Pre-Algebra Foundations
Lesson 3 of 4 7 min +40 XP

Ratios & Proportions

Compare quantities and scale them.

What you'll learn

  • Write a ratio
  • Recognize equivalent ratios
  • Solve a proportion by cross-multiplying
Doubling the pancake recipe

The recipe uses 2 cups of flour for every 1 cup of milk. When friends come over you double it to 4 cups flour and 2 cups milk — the ratio stays 2-to-1 so the pancakes taste the same. Proportions are recipes scaled up or down.

A ratio compares two amounts

A ratio compares quantities, written 3:2 or 3/2. Two ratios that describe the same relationship are equivalent, like 1:2 and 3:6. A proportion states that two ratios are equal, and you can solve for a missing value by cross-multiplying.

Cross-multiply

If a/b = c/d, then a·d = b·c. This turns a proportion into a simple equation you can solve.

A recipe uses 2 cups flour per 3 cookies. For 9 cookies: 2/3 = x/9 → 3x = 18 → x = 6 cups.
Lab · Scale the recipe
  1. You have the proportion 4/5 = x/15.
  2. Cross-multiply to form an equation.
  3. Solve for x.

What you should see: 4·15 = 5·x → 60 = 5x → x = 12.

Knowledge Check

+10 XP / correct

1. Which ratio is equivalent to 2:3?

2. Solve the proportion 3/4 = x/12.