Fraction word problems worksheet for practicing multiplication with mixed numbers.

Problem 1:

Gabe is barely 2 3/5 years old. He has spent 1/3 of his life sleeping or crying. How much of his short life has Gabe spent either sleeping or crying in years?

#### Solution:
1. Convert Gabe's age to an improper fraction:
\[
2 \frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5}
\]

2. Calculate the fraction of his life spent sleeping or crying:
\[
\text{Fraction spent sleeping or crying} = \frac{1}{3} \times \frac{13}{5}
\]

3. Multiply the fractions:
\[
\frac{1}{3} \times \frac{13}{5} = \frac{1 \times 13}{3 \times 5} = \frac{13}{15}
\]

4. Convert the result back to a mixed number if necessary:
\[
\frac{13}{15} \text{ is already in its simplest form.}
\]

#### Final Answer:
\[
\boxed{\frac{13}{15}}
\]

---

Problem 2:

Emily needs enough fabric for 3 1/2 hats, since she has half a hat done already. If each hat requires 1 2/7 feet of fabric, how much fabric will she need to make the 3 1/2 hats?

#### Solution:
1. Convert the number of hats to an improper fraction:
\[
3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}
\]

2. Convert the fabric required per hat to an improper fraction:
\[
1 \frac{2}{7} = \frac{1 \times 7 + 2}{7} = \frac{7 + 2}{7} = \frac{9}{7}
\]

3. Calculate the total fabric needed:
\[
\text{Total fabric} = \frac{7}{2} \times \frac{9}{7}
\]

4. Multiply the fractions:
\[
\frac{7}{2} \times \frac{9}{7} = \frac{7 \times 9}{2 \times 7} = \frac{63}{14}
\]

5. Simplify the result:
\[
\frac{63}{14} = \frac{9}{2} = 4 \frac{1}{2}
\]

#### Final Answer:
\[
\boxed{4 \frac{1}{2}}
\]

---

Problem 3:

Steven can run 1 2/9 miles in 10 minutes. How much can Steven run in half an hour if he keeps a consistent pace?

#### Solution:
1. Convert the distance Steven runs in 10 minutes to an improper fraction:
\[
1 \frac{2}{9} = \frac{1 \times 9 + 2}{9} = \frac{9 + 2}{9} = \frac{11}{9}
\]

2. Determine how many 10-minute intervals are in half an hour (30 minutes):
\[
\frac{30}{10} = 3
\]

3. Calculate the total distance Steven can run in 30 minutes:
\[
\text{Total distance} = 3 \times \frac{11}{9}
\]

4. Multiply the fractions:
\[
3 \times \frac{11}{9} = \frac{3 \times 11}{9} = \frac{33}{9}
\]

5. Simplify the result:
\[
\frac{33}{9} = \frac{11}{3} = 3 \frac{2}{3}
\]

#### Final Answer:
\[
\boxed{3 \frac{2}{3}}
\]

---

Problem 4:

Sandra plans to swim a total of 2 5/6 miles every week for 2 1/7 weeks. How much is Sandra planning to swim altogether?

#### Solution:
1. Convert the weekly swimming distance to an improper fraction:
\[
2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6}
\]

2. Convert the number of weeks to an improper fraction:
\[
2 \frac{1}{7} = \frac{2 \times 7 + 1}{7} = \frac{14 + 1}{7} = \frac{15}{7}
\]

3. Calculate the total distance Sandra plans to swim:
\[
\text{Total distance} = \frac{17}{6} \times \frac{15}{7}
\]

4. Multiply the fractions:
\[
\frac{17}{6} \times \frac{15}{7} = \frac{17 \times 15}{6 \times 7} = \frac{255}{42}
\]

5. Simplify the result:
\[
\frac{255}{42} = \frac{85}{14} = 6 \frac{1}{14}
\]

#### Final Answer:
\[
\boxed{6 \frac{1}{14}}
\]

---

Sub-problem 4a:

If Sandra decides to swim for another week, making that 3 1/7 weeks total, how much will she have swum altogether?

#### Solution:
1. Convert the new number of weeks to an improper fraction:
\[
3 \frac{1}{7} = \frac{3 \times 7 + 1}{7} = \frac{21 + 1}{7} = \frac{22}{7}
\]

2. Calculate the total distance Sandra will swim:
\[
\text{Total distance} = \frac{17}{6} \times \frac{22}{7}
\]

3. Multiply the fractions:
\[
\frac{17}{6} \times \frac{22}{7} = \frac{17 \times 22}{6 \times 7} = \frac{374}{42}
\]

4. Simplify the result:
\[
\frac{374}{42} = \frac{187}{21} = 8 \frac{19}{21}
\]

#### Final Answer:
\[
\boxed{8 \frac{19}{21}}
\]

---

Sub-problem 4b:

Sandra gets injured after 2 2/3 weeks. How much did she swim in all?

#### Solution:
1. Convert the number of weeks Sandra swam to an improper fraction:
\[
2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}
\]

2. Calculate the total distance Sandra swam:
\[
\text{Total distance} = \frac{17}{6} \times \frac{8}{3}
\]

3. Multiply the fractions:
\[
\frac{17}{6} \times \frac{8}{3} = \frac{17 \times 8}{6 \times 3} = \frac{136}{18}
\]

4. Simplify the result:
\[
\frac{136}{18} = \frac{68}{9} = 7 \frac{5}{9}
\]

#### Final Answer:
\[
\boxed{7 \frac{5}{9}}
\]

---

Summary of Answers:

1. \(\boxed{\frac{13}{15}}\)
2. \(\boxed{4 \frac{1}{2}}\)
3. \(\boxed{3 \frac{2}{3}}\)
4. \(\boxed{6 \frac{1}{14}}\)
- 4a: \(\boxed{8 \frac{19}{21}}\)
- 4b: \(\boxed{7 \frac{5}{9}}\)