While adding or subtracting two rational numbers having different denominators Class 9

While adding or subtracting two rational numbers having different denominators Class 9

Question 1.

While adding or subtracting two rational numbers having different denominators, how will you make the denominators equal? Class 9

Answer:

To add or subtract two rational numbers with different denominators, first convert them into equivalent fractions having the same denominator.

This is done by taking the LCM of the denominators and multiplying the numerator and denominator of each After making the denominators equal, we add or subtract the numerators and keep the denominator unchanged.

Example:

$\frac{1}{2}+\frac{1}{3}$

LCM of 2 and 3 is 6.

$\begin{array}{ll}\therefore & \frac{1}{2}=\frac{3}{6}, \frac{1}{3}=\frac{2}{6} \\ \therefore & \frac{3}{6}+\frac{2}{6}=\frac{5}{6}\end{array}$

Question 2.

Verify the distributive law for rational numbers. Class 9

Answer:

The distributive law for rational numbers is p(q + r) = pq + pr

$\begin{aligned} & \text { Let } p=\frac{1}{2}, q=\frac{1}{3}, r=\frac{1}{4} \\ & \text { L.H.S. }=\frac{1}{2}\left(\frac{1}{3}+\frac{1}{4}\right)=\frac{1}{2}\left(\frac{4+3}{12}\right)=\frac{1}{2} \times \frac{7}{12}=\frac{7}{24} \\ & \text { R.H.S. }=\frac{1}{2} \times \frac{1}{3}+\frac{1}{2} \times \frac{1}{4}=\frac{1}{6}+\frac{1}{8}=\frac{8+6}{48}=\frac{14}{48}=\frac{7}{24}\end{aligned}$

Therefore, L.H.S. = R.H.S.

The distributive law is verified.