Subtraction of Fraction

Steps for Subtraction of Fractions:
Step 1: Subtract the smaller numerator from the bigger numerator.
Step 2: Retain the (common) denominator.
Step 3: Write the fraction as: `"Result of step 1"/"Result of step 2"`

1. Proper Fraction—Proper Fraction:

`5/6 – 2/6 = (5 - 2)/6` =` 3/6 or 1/2`.

2. Improper Fraction—Improper Fraction:

Subtracting `1/5 "from" 1/2` to get the required number. Since `1/5 and 1/2` are unlike fractions, in order to subtract them, we first find their equivalent fractions with the same denominator. 

`1/2 = (1 xx 5)/(2 xx 5) = 5/10 and 1/5 = (1 xx 2)/(5 xx 2) = 2/10`

Therefore, `1/2 - 1/5 = 5/10 – 2/10 = (5 – 2)/10 = 3/10`

Note that 10 is the least common multiple (LCM) of 2 and 5.

3. Mixed Fraction—Mixed Fraction:

One way to subtract mixed fractions is to do the operation separately for the whole parts and the other way is to write the mixed fractions as improper fractions and then directly subtract them. 
Simplify: `8 1/4 - 2 5/6`
Solution: Here 8 > 2 but `1/4 < 5/6`.
We proceed as follows:

`8 1/4 = ((8 xx 4) + 1)/4 = 33/4 and 2 5/6 = ((2 xx 6) + 5)/6 = 17/6` Now,
`33/4 - 17/6 = (33 xx 3)/12 - (17 xx 2)/12`.......(Since LCM of 4 and 6 = 12)

`33/4 - 17/6 = (99 - 34)/12 = 65/12 = 5 5/12`.