To multiply a fraction by a whole number, multiply the numerator by the whole number and keep the denominator the same. Think of it as repeated addition.
\[\frac{a}{b} \times n = \frac{a \times n}{b}\]
Example 1 — \(\frac{3}{7} \times 4\)
Step 1
Multiply the numerator: \(3 \times 4 = 12\)
Step 2
Keep denominator 7: result is \(\frac{12}{7}\)
Step 3
Convert to mixed number: \(\frac{12}{7} = \mathbf{1\frac{5}{7}}\)
Divide by 3 first (÷3=30), then multiply by 2 (×2=60). Avoids large numbers.
Shortcut: For \(\frac{a}{b} \times n\), divide \(n\) by \(b\) first if possible (cancel down early) to keep numbers small.
✓ Quick Check 1 — Fraction × Whole Number
Question 1 of 10
Fraction × Fraction
To multiply two fractions, multiply the numerators together and multiply the denominators together. You can cross-cancel before multiplying to keep numbers small.
Work out each calculation and write the answer in simplest form. Click Check All when done.
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Question
Answer
Result
1
3/4 × 8
2
2/3 × 3/5
3
1½ × 2⅔
4
1/2 × 10
5
3/5 × 5/6
6
2/3 × 9
7
1/4 × 2/3
8
2⅓ × 3
9
5/6 × 3/10
10
1¼ × 2/5
⚠ Things to Watch Out For
Finding a common denominator (not needed): Unlike adding fractions, you do NOT need a common denominator to multiply. Simply multiply top × top and bottom × bottom.
Forgetting to simplify after multiplying: ¾ × ⅔ = 6/12 = ½. Always simplify the final answer.
Not cross-cancelling: Before multiplying, cancel common factors diagonally to keep numbers small. ¾ × ⅔ → cancel 3s → ¼ × 2/1 = 2/4 = ½.
Mixed numbers — not converting first: To multiply 1½ × 2⅓, convert to improper fractions first: 3/2 × 7/3 = 21/6 = 3½. Never multiply the whole and fractional parts separately.
Confusing multiplication and addition rules: For addition you need common denominators; for multiplication you don't. Applying the addition rule to multiplication is a very common error.