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Maths / Rational Numbers / Subtraction of Rational Numbers
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Subtraction of Rational Numbers

Subtraction of a rational number means we are adding the additive inverse of the number to be subtracted to the other numberIf frac{a}{b} and  frac{c}{d}  are two rational numbers, then subtracting frac{c}{d}  from frac{a}{b} means adding additive inverse (negative) of frac{c}{d}  to   frac{a}{b}.

The subtraction of   frac{c}{d}   from   frac{a}{b} is written as frac{a}{b}-frac{c}{d}.

Thus, we have:

frac{a}{b}-frac{c}{d}=frac{a}{b}+left ( frac{-c}{d} right )                      left [ therefore ;;Additive;;inverse;;of;frac{c}{d};is;frac{-c}{d} right ]

Illustration:  Subtract frac{3}{4}  from  frac{5}{6}

Solution:  The additive inverse of frac{3}{4}  is  frac{-3}{4}.

 therefore   frac{5}{6}-frac{3}{4}=frac{5}{6}+frac{-3}{4}

Next step will be to convert them into rational numbers with same denominator. For this we will find the LCM of denominator and convert them into equivalent numbers with same denominator

LCM of 6 and 4 is 12, So

frac{5}{6}= frac{5times2}{6times2}= frac{10}{12}

frac{-3}{4}= frac{-3times3}{4times3}= frac{-9}{12}

frac{5}{6}+frac{-3}{4}=frac{10}{12}+frac{-9}{12}=frac{10+(-9)}{12}=frac{1}{12}


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