Printable fractions worksheet featuring multiplication exercises with mixed numbers and whole numbers.

To solve the problems in the fractions worksheet, we need to multiply mixed numbers and improper fractions. Here's how to approach each problem step by step:

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General Steps for Multiplying Mixed Numbers:

1. Convert mixed numbers to improper fractions.
2. Multiply the numerators together.
3. Multiply the denominators together.
4. Simplify the resulting fraction if possible.
5. Convert the result back to a mixed number if needed.

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Solutions:

#### 1 a. \( 4 \frac{1}{4} \times 6 \)
- Convert \( 4 \frac{1}{4} \) to an improper fraction:
\[
4 \frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{17}{4}
\]
- Multiply:
\[
\frac{17}{4} \times 6 = \frac{17 \times 6}{4} = \frac{102}{4}
\]
- Simplify:
\[
\frac{102}{4} = \frac{51}{2} = 25 \frac{1}{2}
\]

Answer: \( 25 \frac{1}{2} \)

#### 1 b. \( 1 \frac{5}{6} \times 6 \)
- Convert \( 1 \frac{5}{6} \) to an improper fraction:
\[
1 \frac{5}{6} = \frac{1 \times 6 + 5}{6} = \frac{11}{6}
\]
- Multiply:
\[
\frac{11}{6} \times 6 = \frac{11 \times 6}{6} = \frac{66}{6} = 11
\]

Answer: \( 11 \)

#### 2 a. \( 5 \times 9 \frac{3}{8} \)
- Convert \( 9 \frac{3}{8} \) to an improper fraction:
\[
9 \frac{3}{8} = \frac{9 \times 8 + 3}{8} = \frac{75}{8}
\]
- Multiply:
\[
5 \times \frac{75}{8} = \frac{5 \times 75}{8} = \frac{375}{8}
\]
- Convert back to a mixed number:
\[
\frac{375}{8} = 46 \frac{7}{8}
\]

Answer: \( 46 \frac{7}{8} \)

#### 2 b. \( 6 \times 6 \frac{2}{3} \)
- Convert \( 6 \frac{2}{3} \) to an improper fraction:
\[
6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{20}{3}
\]
- Multiply:
\[
6 \times \frac{20}{3} = \frac{6 \times 20}{3} = \frac{120}{3} = 40
\]

Answer: \( 40 \)

#### 3 a. \( 10 \frac{2}{6} \times 3 \)
- Simplify \( \frac{2}{6} \) to \( \frac{1}{3} \):
\[
10 \frac{2}{6} = 10 \frac{1}{3}
\]
- Convert \( 10 \frac{1}{3} \) to an improper fraction:
\[
10 \frac{1}{3} = \frac{10 \times 3 + 1}{3} = \frac{31}{3}
\]
- Multiply:
\[
\frac{31}{3} \times 3 = \frac{31 \times 3}{3} = 31
\]

Answer: \( 31 \)

#### 3 b. \( 4 \times 3 \frac{2}{6} \)
- Simplify \( \frac{2}{6} \) to \( \frac{1}{3} \):
\[
3 \frac{2}{6} = 3 \frac{1}{3}
\]
- Convert \( 3 \frac{1}{3} \) to an improper fraction:
\[
3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}
\]
- Multiply:
\[
4 \times \frac{10}{3} = \frac{4 \times 10}{3} = \frac{40}{3}
\]
- Convert back to a mixed number:
\[
\frac{40}{3} = 13 \frac{1}{3}
\]

Answer: \( 13 \frac{1}{3} \)

#### 4 a. \( 1 \frac{1}{2} \times 4 \)
- Convert \( 1 \frac{1}{2} \) to an improper fraction:
\[
1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2}
\]
- Multiply:
\[
\frac{3}{2} \times 4 = \frac{3 \times 4}{2} = \frac{12}{2} = 6
\]

Answer: \( 6 \)

#### 4 b. \( 6 \times 1 \frac{3}{4} \)
- Convert \( 1 \frac{3}{4} \) to an improper fraction:
\[
1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{7}{4}
\]
- Multiply:
\[
6 \times \frac{7}{4} = \frac{6 \times 7}{4} = \frac{42}{4} = \frac{21}{2}
\]
- Convert back to a mixed number:
\[
\frac{21}{2} = 10 \frac{1}{2}
\]

Answer: \( 10 \frac{1}{2} \)

#### 5 a. \( 2 \times 6 \frac{4}{8} \)
- Simplify \( \frac{4}{8} \) to \( \frac{1}{2} \):
\[
6 \frac{4}{8} = 6 \frac{1}{2}
\]
- Convert \( 6 \frac{1}{2} \) to an improper fraction:
\[
6 \frac{1}{2} = \frac{6 \times 2 + 1}{2} = \frac{13}{2}
\]
- Multiply:
\[
2 \times \frac{13}{2} = \frac{2 \times 13}{2} = 13
\]

