How to Subtract Fractions

The fractions have unlike denominators.
Finding the LCD;

Converting the fractions into equivalent fractions with 10 as the denominator;
`9/10 × 1/1 = 9/10`
`3/5 × 2/2 = 6/10`
Since the fractions have similar denominators, subtract the numerators and remain the LCD as it is.
`9/10 - 3/5 = 9/10 - 6/10 = (9-6)/10 = 3/10`
Therefore, `9/10 - 3/5 = 3/10`

Convert the mixed numbers into improper fractions.
`5 3/4 = ((5 × 4)+ 3)/4 = (20+3)/4 = 23/4`
`2 1/2 = ((2 × 2)+ 1)/2 = (4+1)/2 = 5/2`

Finding the LCD;

Converting the proper fractions into equivalent fractions with 4 as the denominator;
`23/4 × 1/1 = 23/4`
`5/2 × 2/2 = 10/4`
Since the fractions have similar denominators, subtract the numerators and remain the LCD as it is.
`5 3/4 – 2 1/2 = 23/4 - 5/2 = 23/4 - 10/4 = (23-10)/4 = 13/4 or 3 1/4`
Therefore, `5 3/4 – 2 1/2 = 3 1/4`

The mixed numbers have similar proper fractions.
The larger mixed number has a smaller proper fraction than the smaller mixed number.
Transforming the larger mixed number;
`3 1/3 = 2 + 1 + 1/3 = 2 + 1 1/3 = 2 4/3` Subtract the whole numbers and subtract the fractions.
`3 1/3 - 1 2/3 = 2 4/3 - 1 2/3 = (2 – 1) + ( 4/3 - 2/3 ) = 1 2/3`
Therefore, `3 1/3 - 1 2/3 = 1 2/3`