What Are Ratios?
Comparing two quantities side by side — the math behind recipes, maps, scale models, and fair shares.
What Is a Ratio?
A ratio compares two quantities by showing how much of one thing there is relative to another. If a classroom has 12 boys and 15 girls, the ratio of boys to girls is 12 to 15, written as 12:15 or 12/15. Ratios tell you the relationship between amounts — not just the amounts themselves. They answer questions like "for every 4 boys, how many girls are there?" (the simplified ratio is 4:5).
Writing and Simplifying Ratios
Ratios can be written three ways: with a colon (3:4), as a fraction (3/4), or with the word "to" (3 to 4). Like fractions, ratios can be simplified by dividing both numbers by their greatest common factor. The ratio 10:15 simplifies to 2:3 (divide both by 5). Simplified ratios are easier to understand and compare.
Equivalent Ratios
Just like equivalent fractions, equivalent ratios express the same relationship with different numbers. 2:3 is the same ratio as 4:6, 6:9, and 10:15 — they all describe the same proportion. To find equivalent ratios, multiply or divide both sides by the same number. This concept is crucial for scaling recipes (doubling a recipe means multiplying every ingredient by 2 while keeping the ratios the same) and reading maps (a 1:100,000 scale means 1 cm on the map equals 100,000 cm in real life).
Ratios in Real Life
Cooking: A lemonade recipe calls for 2 cups of sugar for every 8 cups of water — a 2:8 (or 1:4) ratio. Want to make a bigger batch? Keep the ratio. Maps: A map scale of 1:50,000 means every centimeter on paper represents 50,000 centimeters (500 meters) in reality. Mixing paint: To make orange, you mix red and yellow in a specific ratio — change the ratio and you get a different shade.
Ratios vs. Fractions
Ratios and fractions look similar but serve different purposes. A fraction represents part of a whole: 3/7 of the class likes soccer. A ratio compares two separate quantities: the ratio of soccer fans to non-soccer fans is 3:4. The fraction uses the total (7) as the denominator; the ratio compares the two groups directly. Understanding this distinction prevents confusion as math gets more complex.
The Golden Ratio (approximately 1:1.618) is a special ratio that appears throughout nature and has fascinated mathematicians for over 2,400 years. It shows up in the spiral pattern of sunflower seeds, the proportions of nautilus shells, the branching of trees, and even the arrangement of petals on flowers. Many artists and architects — from the ancient Greeks to Leonardo da Vinci — have used the Golden Ratio to create compositions that humans find naturally pleasing to the eye.
Last reviewed: April 2026