How to Subtract Fractions

Just like with addition, subtracting fractions having similar denominators will just subtract the numerators and remain the denominator. Also similar with the case of fractions having unlike denominators, the least common denominator (LCD) should be get first then change the fractions into equivalent fractions with the LCD as the denominator. But these conditions are only applicable if the fractions are not mixed numbers.

First Method

Convert the mixed number into an improper fraction.

If the proper fractions have unlike denominators, get the LCD and change the fractions into equivalent fractions using the LCD as the denominator.

Subtract the numerators and remain the LCD as the denominator.

Reduce to lowest terms.

Second Method

If the larger mixed number has a smaller proper fraction than the smaller mixed number, subtract the whole number of the larger mixed fraction by 1 and add 1 to the proper fraction.

By adding 1 to the proper fraction, it will become a mixed number. The new larger mixed number will be a whole number added by a mixed number with 1 as the whole number.

Change the mixed number (with 1 as the whole number) into an improper fraction.

Subtract the whole number of the smaller mixed number from the whole number of the new larger mixed number.

If the proper fractions have similar denominators, subtract the numerators directly and remain the denominator as it is. But if the proper fractions have unlike denominators, get the LCD and change the fractions into equivalent fractions using the LCD as the denominator then subtract the numerators and remain the LCD as the denominator.  Reduce to lowest terms.

Note:
The second method is only applicable when the larger mixed number has a smaller proper fraction than the smaller mixed number.

Solve 4/7 - 1/7?

Explanation:

The fractions have similar denominators.
Subtract the numerators directly and remain the denominator as it is.
4/7 - 1/7 = (4-1)/7 = 3/7
Therefore, 4/7 - 1/7 = 3/7

Solve 9/10 - 3/5?

Explanation:

The fractions have unlike denominators.
Finding the LCD;

 5 = 5 10 = 2 × 5 LCD = 2 × 5 = 10

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

Solve 5 3/4 – 2 1/2?

Explanation:

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;

 2 = 2 4 = 2 × 2 LCD = 2 × 2 = 4

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

Solve 3 1/3 – 1 2/3?

Explanation:

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

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