# How to solve addition and subtraction of fractions

1
by eleodesamangubat

2016-06-23T18:07:24+08:00
For similar fractions, simply add the numerator and copy their denominator.
Ex.: 2/5 + 1/5 = 3/5
For dissimilar fractions, find their LCD (Least Common Denominator; LCM of the denominator or Least Common Multiple). Follow the following steps in order to make the fractions similar.
Ex.: 1/2 + 3/4
The LCM of 2 and 4 is 4.

Quotient of LCD ÷ denominator multiplied by the numerator (4 ÷ 2) × 1 = 2 × 1 = 2 ⇒ new numerator
Therefore, we'll have 4 (LCD) as the denominator and 2 as the numerator.
Do the same with the other fraction. But in this case, the LCD and the denominator of the other fraction (3/4) are just the same, all we have to do is simply copy it. Then add.
1/2 ⇒ 2/4
3/4 ⇒ 3/4
Now, we have them as similar fractions. Simply add them.
2/4 + 3/4 = 5/4 ⇒ 1  1/4  (5/4 is an improper fraction, we need, I guess, convert the improper fraction to a Mixed number.)

Same as subtraction.

If we have similar fractions, simply subtract the numerators and copy the denominator.
Ex.: 5/6 - 1/6 = 4/6 ⇒ 2/3 (lower term of 4/6 is 2/3, we need to reduce the fraction into the lowest term, always remember that).

And for dissimilar fractions, follow the steps above of converting the dissimilar fractions into similar fractions.
Ex.:  7/8 - 1/4
LCD - 8
7/8 ⇒ 7/8
1/4 ⇒ 2/8
7/8 - 2/8 = 5/8

In case you have encountered subtracting a mixed number (the one with the whole number and a fraction, one example is that 1 1/4). Make sure that its denominators already are similar. Just in case you have this:
5 1/6 - 2 5/6
We cannot subtract this - 1 - 5, so we have to borrow.
(Sorry I'll just use this for simpler explanation)
We can simply convert the mixed number into an improper fraction. How? Simply multiply the whole number to the denominator then add the product to the numerator and that'll be the new numerator while the denominator remains the same.
(5 × 6) + 1 = 30 + 1 = 31 ⇒ new numerator
(2 × 6) + 5 = 12 + 5 = 17 ⇒ new numerator
5 1/6 ⇒ 31/6
2 5/6 ⇒ 17/6
Now, subtract.
31/6 - 17/6 = 14/6 or 2 2/6 or 2 1/3

I know it's a little bit confusing but I still hope that this helps.