Dividing a fraction by a whole number is the same as multiplying the denominator by that number. Think of it as splitting each piece into smaller parts.
\[\frac{a}{b} \div n = \frac{a}{b \times n}\]
Example 1 — \(\frac{3}{4} \div 2\)
Step 1
Multiply the denominator by 2: \(\frac{3}{4 \times 2} = \frac{3}{8}\)
3 cancels: \(\frac{1}{8} \times \frac{4}{1}\). Then 4 and 8 cancel: \(\frac{1}{2} \times \frac{1}{1}\)
Answer
\(\mathbf{\frac{1}{2}}\)
Common mistake: Students sometimes flip the first fraction instead of the second. Always flip the divisor (the number you are dividing by — the one after ÷).
✓ Quick Check 2 — The KCF Rule
Question 1 of 10
Mixed Numbers and Multi-Step Real-Life Problems
For mixed numbers: convert to improper fractions first, then apply KCF. Real-life problems often need an extra step — set up the division carefully before calculating.
Use KCF to work out each division. Simplify your answer. Click Check All when done.
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Question
Answer
Result
1
½ ÷ ¼
2
2/3 ÷ 4/9
3
2½ ÷ 1¼
4
¾ ÷ ⅜
5
1/3 ÷ 2/9
6
3 ÷ ¼
7
4/5 ÷ 2/5
8
1½ ÷ ¾
9
5/6 ÷ 5/12
10
2¼ ÷ ¾
⚠ Things to Watch Out For
Not flipping the right fraction: Keep-Change-Flip (KCF): keep the first fraction, change ÷ to ×, flip ONLY the second fraction. 2/3 ÷ 4/5 = 2/3 × 5/4. Do not flip the first fraction.
Flipping then forgetting to multiply: After applying KCF, you still need to multiply. The flip converts division into multiplication — then complete the multiplication step.
Dividing by a whole number: 3/4 ÷ 2 = 3/4 ÷ 2/1 = 3/4 × ½ = 3/8. Write whole numbers as fractions over 1 before applying KCF.
Not simplifying the final answer: After dividing, always check if the result simplifies. 10/12 = 5/6.
Mixed numbers: Convert to improper fractions BEFORE dividing. Never apply KCF to mixed numbers directly.