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Subtraction of Fraction

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notes

Subtraction of fractions:

1. Proper Fraction - Proper Fraction:

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"`

`5/6 – 2/6 = (5 - 2)/6 = 3/6 or 1/2`.

2. Improper Fraction - Improper Fraction:

What added to `1/5 "gives" 1/2`?

This means subtract `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. These are `2/10 and 5/10` respectively.

This is because `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:

  • Mixed fractions can be written either as a whole part plus a proper fraction or entirely as an improper 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.

Simiplify: `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 = (19 - 34)/12 = 65/12 = 5 5/12`.

Example

Subtract:`3 2/5 – 2 1/7`

`3 2/5 – 2 1/7`

= `(3 – 2) + (2/5 – 1/7)`

= 1 + `(2 xx 7)/(5 xx 7) – (1 xx 5)/(7 xx 5)`

= 1 + `14/35 – 5/35`

= `1 + 9/(35)`

= `1 9/(35)`.

Example

Subtract: `7 1/2 – 3 1/5`

`7 1/2 – 3 1/5`

= `15/2 – 16/5`

= `(15 xx 5)/(2 xx 5) – (16 xx 2)/(5 xx 2)`

= `(75)/(10) – (32)/(10)`

= `(75 – 32)/10`

= `43/10`

= `4 3/10`.

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