Understanding Percentage Proportion with Examples

Percentage proportion problems are a powerful way to solve real-world math situations using ratios. This method involves setting up a proportion — a statement that two ratios are equal — to find missing values involving percentages.

What Is a Percentage Proportion?

A percentage proportion expresses the relationship between a part and a whole using a ratio that equals a percentage over 100.

The Formula: Setting Up a Percentage Proportion

Use this proportion to solve for unknowns:

part / whole = percent / 100

You can solve for any missing value by cross-multiplying.

Example 1: Finding the Percentage

What percent of 80 is 20?

20 / 80 = x / 100

Cross-multiply:

80 × x = 2000

Solve for x:

x = 25%

Example 2: Finding the Part

What is 15% of 120?

x / 120 = 15 / 100

100 × x = 15 × 120 → x = 1800 / 100 = 18

Example 3: Finding the Whole

30 is 20% of what number?

30 / x = 20 / 100

20 × x = 3000 → x = 150

Quick Tip: The percentage proportion formula is great when you're given three of the four values (part, whole, percent, or 100) and need to solve for the missing one.

Real-Life Applications

Business: Calculate commission or discount rates.
Health: Work out body fat or nutrient percentages.
School: Solve percentage questions in exams with ease.

Practice Questions

What percent of 250 is 50?
What is 22% of 90?
45 is 75% of what number?

Answers:

20%
19.8
60

Summary

Percentage proportions are a flexible and intuitive way to handle all types of percent-related math. By setting up a simple ratio and using cross multiplication, you can quickly find unknown values without memorizing complex formulas.

part / whole = percent / 100

Use this method confidently in school, shopping, budgeting, and more!