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# Rational Expressions

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 Sub Topics Rational Numbers can form expressions when we join Rational Numbers with various mathematical operators namely addition, subtraction, multiplication and division. Rational Numbers are the numbers which are written in form of $\frac{p}{q}$ , where p and q are integers, and q $\neq$ 0. Always remember all natural, whole numbers, integers including zero(0) are all the members of the family of rational numbers because they all have 1 as the denominator, which is not 0.

## Rational Expressions Operation

2 + $\frac{4}{7}$ + $\frac{-3}{2}$.

Here, we find that the denominators are 1, 7 and 2. So we take the L.C.M. of the three numbers is 14.

Further, we try to make all the denominators = L.C.M. i.e. 14. For this we multiply numerator and denominator of 2 by 14, numerator and denominator of $\frac{4}{7}$ by 2 and numerator and denominator of $\frac{-3}{2}$ by 7, We get

= $\frac{28}{14}$ + $\frac{8}{14}$ + $\frac{-21}{14}$

= $\frac{28 + 8 -21}{14}$

= $\frac{15}{14}$.

Subtracting the given two rational numbers:

=> $\frac{-4}{6}$ - $\frac{-2}{4}$

L.C.M. of 6 and 4 is 12, So now we make the denominator =12.

For this we multiply and divide $\frac{-4}{6}$ by 2, and multiply and divide $\frac{-2}{4}$ by 3, We get

= - $\frac{8}{12}$ - $\frac{-6}{12}$

= $\frac{-8 +6}{12}$

= - $\frac{2}{12}$

Now further we simplify to get $\frac{-1}{6}$.

Multiply the given two rational numbers:

=> $\frac{-4}{7}$ $\times$ $\frac{5}{4}$

Here we multiply numerator by numerator and denominator by denominator, we get

= $\frac{-4 \times 5 }{7 \times 4}$

= - $\frac{20}{28}$.

Now we simplify to get $\frac{-5}{7}$

= $\frac{-5}{7}$.

Divide the given two rational numbers:

To divide $\frac{-4}{5}$ by $\frac{3}{6}$,
Here $\frac{-4}{5}$ = dividend
$\frac{3}{6}$ = divisor.

Multiply the reciprocal of divisor with the dividend to get

= $\frac{-4}{5}$ $\times$ $\frac{6}{3}$,

= $\frac{-4 \times 6}{5 \times 3}$,

= $\frac{-24}{15}$.

H.C.F of 24 and 15 is 3 , so we divide -24 and 15 by 3, we get

= $\frac{-8}{5}$.

If more than one operator exists in the given expression, then we apply the Laws of BODMAS to solve the expressions of rational numbers, where

'B'- 'Brackets',
'O'- 'Of operation',
'D'- 'Division',
'M'- 'Multiplication',