Two ratios are equivalent when they compare quantities in the same way, even though the numbers differ. You make an equivalent ratio by multiplying both terms by the same number. In 3:5 = 6:?, the first term goes from 3 to 6, which is × 2, so the second term is 5 × 2 = 10, giving 6:10. The key is to find the scale factor from the pair you know, then apply that same factor to the other term. You multiply by the factor — you never add the difference, and you never leave a term unchanged.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- equivalent ratios
- ratios that make the same comparison
- scale factor
- the number you multiply both terms by
- proportion
- a statement that two ratios are equal
Worked examples
3:5 = 6:?
- 1.First term × 2 (3 to 6).
- 2.5 × 2 = 10.
= 10
2:7 = 8:?
- 1.First term × 4 (2 to 8).
- 2.7 × 4 = 28.
= 28
4:3 = 12:?
- 1.First term × 3 (4 to 12).
- 2.3 × 3 = 9.
= 9
For parents
Method: Find the scale factor, then multiply the other term by it.
What to say: Ask 'how many times bigger did the first term get?' Do the same to the second.
Common mistakes:
- Adding the difference instead of multiplying (3:5 = 6:8).
- Copying the second term down unchanged (leaving it as 5).