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Friday 13th of September
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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Adding Fractions with Unlike Denominators

Finding equivalent fractions with like denominators can be accomplished by multiplying both the numerator and denominator of each fraction by the denominator of the other fraction

Example 1

Find .

Solution

Multiply both the numerator and denominator of by 7 ( the denominator of ) .

Multiply both the numerator and denominator of by 3 ( the denominator of ) .

Now replace each original fraction with its equivalent fraction and add.

The fraction is an improper fraction, which is a fraction whose numerator is greater than its denominator. Since 21 goes into 23 once with a remainder of 2, the sum can also be written as a mixed number. So,

Here is an algorithm for adding fractions with unlike denominators.

Algorithm for Adding Fractions with Unlike Denominators

1. Multiply both the numerator and denominator of each fraction by the denominator of the other fraction. The resulting equivalent fractions will have the same denominator.

2. Add the equivalent fractions by adding their numerators and retaining the like denominator.

Example 2

Find .

Solution

Step 1 Multiply both the numerator and denominator of by 11, and multiply both the numerator and denominator of by 9.

Step 2 Add the equivalent fractions.