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Ratio & Proportion Visualizer

Enter two numbers to see their ratio as a tape diagram, build a table of equivalent ratios, and find unit rates. Switch to proportion mode to solve for a missing value with step-by-step cross-multiplication. All computation runs in your browser.

3
5
3:5

Try an example

Tape Diagram

35

Unit Rate

0.6 per 1

3 / 5

Unit Rate

1.6667 per 1

5 / 3

Equivalent Ratios

Multiplier3 part:5 part
×13:5
×26:10
×39:15
×412:20
×515:25
×618:30
×721:35
×824:40

Reference Guide

What Is a Ratio

A ratio compares two quantities. The ratio 3 : 5 means "for every 3 of the first quantity, there are 5 of the second."

Ratios can be written three ways:

  • Using a colon: 3 : 5
  • As a fraction: 35\frac{3}{5}
  • In words: "3 to 5"

Equivalent Ratios

Multiply (or divide) both parts of a ratio by the same number to get an equivalent ratio. The relationship stays the same.

3:5=6:10=9:15=12:203:5 = 6:10 = 9:15 = 12:20

To simplify a ratio, divide both parts by their greatest common factor. For example, 12 : 8 simplifies to 3 : 2.

Unit Rates

A unit rate tells you how much of one quantity corresponds to exactly 1 of another. Divide one part by the other.

unit rate=ab\text{unit rate} = \frac{a}{b}

If you drive 150 miles in 3 hours, the unit rate is 1503=50\frac{150}{3} = 50 miles per hour.

Cross-Multiplication

When two ratios are equal (a proportion), you can cross-multiply to find a missing value.

ab=cd    a×d=b×c\frac{a}{b} = \frac{c}{d} \implies a \times d = b \times c

Solve for the unknown by dividing. For example, if 35=12d\frac{3}{5} = \frac{12}{d}, then 3d=603d = 60 so d=20d = 20.