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?"

Related Topics

FractionsSlope of a LineVisual Word Problems

Suggested Lessons

Slope Quadratic Equations Unit Circle Word Problems
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).
What can it graph?
It can plot explicit, implicit, and parametric functions, add points and geometry, and animate sliders on the same graph.
Can I use voice or a photo?
Yes. You can talk to the tutor, upload a worksheet or handwritten problem, and let the graph update from that input.
Will it explain the steps?
Yes. The AI explains what it is drawing and why, so you see the answer on the graph instead of getting only a final number.