Fraction of a Number Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Fraction of a Number.

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

Concept Recap

Finding a fractional part of a whole number by multiplying the fraction by that number.

\frac{3}{4} of 20 means split 20 into 4 equal groups (5 each), then take 3 groups: 3 \times 5 = 15.

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: Finding a fraction of a number is multiplication: 'of' means multiply.

Common stuck point: Students confuse 'fraction of' with 'fraction plus'—\frac{1}{3} of 12 is 4, not 12\frac{1}{3}.

Sense of Study hint: Divide the number by the denominator first, then multiply that result by the numerator -- break it into two simple steps.

Worked Examples

Example 1

easy
Find \frac{3}{4} of 28.

Solution

  1. 1
    Divide by the denominator first: 28 \div 4 = 7.
  2. 2
    Multiply by the numerator: 7 \times 3 = 21.
  3. 3
    Alternatively: \frac{3}{4} \times 28 = \frac{3 \times 28}{4} = \frac{84}{4} = 21.

Answer

21
Finding a fraction of a number is multiplication: 'of' means multiply. A practical two-step method is to divide by the denominator first (to find one equal part) and then multiply by the numerator (to count the required parts).

Example 2

medium
A school has 360 students. \frac{5}{9} of them play a sport. How many students play a sport?

Practice Problems

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

Example 1

easy
A bag holds 45 marbles. \frac{2}{5} of them are red. How many marbles are red?

Example 2

hard
A shop has \2400 in sales. \frac{3}{8} is spent on materials, and \frac{1}{6}$ of the remainder is set aside for rent. How much money is set aside for rent?
← Back to Fraction of a Number Formula Explained Practice Mode

Background Knowledge

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

multiplying fractions