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