Ratios and Proportions • Topic 2 of 7

Equivalent Ratios

Two ratios are equivalent if one can be obtained from the other by multiplying or dividing both parts by the same nonzero number — just like equivalent fractions. So 2 : 3, 4 : 6 and 10 : 15 are all the same ratio. To test whether a : b and c : d are equivalent, cross-multiply: they match exactly when a·d = b·c. Building a table of equivalent ratios is a fast way to scale a recipe or a map distance up or down. On the SAT, recognising equivalent ratios lets you jump straight to the value you need without solving a full equation.

✅ Solved examples

1. Is 3 : 4 equivalent to 9 : 12?
Cross-multiply: 3·12 = 36 and 4·9 = 36. They are equal, so the ratios are equivalent.
2. Fill in: 2 : 5 = 8 : ?
2 × 4 = 8, so multiply the other part by 4: 5 × 4 = 20.
3. Is 6 : 9 equivalent to 4 : 6?
Both reduce to 2 : 3, so yes.
4. Complete: 7 : 3 = ? : 9.
3 × 3 = 9, so 7 × 3 = 21.

✏️ Practice — try these, take hints as needed

1. Is 5 : 8 equivalent to 15 : 24?
Cross-multiply 5·24 and 8·15.
120 and 120.
Equal means equivalent.
Yes.
2. Fill in: 3 : 7 = 12 : ?
3 × 4 = 12.
Multiply the other part by 4.
7 × 4.
28.
3. Is 4 : 10 equivalent to 6 : 15?
Reduce both ratios.
4 : 10 = 2 : 5 and 6 : 15 = 2 : 5.
Compare.
Yes.
4. Complete: 9 : 4 = ? : 12.
4 × 3 = 12.
Multiply the first part by 3.
9 × 3.
27.
5. Fill in: 5 : 6 = 25 : ?
5 × 5 = 25.
Multiply the other part by 5.
6 × 5.
30.

📝 Topic test — 8 questions

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