EZ Math

Pre-Algebra · Ratios, rates and proportions

How to Check if Two Ratios Are Equivalent

Problem

6:8 and 9:126 : 8 \text{ and } 9 : 12

Answer

equivalent\text{equivalent}

Two ratios are equivalent when they describe the same comparison, even if the numbers differ. Cross-multiplication is the quick test.

Step-by-step solution

  1. Write the ratios as fractions.

    68 and 912\frac{6}{8} \text{ and } \frac{9}{12}

    Why: A ratio compares two numbers by division, so it can be written as a fraction.

  2. Cross-multiply.

    6×12=72,8×9=726 \times 12 = 72,\quad 8 \times 9 = 72

    Why: Cross-multiplication turns the comparison into two plain numbers.

  3. Compare the products.

    72=72⇒equivalent72 = 72 \Rightarrow \text{equivalent}

    Why: Equal cross-products mean the fractions describe the same ratio.

Common mistakes

  • Multiplying straight across: 6 x 9 and 8 x 12.
  • Comparing the difference between the top and bottom instead of the products.
  • Stopping at 72 = 72 without saying the ratios are equivalent.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

  1. 2:5 and 6:152 : 5 \text{ and } 6 : 15

    Show answer

    equivalent\text{equivalent}

  2. 3:4 and 5:63 : 4 \text{ and } 5 : 6

    Show answer

    not equivalent\text{not equivalent}

  3. 4:10 and 6:154 : 10 \text{ and } 6 : 15

    Show answer

    equivalent\text{equivalent}

  4. 7:9 and 14:187 : 9 \text{ and } 14 : 18

    Show answer

    equivalent\text{equivalent}

  5. 5:8 and 10:165 : 8 \text{ and } 10 : 16

    Show answer

    equivalent\text{equivalent}