Equivalent Fractions Math Example 2

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

Example 2

medium
Simplify 3648\frac{36}{48} to its lowest terms.

Solution

  1. 1
    Find gcd⁡(36,48)\gcd(36, 48). The factors of 36 are 1,2,3,4,6,9,12,18,361, 2, 3, 4, 6, 9, 12, 18, 36 and the factors of 48 include 1,2,3,4,6,8,12,16,24,481, 2, 3, 4, 6, 8, 12, 16, 24, 48. So gcd⁡(36,48)=12\gcd(36, 48) = 12.
  2. 2
    Divide both numerator and denominator by 12: 36÷1248÷12=34\frac{36 \div 12}{48 \div 12} = \frac{3}{4}.
  3. 3
    Verify: gcd⁡(3,4)=1\gcd(3, 4) = 1, confirming the fraction is fully simplified.

Answer

34\frac{3}{4}
Simplifying a fraction means dividing both parts by their greatest common divisor. The result is the simplest equivalent fraction.

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 1 easy

Find three fractions equivalent to [formula].

Example 3 easy

Fill in the blank: [formula].

Example 4 hard

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

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