Adding and Subtracting Fractions with unlike Denominators
To add and subtract fractions you first need a common denominator. Therefore, if the fractions don’t have a common denominator, then follow the steps above to build up the fractions so that they have the least common denominator. Once the fractions have a common denominator, we add or subtract the numerators and keep the common denominator.
Example
To add 2/3 + ¼ , we first determine the common denominator.
Multiples of 3 / Multiples of 41x3 = 3 / 1x4 = 4
2x3 = 6 / 2x4 = 8
3x3 = 9 / 3x4 = 12
3x4 = 12 / 4x4 = 16
The lowest common multiple (denominator) for both 3 and 4 is 12.
Now we want to build up the fractions so that they have the low common denominator. In order to get a common denominator of 12, multiple 2/3 times 4/4 to get 8/12. 23×44=812 . For the fraction ¼ , we need to multiply it by 3/3 to get 3/12. 14×33=312 . Now that our fractions have common denominators, we can add them by adding the numerators and keeping the common denominator. Therefore 812+312=1112
Guided Practice
Add the fraction: 5/12 + 7/18 and then subtract the fraction 5/12 – 7/18
1. Determine the LCD for the following fractions: 5/12 and 7/18. First list the multiples of both 12 and 18.
Multiples of 12 / Multiples of 181x12 = 12 / 1x18 = 18
2x12 = 24 / 2x18 = 36
3x12 = 36 / 3x18 = 54
The first common multiple listed is the Least Common Multiple.
The Least Common Multiple for 12 and 18 is 36.
The Least Common Denominator is determined the same way as the Least Common Multiple. Therefore, the Least Common Denominator for 5/12 and 7/18 is 36.
1. Build up equivalent fractions so that they have the LCD determined the previous step. Remember that you can only multiply by one. In other words, you want the numerator and the denominator to be the same number and at the same time end up with the LCD. Remember with fractions you multiply straight across: numerator times numerator and denominator times denominator.
2.
33×512=1536
22×718=1436
3. Add the two fractions from step 2 with the LCD. Remember that when you add fractions with the same denominator, you keep the common denominator and add the numerators.
1536+1436=2936
4. Now subtract the two fractions from step 2 with the LCD. Remember that when you subtract fractions with the same denominator, you keep the common denominator and subtract the numerators.
1536-1436=136