Ratios and proportions
What you'll learn
Set up a proportion and solve it by cross-multiplying — the workhorse of scaling and conversions.
A ratio compares two quantities; a proportion says two ratios are equal. Together they're how you scale recipes, read maps, and convert units.
Ratios
3 cups of flour to 2 cups of sugar is the ratio 3 : 2, also written as the fraction 3/2. Note it's not "3 out of 5" — it's 3 compared to 2.
Proportions and cross-multiplying
A proportion sets two ratios equal, with one unknown: 3/4 = 9/x. To solve, you cross-multiply — multiply each top by the other bottom:
3 · x = 4 · 9 → 3x = 36 → x = 12
Cross-multiply, then divide — that single move solves any proportion. The pre-algebra solver walks through it step by step if you want to check your work.
Check your understanding
Question 1 of 2
Solve the proportion 2/5 = x/20.