Ratios and Proportions

Ratio

A ratio compares two quantities. It can be written as a:b, a/b, or "a to b".

Proportion

A proportion is an equation stating that two ratios are equal: a/b = c/d.

Cross Products Property

If a/b = c/d, then ad = bc. This is the fundamental tool for solving proportions.

Properties of Proportions

• Reciprocal: If a/b = c/d, then b/a = d/c.
• Cross-multiply: ad = bc.
• Alternation: If a/b = c/d, then a/c = b/d.

Solving Proportions

Example: Solve x/6 = 10/15

Cross-multiply: 15x = 60 → x = 4