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Glacius
FoundationsConcept reference

Equivalent fractions

Equivalent fractions represent the same quotient, obtained by scaling numerator and denominator by the same nonzero factor.

1 min read1 figureSources & further reading
On this page 8 sections
  1. Overview
  2. Equivalent fractions name the same number
  3. Check your understanding
  4. Check your understanding
  5. Key takeaway
  6. Further questions
  7. Sources & further reading
  8. Concept connections

01Equivalent fractions name the same number#

Equivalent fractions name the same number. Split every half into three smaller pieces: one selected half becomes three selected sixths. The selected amount is unchanged.

Half of each identical whole is selected; dividing both halves into three equal smaller pieces changes 1/2 into 3/6 without changing length.Half of each identical whole is selected; dividing both halves into three equal smaller pieces changes 1/2 into 3/6 without changing length.
Figure 1Half of each identical whole is selected; dividing both halves into three equal smaller pieces changes 1/2 into 3/6 without changing length.
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Scale the numerator and denominator by the same nonzero number. Multiplying both by 33 gives 12=36\dfrac{1}{2}=\dfrac{3}{6}.

12=1×32×3=36\frac{1}{2}=\frac{1\times3}{2\times3}=\frac{3}{6}

You can reverse the scaling when both numbers divide evenly: 68=34\dfrac{6}{8}=\dfrac{3}{4} after dividing both by 22. Scaling just one part changes the value. Never scale by zero, which would create an undefined denominator. Negative scaling also works: 12=−2−4\dfrac{1}{2}=\dfrac{-2}{-4}.

Check your reasoning

Complete the equivalent fraction: 34=?12\dfrac{3}{4}=\dfrac{?}{12}.

Show answer and explanation
9

The denominator was tripled, so triple the numerator: 3×3=93\times3=9.

02Check your understanding#

Check your reasoning

Which fraction equals 25\dfrac{2}{5}?

  1. A45\dfrac{4}{5}
  2. B210\dfrac{2}{10}
  3. C410\dfrac{4}{10}
Show answer and explanation
410\dfrac{4}{10}

Multiplying both parts by 2 preserves the value.

03Check your understanding#

Check your reasoning

A strip has 33 equal pieces; 22 are selected. Split each into 33 equal parts. How many selected parts now?

Show answer and explanation
6

Each selected piece becomes three: 2×3=62\times3=6.

Key takeaway

Scale the numerator and denominator together.

  • Generate an equivalent fraction by scaling its numerator and denominator by the same nonzero integer

Further questions

Why must the scaling factor be nonzero?
Scaling by zero produces a zero denominator. The resulting expression is undefined, so it cannot preserve the original fraction.

Sources & further reading

  1. [1]

Reference this concept

Link to this page, a section, or an individual figure.

Glacius. “Equivalent fractions.” Math behind ML. /learn/f-fraction-equivalent