Question

Subtract the second expression from the first:

(i) $\frac{m}{3}+\frac{n}{2};\frac{m}{6}+\frac{n}{4}$

(ii) $0.07p^{2}q+3.6p{q}^2-p^2{q}^2-0.003p{q}^2+2p^{2}q-8.5p^2{q}^2$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right) \\ \mathrm{We}\mathrm{have}\left(\frac{m}{3}+\frac{n}{2}\right)-\left(\frac{m}{6}+\frac{n}{4}\right) \\ =\frac{m}{3}+\frac{n}{2}-\frac{m}{6}-\frac{n}{4} \\ =\frac{m}{3}-\frac{m}{6}+\frac{n}{2}-\frac{n}{4} \\ =\frac{2m}{6}-\frac{m}{6}+\frac{2n}{4}-\frac{n}{4} \\ =\frac{m}{6}+\frac{n}{4} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ii}\right) \\ \mathrm{We}\mathrm{have}\left(0.07p^{2}q+3.6p{q}^2-p^2{q}^2\right)-\left(0.003p{q}^2-2p^{2}q+8.5p^2{q}^2\right) \\ =0.07p^{2}q+3.6p{q}^2-p^2{q}^2-0.003p{q}^2+2p^{2}q-8.5p^2{q}^2 \\ =0.07p^{2}q+2p^{2}q+3.6p{q}^2-0.003p{q}^2-p^2{q}^2-8.5p^2{q}^2 \\ =2.07p^{2}q+3.597p{q}^2-9.5p^2{q}^2 \end{gathered}$$