How to Solve Proportions: Cross Multiplication, Ratios & Scaling

What Is a Proportion?

A proportion states that two ratios are equal. The classic form:

a / b = c / d

If you know any three of the four values, you can solve for the fourth. This simple pattern solves problems across cooking, chemistry, photography, finance, and construction.

Cross Multiplication

The standard method for solving proportions:

If a/b = c/d, then a × d = b × c

Example: 3/5 = x/20
3 × 20 = 5 × x
60 = 5x
x = 12

Common Proportion Problems

Recipe Scaling

A recipe for 4 people needs 2 cups of flour. How much for 10 people?

2 cups / 4 people = x cups / 10 people
x = (2 × 10) / 4 = 5 cups

Aspect Ratio (Image Resizing)

An image is 1920×1080 (16:9). What's the height if the width is scaled to 640?

1920 / 1080 = 640 / h
h = (1080 × 640) / 1920 = 360

640×360 preserves the 16:9 aspect ratio.

Unit Conversion

1 inch = 2.54 cm. How many inches is 30 cm?

1 inch / 2.54 cm = x inches / 30 cm
x = (1 × 30) / 2.54 = 11.81 inches

Percentage as Proportion

What is 15% of 200? Percent = "per 100":

15 / 100 = x / 200
x = (15 × 200) / 100 = 30

Simplifying Ratios

Divide both sides by their greatest common divisor (GCD):

48:72 → divide by 24 → 2:3
0.5:2 → multiply by 2 → 1:4

Direct vs. Inverse Proportion

• Direct proportion: As one quantity increases, the other increases at the same rate. More hours worked → more money earned. Use a/b = c/d.
• Inverse proportion: As one increases, the other decreases. More workers on a job → less time to complete. Use a × b = c × d.

Solve Proportions Instantly

Use ToolsVito's Proportion Calculator to solve missing values in proportions, simplify ratios, and scale values. Enter the values you know and get the missing one immediately. All in your browser.