Equivalent Fractions Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Find three fractions equivalent to 34\frac{3}{4}.

Solution

  1. 1
    Multiply numerator and denominator by 2: 3×24×2=68\frac{3 \times 2}{4 \times 2} = \frac{6}{8}.
  2. 2
    Multiply by 3: 3×34×3=912\frac{3 \times 3}{4 \times 3} = \frac{9}{12}.
  3. 3
    Multiply by 5: 3×54×5=1520\frac{3 \times 5}{4 \times 5} = \frac{15}{20}.

Answer

68,  912,  1520\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.

About Equivalent Fractions

Two fractions ab\frac{a}{b} and cd\frac{c}{d} are equivalent if they represent the same value, which happens exactly when a×d=b×ca \times d = b \times c (cross-multiplication gives equal products).

Learn more about Equivalent Fractions →

More Equivalent Fractions Examples

Example 2 medium

Simplify [formula] to its lowest terms.

Example 3 easy

Fill in the blank: [formula].

Example 4 hard

Are [formula] and [formula] equivalent? Show your reasoning.

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