44}{15}
\]

4. Convert the improper fraction to a mixed number:
\[
\frac{44}{15} = 2 \frac{14}{15}
\]
- This means Sheila can bake 2 whole cakes and will have enough sugar left over for \(\frac{14}{15}\) of another cake.

5. Final Answer:
\[
\boxed{2}
\]

---

Problem 2: Sheldon is running

Question: 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?

#### Solution:
1. Convert the pace to an improper fraction:
- Sheldon's pace is \( 6 \frac{4}{5} \) minutes per mile.
\[
6 \frac{4}{5} = \frac{6 \times 5 + 4}{5} = \frac{34}{5}
\]

2. Set up the division problem:
- To find how many miles Sheldon can run in 30 minutes, divide the total time by the time per mile:
\[
\text{Miles} = \frac{\text{Total time}}{\text{Time per mile}} = \frac{30}{\frac{34}{5}}
\]

3. Divide fractions by multiplying by the reciprocal:
\[
\frac{30}{\frac{34}{5}} = 30 \times \frac{5}{34} = \frac{30 \times 5}{34} = \frac{150}{34}
\]

4. Simplify the fraction:
- Both 150 and 34 can be divided by 2:
\[
\frac{150}{34} = \frac{75}{17}
\]

5. Convert the improper fraction to a mixed number:
\[
\frac{75}{17} = 4 \frac{7}{17}
\]
- This means Sheldon can run 4 full miles and will have enough time left over for \(\frac{7}{17}\) of another mile.

6. Final Answer:
\[
\boxed{4}
\]

---

Problem 3: Lourdes' plant growth

Question: 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?

#### Solution:
1. Convert the growth rate and target height to improper fractions:
- Growth rate: \( 1 \frac{2}{5} \) inches per month.
\[
1 \frac{2}{5} = \frac{1 \times 5 + 2}{5} = \frac{7}{5}
\]
- Target height: \( 10 \frac{2}{3} \) inches.
\[
10 \frac{2}{3} = \frac{10 \times 3 + 2}{3} = \frac{32}{3}
\]

2. Set up the division problem:
- To find how many months it will take for the plant to grow to the target height, divide the target height by the growth rate:
\[
\text{Months} = \frac{\text{Target height}}{\text{Growth rate}} = \frac{\frac{32}{3}}{\frac{7}{5}}
\]

3. Divide fractions by multiplying by the reciprocal:
\[
\frac{\frac{32}{3}}{\frac{7}{5}} = \frac{32}{3} \times \frac{5}{7} = \frac{32 \times 5}{3 \times 7} = \frac{160}{21}
\]

4. Convert the improper fraction to a mixed number:
\[
\frac{160}{21} = 7 \frac{13}{21}
\]
- This means it will take 7 full months and an additional \(\frac{13}{21}\) of a month.

5. Final Answer:
\[
\boxed{7}
\]

---

Problem 4: Elsa's bathroom tiling

Question: 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 cover the length of the bathroom?

#### Solution:
1. Convert the bathroom length to an improper fraction:
- Bathroom length: \( 7 \frac{1}{3} \) feet.
\[
7 \frac{1}{3} = \frac{7 \times 3 + 1}{3} = \frac{22}{3}
\]

2. Set up the division problem:
- To find how many tiles are needed to cover the length, divide the bathroom length by the tile length:
\[
\text{Number of tiles} = \frac{\text{Bathroom length}}{\text{Tile length}} = \frac{\frac{22}{3}}{\frac{4}{9}}
\]

3. Divide fractions by multiplying by the reciprocal:
\[
\frac{\frac{22}{3}}{\frac{4}{9}} = \frac{22}{3} \times \frac{9}{4} = \frac{22 \times 9}{3 \times 4} = \frac{198}{12}
\]

4. Simplify the fraction:
- Both 198 and 12 can be divided by 6:
\[
\frac{198}{12} = \frac{33}{2}
\]

5. Convert the improper fraction to a mixed number:
\[
\frac{33}{2} = 16 \frac{1}{2}
\]
- This means Elsa needs 16 full tiles and half of another tile. Since she cannot use half a tile, she will need 17 tiles in total.

6. Final Answer:
\[
\boxed{17}
\]

---

Subquestion 4a: Tiles for the width

Question: 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?

#### Solution:
1. Convert the bathroom width to an improper fraction:
- Bathroom width: \( 5 \frac{3}{4} \) feet.
\[
5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{23}{4}
\]

2. Set up the division problem:
- To find how many tiles are needed to cover the width, divide the bathroom width by the tile width:
\[
\text{Number of tiles} = \frac{\text{Bathroom width}}{\text{Tile width}} = \frac{\frac{23}{4}}{\frac{4}{9}}
\]

3. Divide fractions by multiplying by the reciprocal:
\[
\frac{\frac{23}{4}}{\frac{4}{9}} = \frac{23}{4} \times \frac{9}{4} = \frac{23 \times 9}{4 \times 4} = \frac{207}{16}
\]

4. Convert the improper fraction to a mixed number:
\[
\frac{207}{16} = 12 \frac{15}{16}
\]
- This means Elsa needs 12 full tiles and \(\frac{15}{16}\) of another tile. Since she cannot use a fraction of a tile, she will need 13 tiles in total.

5. Final Answer:
\[
\boxed{13}
\]

---

Final Summary of Answers:

1. Sheila's cakes: \(\boxed{2}\)
2. Sheldon's miles: \(\boxed{4}\)
3. Lourdes' plant growth: \(\boxed{7}\)
4. Elsa's tiles (length): \(\boxed{17}\)
5. Elsa's tiles (width): \(\boxed{13}\)