Answer: \( 13 \)

#### 5 b. \( \frac{5}{6} \times 4 \)
- Multiply:
\[
\frac{5}{6} \times 4 = \frac{5 \times 4}{6} = \frac{20}{6}
\]
- Simplify:
\[
\frac{20}{6} = \frac{10}{3} = 3 \frac{1}{3}
\]

Answer: \( 3 \frac{1}{3} \)

#### 6 a. \( 3 \frac{2}{4} \times 5 \)
- Simplify \( \frac{2}{4} \) to \( \frac{1}{2} \):
\[
3 \frac{2}{4} = 3 \frac{1}{2}
\]
- Convert \( 3 \frac{1}{2} \) to an improper fraction:
\[
3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2}
\]
- Multiply:
\[
\frac{7}{2} \times 5 = \frac{7 \times 5}{2} = \frac{35}{2}
\]
- Convert back to a mixed number:
\[
\frac{35}{2} = 17 \frac{1}{2}
\]

Answer: \( 17 \frac{1}{2} \)

#### 6 b. \( 2 \times 11 \frac{1}{2} \)
- Convert \( 11 \frac{1}{2} \) to an improper fraction:
\[
11 \frac{1}{2} = \frac{11 \times 2 + 1}{2} = \frac{23}{2}
\]
- Multiply:
\[
2 \times \frac{23}{2} = \frac{2 \times 23}{2} = 23
\]

Answer: \( 23 \)

#### 7 a. \( 5 \times 1 \frac{5}{8} \)
- Convert \( 1 \frac{5}{8} \) to an improper fraction:
\[
1 \frac{5}{8} = \frac{1 \times 8 + 5}{8} = \frac{13}{8}
\]
- Multiply:
\[
5 \times \frac{13}{8} = \frac{5 \times 13}{8} = \frac{65}{8}
\]
- Convert back to a mixed number:
\[
\frac{65}{8} = 8 \frac{1}{8}
\]

Answer: \( 8 \frac{1}{8} \)

#### 7 b. \( 4 \times 7 \frac{4}{6} \)
- Simplify \( \frac{4}{6} \) to \( \frac{2}{3} \):
\[
7 \frac{4}{6} = 7 \frac{2}{3}
\]
- Convert \( 7 \frac{2}{3} \) to an improper fraction:
\[
7 \frac{2}{3} = \frac{7 \times 3 + 2}{3} = \frac{23}{3}
\]
- Multiply:
\[
4 \times \frac{23}{3} = \frac{4 \times 23}{3} = \frac{92}{3}
\]
- Convert back to a mixed number:
\[
\frac{92}{3} = 30 \frac{2}{3}
\]

Answer: \( 30 \frac{2}{3} \)

#### 8 a. \( 4 \frac{4}{6} \times 5 \)
- Simplify \( \frac{4}{6} \) to \( \frac{2}{3} \):
\[
4 \frac{4}{6} = 4 \frac{2}{3}
\]
- Convert \( 4 \frac{2}{3} \) to an improper fraction:
\[
4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{14}{3}
\]
- Multiply:
\[
\frac{14}{3} \times 5 = \frac{14 \times 5}{3} = \frac{70}{3}
\]
- Convert back to a mixed number:
\[
\frac{70}{3} = 23 \frac{1}{3}
\]

Answer: \( 23 \frac{1}{3} \)

#### 8 b. \( 6 \frac{1}{8} \times 6 \)
- Convert \( 6 \frac{1}{8} \) to an improper fraction:
\[
6 \frac{1}{8} = \frac{6 \times 8 + 1}{8} = \frac{49}{8}
\]
- Multiply:
\[
\frac{49}{8} \times 6 = \frac{49 \times 6}{8} = \frac{294}{8}
\]
- Simplify:
\[
\frac{294}{8} = \frac{147}{4} = 36 \frac{3}{4}
\]

Answer: \( 36 \frac{3}{4} \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1 \text{ a. } 25 \frac{1}{2} & 1 \text{ b. } 11 \\
2 \text{ a. } 46 \frac{7}{8} & 2 \text{ b. } 40 \\
3 \text{ a. } 31 & 3 \text{ b. } 13 \frac{1}{3} \\
4 \text{ a. } 6 & 4 \text{ b. } 10 \frac{1}{2} \\
5 \text{ a. } 13 & 5 \text{ b. } 3 \frac{1}{3} \\
6 \text{ a. } 17 \frac{1}{2} & 6 \text{ b. } 23 \\
7 \text{ a. } 8 \frac{1}{8} & 7 \text{ b. } 30 \frac{2}{3} \\
8 \text{ a. } 23 \frac{1}{3} & 8 \text{ b. } 36 \frac{3}{4} \\
\end{array}
}
\]