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Functional Skills Level 2 — Fractions

Dividing Fractions

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How Do You Divide a Fraction by a Whole Number?

To divide a fraction by a whole number, multiply the denominator (the bottom number) by that whole number and keep the numerator the same. This works because dividing means splitting each piece you already have into smaller, equal parts.

\[\frac{a}{b} \div n = \frac{a}{b \times n}\]
3/4 ÷ 2 = Share 3/4 between 2 people Start: 3/4 (shaded) Split: Person 1: 3/8 Person 2: 3/8 3/4 ÷ 2 = 3/8   (denominator doubled) Why It Works: Dividing = Multiplying by the Reciprocal KEEP 3/4 first fraction unchanged CHANGE ÷ → × change ÷ to × FLIP 2/1 → 1/2 flip the divisor

Example 1 — \(\frac{3}{4} \div 2\)

Step 1
Multiply the denominator by 2: \(\frac{3}{4 \times 2} = \frac{3}{8}\)
Step 2
Answer: \(\mathbf{\frac{3}{8}}\)
Alternatively (KCF)
\(\frac{3}{4} \div 2 = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}\)

Example 2 — \(\frac{5}{6} \div 5\)

Step 1
Multiply denominator: \(\frac{5}{6 \times 5} = \frac{5}{30}\)
Step 2
Simplify: \(\frac{5}{30} = \mathbf{\frac{1}{6}}\)
Shortcut
Cancel the 5 in the numerator first: \(\frac{\cancel{5}}{6} \div \cancel{5} = \frac{1}{6}\)
Shortcut: If the whole number divides into the numerator exactly, cancel it — the answer is immediate. \(\frac{6}{7} \div 3 = \frac{2}{7}\).

✓ Quick Check 1 — Dividing a Fraction by a Whole Number

Question 1 of 10

The Keep-Change-Flip (KCF) Rule

To divide any fraction by any fraction: Keep the first fraction, Change the ÷ to ×, Flip the second fraction (find its reciprocal). Then multiply.

\[\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}\]
KCF: 2/3 ÷ 4/5 1. KEEP 2 3 unchanged 2. CHANGE ÷ → × change the operation 3. FLIP 5 4 4/5 flipped to 5/4 Result: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6 2/3 ÷ 4/5 → 2/3 × 5/4 = 10/12 = 5/6 simplify by dividing top and bottom by 2

Example 3 — \(\frac{2}{3} \div \frac{4}{5}\)

Keep
Keep \(\frac{2}{3}\)
Change
Change ÷ to ×
Flip
Flip \(\frac{4}{5}\) to \(\frac{5}{4}\)
Multiply
\(\frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \mathbf{\frac{5}{6}}\)

Example 4 — \(\frac{3}{8} \div \frac{3}{4}\)

KCF
\(\frac{3}{8} \times \frac{4}{3}\)
Cross-cancel
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.

Dividing Mixed Numbers — 3-Step Process STEP 1 Convert mixed numbers to improper fractions → STEP 2 Apply KCF (Keep, Change, Flip) → STEP 3 Multiply and simplify; convert back if needed Rope ⅚ m ÷ ¼ m pieces = how many pieces? piece 1 piece 2 piece 3 1/3 5/6 ÷ 1/4 = 5/6 × 4 = 20/6 = 10/3 = 3⅓ → 3 full pieces

Example 5 — \(2\frac{1}{2} \div 1\frac{1}{4}\)

Step 1
Convert: \(2\frac{1}{2} = \frac{5}{2}\)   \(1\frac{1}{4} = \frac{5}{4}\)
Step 2
KCF: \(\frac{5}{2} \times \frac{4}{5}\)
Step 3
Cross-cancel 5s: \(\frac{1}{2} \times \frac{4}{1} = \frac{4}{2} = \mathbf{2}\)

Example 6 — A task takes \(2\frac{1}{2}\) hours. How many \(\frac{1}{4}\)-hour slots does it fill?

Step 1
Set up: \(2\frac{1}{2} \div \frac{1}{4}\)
Step 2
Convert: \(\frac{5}{2} \div \frac{1}{4}\)
Step 3
KCF: \(\frac{5}{2} \times \frac{4}{1} = \frac{20}{2} = \mathbf{10}\) quarter-hour slots

✓ Quick Check 3 — Mixed Numbers and Real-Life

Question 1 of 10

Practice: Dividing Fractions

Use KCF to work out each division. Simplify your answer. Click Check All when done.

#QuestionAnswerResult
1½ ÷ ¼
22/3 ÷ 4/9
32½ ÷ 1¼
4¾ ÷ ⅜
51/3 ÷ 2/9
63 ÷ ¼
74/5 ÷ 2/5
81½ ÷ ¾
95/6 ÷ 5/12
102¼ ÷ 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.
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