Functions
AI Assistant

Ratios & Proportions

Compare quantities visually and scale them up or down

A ratio compares two quantities: "3 cups of flour to 2 cups of sugar" is the ratio 3:2. A proportion says two ratios are equal: 3/2 = 6/4.

In this lesson, the AI builds bar models to make ratios visible. You can see that doubling both parts of 3:2 gives 6:4 — the bars grow proportionally. Cross-multiplication is just a shortcut for what the bars show.

Ask the AI "Show me the ratio 3:5" or "If 4 apples cost $3, how much do 10 apples cost?"

Graph

FAQ

What is a ratio?
A ratio compares two quantities. The ratio 3:2 means "for every 3 of one thing, there are 2 of another." You can write it as 3:2, 3/2, or "3 to 2." The order matters — 3:2 is different from 2:3.
What is a proportion?
A proportion states that two ratios are equal. For example, 3/2 = 6/4 is a proportion. If a recipe calls for 3 cups flour and 2 cups sugar, doubling it to 6 cups flour and 4 cups sugar keeps the same proportion.
What is cross-multiplication?
To solve a/b = c/d, cross-multiply: a × d = b × c. For example, 3/2 = x/8 becomes 3 × 8 = 2 × x, so 24 = 2x, giving x = 12. The bar model shows this visually — the two rectangles have the same aspect ratio.
Where do we use ratios in real life?
Recipes (flour to sugar), maps (1 cm = 10 km), scale models (1:24), unit prices ($3 per pound), speed (60 miles per hour), and mixing paint colors (2 parts blue to 1 part white).

Related Topics

FractionsSlope of a LineVisual Word Problems