Question

Find the sum of $-ab,\frac{5}{3}ab$

Answer 1

Adding the monomials

The given terms are $-ab,\frac{5}{3}ab$

Since the given terms are like terms. So, the sum of two or more like terms is a like term whose numerical coefficient is the sum of coefficients of given like terms.

Therefore, by adding their coefficients we get

$$\begin{gathered} -\mathrm{ab}+\frac{5}{3}\mathrm{ab}=\frac{-1}{1}\mathrm{ab}+\frac{5}{3}\mathrm{ab} \\ =\left(\frac{-1}{1}+\frac{5}{3}\right)\mathrm{ab} \\ =\left(\frac{-1\times 3}{1\times 3}+\frac{5\times 1}{3\times 1}\right)\mathrm{ab}[\mathrm{Taking}\mathrm{LCM}] \\ =\left(\frac{-3}{3}+\frac{5}{3}\right)\mathrm{ab} \\ =\left(\frac{-3+5}{3}\right)\mathrm{ab} \\ =\frac{2}{3}\mathrm{ab} \end{gathered}$$

Hence, the required sum is $\frac{2}{3}ab$