freeCodeCamp/guide/english/mathematics/example-of-subtracting-fractions-with-unlike-denominators/index.md

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Example of Subtracting Fractions with Unlike Denominators

Example of Subtracting Fractions with Unlike Denominators

Subtracting fractions with unlike denominators is similar to addition of fractions with unlike denominators. Here are the steps,

1. Convert the fractions to equivalent fractions with common denominator

2. To convert two fractions to common denominator, multiply the numerator and denominator of a fraction with the denominator of the other fraction.

3. Now that the fractions have common denominators, subtract the numerators of both fractions and put the resultant over the denominator

   Consider, ^a⁄_b and ^c⁄_d are fractions with different denominators, you can subtract these fractions in a single step like below,
   

  a⁄b - c⁄d = (a * d) - (b * c)⁄(b * d) 

Example

Consider fractions ⁵⁄₆ and ⁵⁄₁₅

1. The denominators are different. So you need to make the denominators common
2. Before that, if possible, simplify the fractions. In this case, ⁵⁄₁₅ can be simplified as ¹⁄₃. Here ⁵⁄₁₅ and ¹⁄₃ are called equivalent fractions.
3. After simplification, the fractions are ⁵⁄₆ and ¹⁄₃.
4. Now to subtract these fractions, you must make the denominators common
5. Multiply the numerator and denominator of a fraction with denominator of the other
6. For fraction ⁵⁄₆ , the denominator of the other fraction is 3. For fraction ¹⁄₃ , the denominator of the other fraction is 6

  ((5 * 3) - (1 * 6))⁄(6 * 3) = 9⁄18 

7. The resultant fraction is ⁹⁄₁₈. This can be further simplified as ¹⁄₂

  5⁄6 - 5⁄15 = 1⁄2