Rational Expressions

Add the following rational numbers:

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

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

'B'- 'Brackets',
'O'- 'Of operation',
'D'- 'Division',
'M'- 'Multiplication',
'A'- 'Addition',
'S'- 'Subtraction'.