Multiplying Fractions by a Mixed Number worksheet - Free Printable

Sure! Let’s solve each problem step by step. The key to multiplying fractions by mixed numbers is to:

1. Convert any mixed number to an improper fraction.
2. Multiply the numerators together and the denominators together.
3. Simplify the result (if needed) and convert back to a mixed number if required.

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Problem 1:

$\frac{2}{3} \times 3\frac{1}{5}$

Step 1: Convert $3\frac{1}{5}$ to an improper fraction:
$3\frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{16}{5}$

Step 2: Multiply:
$\frac{2}{3} \times \frac{16}{5} = \frac{2 \times 16}{3 \times 5} = \frac{32}{15}$

Step 3: Simplify/convert to mixed number:
$\frac{32}{15} = 2\frac{2}{15}$ (since 15 × 2 = 30, remainder 2)

✔ Final Answer = $2\frac{2}{15}$

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Problem 2:

$2\frac{1}{2} \times \frac{3}{7}$

Step 1: Convert $2\frac{1}{2}$ to improper fraction:
$2\frac{1}{2} = \frac{5}{2}$

Step 2: Multiply:
$\frac{5}{2} \times \frac{3}{7} = \frac{15}{14}$

Step 3: Convert to mixed number:
$\frac{15}{14} = 1\frac{1}{14}$

✔ Final Answer = $1\frac{1}{14}$

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Problem 3:

$1\frac{1}{2} \times 7$

Step 1: Convert $1\frac{1}{2}$ to improper fraction:
$1\frac{1}{2} = \frac{3}{2}$

Step 2: Multiply by 7 (which is $\frac{7}{1}$):
$\frac{3}{2} \times \frac{7}{1} = \frac{21}{2}$

Step 3: Convert to mixed number:
$\frac{21}{2} = 10\frac{1}{2}$

✔ Final Answer = $10\frac{1}{2}$

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Problem 4:

$\frac{5}{6} \times 3\frac{1}{3}$

Step 1: Convert $3\frac{1}{3}$ to improper fraction:
$3\frac{1}{3} = \frac{10}{3}$

Step 2: Multiply:
$\frac{5}{6} \times \frac{10}{3} = \frac{50}{18}$

Step 3: Simplify $\frac{50}{18}$:
Divide numerator and denominator by 2 → $\frac{25}{9}$

Step 4: Convert to mixed number:
$\frac{25}{9} = 2\frac{7}{9}$

✔ Final Answer = $2\frac{7}{9}$

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Problem 5:

$2\frac{1}{3} \times 1\frac{3}{5}$

Step 1: Convert both to improper fractions:
- $2\frac{1}{3} = \frac{7}{3}$
- $1\frac{3}{5} = \frac{8}{5}$

Step 2: Multiply:
$\frac{7}{3} \times \frac{8}{5} = \frac{56}{15}$

Step 3: Convert to mixed number:
$\frac{56}{15} = 3\frac{11}{15}$ (since 15 × 3 = 45, 56 - 45 = 11)

✔ Final Answer = $3\frac{11}{15}$

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## ✔ Final Answers Summary:

1. $\frac{2}{3} \times 3\frac{1}{5} = \boxed{2\frac{2}{15}}$

2. $2\frac{1}{2} \times \frac{3}{7} = \boxed{1\frac{1}{14}}$

3. $1\frac{1}{2} \times 7 = \boxed{10\frac{1}{2}}$

4. $\frac{5}{6} \times 3\frac{1}{3} = \boxed{2\frac{7}{9}}$

5. $2\frac{1}{3} \times 1\frac{3}{5} = \boxed{3\frac{11}{15}}$

Let me know if you’d like to see the work written out in a different format!