Dividing fractions
The trick of flipping the second one
What is this about?
Dividing by a fraction is asking how many times one thing fits inside another. How many halves fit in 3? Six. That's why dividing by a fraction smaller than 1 gives a BIGGER result than you'd expect: when you cut into small pieces, you get more pieces.
The rule to remember
Keep the first fraction as it is, flip the second one (swap numerator and denominator) and multiply. In other words: dividing by 2/3 is the same as multiplying by 3/2.
Example 1
3/4 ÷ 1/2
- 1Leave the first one alone: 3/4.
- 2Flip the second one: 1/2 becomes 2/1.
- 3Swap the division sign for a multiplication sign: 3/4 × 2/1.
- 4Multiply: top 3 × 2 = 6, bottom 4 × 1 = 4. That's 6/4.
- 5Simplify by dividing by 2: 3/2.
Result: 3/2
Example 2
2/5 ÷ 3/4
- 1The first one stays: 2/5.
- 2The second one flips: 3/4 becomes 4/3.
- 3Now multiply: 2/5 × 4/3.
- 4Top 2 × 4 = 8, bottom 5 × 3 = 15.
- 5That's 8/15, already simplified.
Result: 8/15
The most common mistake
Many people write
3/4 ÷ 1/2 = 3/8
Why it's wrong
The wrong fraction was flipped, or nothing was flipped at all before multiplying. Remember: the one that flips is ALWAYS the second one, the one after the division sign.
Did it click?
The best way to find out is to try. These exercises are exactly on this topic.
Practise this topic