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Subtraction of Rational Number

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Subtraction of Rational Number:

i) Subtracting Rational number when the denominator is the same:

  • While subtracting two rational numbers, we add the additive inverse of the rational number that is being subtracted, to the other rational number.
  • When we subtract rational numbers with the same denominators, we subtract the numerators keeping the denominators the same.

Subtract: `7/8 - 5/8`

`= (7/8) + (-5/8)`

`= (7 - 5)/8`

`= 2/8`

`= 1/4`

ii) Subtracting Rational number when the denominator is different:

  • While subtracting two rational numbers, we add the additive inverse of the rational number that is being subtracted, to the other rational number.
  • Two rational numbers with different denominators are subtracted by first taking the LCM of the two denominators and then converting both the rational numbers to their equivalent forms having the LCM as the denominator.

1) Subtract: `2/7 - (-5/6)`

= `2/7 + "additive inverse of" (-5/6)`

= `2/7 + 5/6`

= `47/42`

= `1 5/42`.

2) Subtract: `1 2/3 - 2 4/5`

= `5/3 - 14/5`

= `5/3 + "additive inverse of" 14/5`

= `5/3 + (-14)/5`

= `(-17/15)`

= `- 1 2/15`.

Example

Subtract: `2 1/5 - (- 1)/3`

`2 1/5 - (- 1)/3`

`= 11/5 - (- 1)/3`

`= 11/5 + "additive inverse of" (- 1)/3`

`= 11/5 + 1/3`

`= (33 + 1)/15`

`= 34/15`.

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