What Is a Ratio?
A ratio compares two quantities. If a class has 12 boys and 8 girls, the ratio of boys to girls is 12:8, which simplifies to 3:2. You can write a ratio three ways: 3:2, 3/2, or "3 to 2" — they all mean the same thing.
To simplify a ratio, divide both parts by their GCD (Greatest Common Divisor). 12:8 → both divisible by 4 → 3:2.
Equivalent Ratios
Multiply or divide both parts of a ratio by the same number to get an equivalent ratio. 3:2 = 6:4 = 9:6 = 12:8. These are all the same ratio — they describe the same relationship. Equivalent ratios form a proportion: 3/2 = 9/6.
Solving a Proportion by Cross-Multiplying
If 3/4 = x/12, cross-multiply: 3 × 12 = 4 × x → 36 = 4x → x = 9. Cross-multiplication works because multiplying both fractions by both denominators gives the same result on each side.