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| Adding Fractions |
Adding Fractions
A fraction is generally used to represent a number which is a ratio of two numbers.
Consider the fraction 4⁄5, here 4 is called the numerator and 5 is called the denominator.
Adding fractions with common denominator
Add the numerators of both fractions and put the resultant over the denominator.
Example 1
Consider fractions 4⁄5 and 3⁄5
- The denominator of the fractions is common.
- The numerators are 4 and 3
- Add the numerators, 4 + 3 = 7
- Place the resultant over the common denominator
- Simplify the resultant fraction, if possible
4⁄5 + 3⁄5 = 7⁄5
Example 2
5⁄16 + 3⁄16 = 8⁄16 (Simplifying it further, 8⁄16 = 1⁄2)
Adding fractions with different denominators
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Convert the fractions to equivalent fractions with common denominator
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To convert two fractions to common denominator, multiply the numerator and denominator of a fraction with the denominator of the other fraction.
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Now that the fractions have common denominators, add 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 add 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
- The denominators are different. So you need to make the denominators common
- 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.
- After simplification, the fractions are 5⁄6 and 1⁄3.
- Now to add these fractions, you must make the denominators common
- Multiply the numerator and denominator of a fraction with denominator of the other
- 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) = 21⁄18
- The resultant fraction is 21⁄18. This can be further simplified as 7⁄6
5⁄6 + 5⁄15 = 7⁄6
7⁄6 is equivalent to 1 and 1⁄6