ratioProportion · Year 7 · Suggested learning sequence
Equivalent ratios
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.
Sample questions
Fill in the missing number so the ratios are equal: 2:3 = 6:?
- The first term goes from 2 to 6, which is × 3.
- Scale the second term by the same 3: 3 × 3 = 9.
- So 2:3 = 6:9.
Answer: 9
Fill in the missing number so the ratios are equal: 2:3 = 4:?
- The first term goes from 2 to 4, which is × 2.
- Scale the second term by the same 2: 3 × 2 = 6.
- So 2:3 = 4:6.
Answer: 6
Fill in the missing number so the ratios are equal: 3:5 = 9:?
- The first term goes from 3 to 9, which is × 3.
- Scale the second term by the same 3: 5 × 3 = 15.
- So 3:5 = 9:15.
Answer: 15