Dividing asks how many of one thing fit into another. How many quarters fit in 3? Each whole has 4 quarters, so 3 ÷ 1/4 = 12. Dividing a fraction by a whole number shares it: 3/4 ÷ 2 = 3/8. For any division by a fraction, keep the first number, change ÷ to ×, and flip the second: 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9.
Explore this idea with maths tools
Equal parts, equal wholes
2/4 = 4/8
Both bars are the same length. Find a division of the second bar that lines up exactly with the coloured edge.
Words to know
- reciprocal
- a fraction flipped over, like 4/3 for 3/4
- divisor
- the number you divide by
- keep, change, flip
- keep the first number, change ÷ to ×, flip the divisor
Worked examples
3 ÷ 1/4 = ?
- 1.Each whole has 4 quarters.
- 2.3 wholes have 3 × 4 = 12 quarters.
= 12
3/4 ÷ 2 = ?
- 1.Dividing by 2 is multiplying by 1/2.
- 2.3/4 × 1/2 = 3/8.
= 3/8
2/3 ÷ 3/4 = ?
- 1.Keep 2/3, change to ×, flip 3/4 to 4/3.
- 2.2/3 × 4/3 = 8/9.
= 8/9
For parents
Method: Keep, change, flip
What to say: How many of these fit into that? Which number gets flipped?
Common mistakes:
- Multiplies by the second number instead of dividing (3 ÷ 1/4 → 3/4).
- Gives the number of unit pieces in one whole, ignoring how many wholes there are.
- Flips the first number (the dividend) instead of the divisor before multiplying.
- Multiplies the numerator and denominator by the whole number, making an equivalent fraction instead of dividing.
- Flips both fractions before multiplying.