Two fractions are equivalent when they show the same amount, even though the numbers look different. You make an equivalent fraction by multiplying the numerator (top) and the denominator (bottom) by the very same number. For 2/3, multiplying both by 4 gives 8/12 — the same slice of the whole, just cut into more pieces. The golden rule is 'whatever you do to the bottom, do to the top', and you must multiply, not add. Ask 'what was the bottom multiplied by?' then do exactly that to the top.
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
- numerator
- the top number — how many parts you have
- denominator
- the bottom number — how many equal parts the whole is cut into
- equivalent
- equal in value, even though written differently
Worked examples
2/3 = ?/12
- 1.The bottom goes 3 to 12, that is × 4.
- 2.Multiply the top by 4: 2 × 4 = 8.
= 8/12
1/4 = ?/8
- 1.The bottom goes 4 to 8, that is × 2.
- 2.Multiply the top by 2: 1 × 2 = 2.
= 2/8
3/5 = ?/15
- 1.The bottom goes 5 to 15, that is × 3.
- 2.Multiply the top by 3: 3 × 3 = 9.
= 9/15
For parents
Method: Multiply the top and bottom by the same factor.
What to say: Ask 'what did you multiply the bottom by?' then do the very same thing to the top.
Common mistakes:
- Adding the same number to top and bottom instead of multiplying (2/3 → 11/12).
- Changing only the bottom and leaving the top the same (2/3 → 2/12).