Arithmetic » Fractions » Fraction operations

Fraction Operations

Addition of Fractions

Rule 1: When adding fractions having same denominator, first express them with the same common denominator and simply add the numerators. An example is stated below.

 

Rule 2: When adding fractions having different denominator, first find a Least common denominator (LCD) and express the fractions in LCD and add the numerators. An example with sequential steps is stated below.

  • To solve the above problem, first find the LCD of 6 and 9.

6 = 6, 12, 18, 24

9 = 9, 18, 27

  • Now convert both fractions to a common denominator ‘18’.
  • To convert the fraction 5/6 with the denominator 18, multiply denominator and numerator by 3.

  • To convert the fraction 7/9 with the denominator 18, multiply denominator and numerator by 2.

  • Now add the two fractions (same as adding common denominator fractions).

  • Since 44/18 is an improper fraction, simplify it to a mixed fraction.

 

Rule 3: When adding mixed fractions, we can add whole numbers separately and rewrite the fractions as stated in the example below.

 

Subtraction of Fractions

Rule 1: When subtracting fractions having same denominator, first express them with the same common denominator and simply subtract the numerators. An example is stated below.

 

Rule 2: When subtracting fractions having different denominator like the below example, follow the same rules as stated in addition operation with different denominators.

 

Multiplication of Fractions

Rule 1: Follow the three steps below, when multiplying common fractions.

  • Multiply the numerators.
  • Multiply the denominators.
  • Simplify the fraction, if required.

Example 1

 

Example 2

 

Rule 2: Follow these steps, when multiplying mixed fractions.

  • Change all mixed fractions to improper fractions.
  • Multiply the numerators.
  • Multiply the denominators
  • Simplify the fraction, if required.

Example

 

Division of Fractions

Follow the steps below, when dividing fractions.

  • Exchange the numerator and denominator in the second fraction.
  • Multiply the first fraction by the reciprocal fraction.
  • Simplify the fraction, if required.

Example