Percent as Ratio Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Percent as Ratio.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A ratio comparing a quantity to 100, written with the % symbol; 'per cent' literally means 'per hundred'.

'Per cent' means 'per hundred'—25\% means 25 out of every 100.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Percent standardizes comparisons by always using 100 as the reference.

Common stuck point: Converting between percent, decimal, and fraction forms—remember: \% \div 100 = \text{decimal}, e.g., 45\% = 0.45.

Sense of Study hint: Write the percent over 100 as a fraction, then simplify. For decimals, just divide by 100 (move the decimal two places left).

Worked Examples

Example 1

easy
A shirt originally costs \45. It is on sale for 20\%$ off. Find the sale price.

Solution

  1. 1
    Interpret 20\% as a ratio: 20\% = \dfrac{20}{100} = 0.20.
  2. 2
    Calculate the discount: 0.20 \times 45 = \9.00$.
  3. 3
    Sale price = 45 - 9 = \36.00$.

Answer

The sale price is \36.00$.
Percent means 'per hundred' — it is a ratio with denominator 100. Converting the percent to a decimal ratio makes multiplication straightforward. The discount amount is then subtracted from the original price.

Example 2

medium
A student scores 34 out of 40 on a test. Express this as a percentage. Then determine what score out of 40 corresponds to 90\%.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Convert each to the indicated form: (a) 0.045 to percent, (b) 130\% to decimal, (c) \dfrac{3}{8} to percent.

Example 2

medium
A population grew from 8{,}000 to 9{,}400. What is the percent increase?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

fractionsdecimal representation