Math worksheet from SplashLearn for practicing multiplication of mixed numbers and fractions through real-life word problems.

Let's solve each problem step by step.

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Problem 1:

Amy bought three and one-half lbs of flour and used half of it to bake cookies. How much flour did Amy use?

#### Step-by-Step Solution:
1. Convert the mixed number to an improper fraction:
- Three and one-half lbs = \( 3 \frac{1}{2} \)
- Convert \( 3 \frac{1}{2} \) to an improper fraction:
\[
3 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}
\]

2. Calculate half of the flour:
- Half of \( \frac{7}{2} \) is:
\[
\frac{1}{2} \times \frac{7}{2} = \frac{1 \times 7}{2 \times 2} = \frac{7}{4}
\]

3. Convert the result back to a mixed number (if needed):
- \( \frac{7}{4} = 1 \frac{3}{4} \)

#### Final Answer:
\[
\boxed{1 \frac{3}{4}}
\]

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Problem 2:

Tom has a rectangular cloth of length four and one-third inches and breadth one-fourth inch. Find the area of the fabric.

#### Step-by-Step Solution:
1. Convert the mixed number to an improper fraction:
- Length = four and one-third inches = \( 4 \frac{1}{3} \)
- Convert \( 4 \frac{1}{3} \) to an improper fraction:
\[
4 \frac{1}{3} = \frac{(4 \times 3) + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3}
\]

2. Breadth is already a fraction:
- Breadth = \( \frac{1}{4} \) inch

3. Calculate the area of the rectangle:
- Area = Length × Breadth
- \[
\text{Area} = \frac{13}{3} \times \frac{1}{4} = \frac{13 \times 1}{3 \times 4} = \frac{13}{12}
\]

4. Convert the result to a mixed number (if needed):
- \( \frac{13}{12} = 1 \frac{1}{12} \)

#### Final Answer:
\[
\boxed{1 \frac{1}{12}}
\]

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Problem 3:

Sia bought five and one-half lbs of fruits and used one-third of it to make smoothies. How much fruit did Sia use?

#### Step-by-Step Solution:
1. Convert the mixed number to an improper fraction:
- Five and one-half lbs = \( 5 \frac{1}{2} \)
- Convert \( 5 \frac{1}{2} \) to an improper fraction:
\[
5 \frac{1}{2} = \frac{(5 \times 2) + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2}
\]

2. Calculate one-third of the fruit:
- One-third of \( \frac{11}{2} \) is:
\[
\frac{1}{3} \times \frac{11}{2} = \frac{1 \times 11}{3 \times 2} = \frac{11}{6}
\]

3. Convert the result to a mixed number (if needed):
- \( \frac{11}{6} = 1 \frac{5}{6} \)

#### Final Answer:
\[
\boxed{1 \frac{5}{6}}
\]

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Problem 4:

Emily has a rectangular flower patch of length two and one-fifth yards and breadth three-fourths yard. Find the area of the patch.

#### Step-by-Step Solution:
1. Convert the mixed number to an improper fraction:
- Length = two and one-fifth yards = \( 2 \frac{1}{5} \)
- Convert \( 2 \frac{1}{5} \) to an improper fraction:
\[
2 \frac{1}{5} = \frac{(2 \times 5) + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5}
\]

2. Breadth is already a fraction:
- Breadth = \( \frac{3}{4} \) yard

3. Calculate the area of the rectangle:
- Area = Length × Breadth
- \[
\text{Area} = \frac{11}{5} \times \frac{3}{4} = \frac{11 \times 3}{5 \times 4} = \frac{33}{20}
\]

4. Convert the result to a mixed number (if needed):
- \( \frac{33}{20} = 1 \frac{13}{20} \)

#### Final Answer:
\[
\boxed{1 \frac{13}{20}}
\]

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Problem 5:

Ben bought seven and one-third yards of fabric and used one-fifth of it to make a scarf. How much fabric did Ben use?

#### Step-by-Step Solution:
1. Convert the mixed number to an improper fraction:
- Seven and one-third yards = \( 7 \frac{1}{3} \)
- Convert \( 7 \frac{1}{3} \) to an improper fraction:
\[
7 \frac{1}{3} = \frac{(7 \times 3) + 1}{3} = \frac{21 + 1}{3} = \frac{22}{3}
\]

2. Calculate one-fifth of the fabric:
- One-fifth of \( \frac{22}{3} \) is:
\[
\frac{1}{5} \times \frac{22}{3} = \frac{1 \times 22}{5 \times 3} = \frac{22}{15}
\]

3. Convert the result to a mixed number (if needed):
- \( \frac{22}{15} = 1 \frac{7}{15} \)

#### Final Answer:
\[
\boxed{1 \frac{7}{15}}
\]

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Final Answers:

1. \( \boxed{1 \frac{3}{4}} \)
2. \( \boxed{1 \frac{1}{12}} \)
3. \( \boxed{1 \frac{5}{6}} \)
4. \( \boxed{1 \frac{13}{20}} \)
5. \( \boxed{1 \frac{7}{15}} \)