Equivalent Fractions Math Example 4

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

Example 4

hard
Are 1421\frac{14}{21} and 1015\frac{10}{15} equivalent? Show your reasoning.

Solution

  1. 1
    Simplify 1421\frac{14}{21}: gcd⁡(14,21)=7\gcd(14, 21) = 7, so 1421=23\frac{14}{21} = \frac{2}{3}.
  2. 2
    Simplify 1015\frac{10}{15}: gcd⁡(10,15)=5\gcd(10, 15) = 5, so 1015=23\frac{10}{15} = \frac{2}{3}.
  3. 3
    Both simplify to 23\frac{2}{3}, so they are equivalent.

Answer

Yes, both equal 23\text{Yes, both equal } \frac{2}{3}
Two fractions are equivalent if and only if they reduce to the same simplest form. Reducing each fraction to lowest terms and comparing is a reliable method to test equivalence.

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 2 medium

Simplify [formula] to its lowest terms.

Example 3 easy

Fill in the blank: [formula].

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