Equivalent Fractions Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Equivalent Fractions.

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

Concept Recap

Two or more fractions that look different but represent exactly the same amount or value.

Half a pizza is the same whether cut into 2 or 4 pieces: \frac{1}{2} = \frac{2}{4}.

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: Multiplying or dividing both parts by the same number keeps the value.

Common stuck point: Recognizing when fractions need a common denominator before adding, comparing, or simplifying.

Sense of Study hint: Pick a small number like 2 or 3, multiply both the top and bottom by it, and check whether the new fraction matches the one you're comparing to.

Worked Examples

Example 1

easy
Find three fractions equivalent to \frac{3}{4}.

Solution

  1. 1
    Multiply numerator and denominator by 2: \frac{3 \times 2}{4 \times 2} = \frac{6}{8}.
  2. 2
    Multiply by 3: \frac{3 \times 3}{4 \times 3} = \frac{9}{12}.
  3. 3
    Multiply by 5: \frac{3 \times 5}{4 \times 5} = \frac{15}{20}.

Answer

\frac{6}{8},\; \frac{9}{12},\; \frac{15}{20}
Multiplying both the numerator and denominator by the same nonzero number produces an equivalent fraction. The value of the fraction does not change because you are effectively multiplying by 1.

Example 2

medium
Simplify \frac{36}{48} to its lowest terms.

Practice Problems

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

Example 1

easy
Fill in the blank: \frac{5}{6} = \frac{?}{30}.

Example 2

hard
Are \frac{14}{21} and \frac{10}{15} equivalent? Show your reasoning.
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Background Knowledge

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

fractionsmultiplication