Question

Solve the following: Select the rational numbers from the list which are also the integers.

$\frac{9}{4},\frac{8}{4},\frac{7}{4},\frac{6}{4},\frac{9}{3},\frac{8}{3},\frac{7}{3},\frac{6}{3},\frac{5}{2},\frac{4}{2},\frac{3}{1},\frac{3}{2},\frac{1}{1},\frac{0}{1},\frac{-1}{1},\frac{-2}{1},\frac{-3}{2},\frac{-4}{2},\frac{-5}{2},\frac{-6}{2}$

Answer 1

Given rational can be written as:

$$\begin{gathered} \frac{9}{4}=\frac{9}{4} \\ \frac{8}{4}=2 \\ \frac{7}{4}=\frac{7}{4} \\ \frac{6}{4}=\frac{3}{2} \\ \frac{9}{3}=3 \\ \frac{8}{3}=\frac{8}{3} \\ \frac{7}{3}=\frac{7}{3} \\ \frac{6}{3}=2 \\ \frac{5}{2}=\frac{5}{2} \\ \frac{4}{2}=2 \\ \frac{3}{1}=3 \\ \frac{3}{2}=\frac{3}{2} \\ \frac{1}{1}=1 \\ \frac{0}{1}=0 \\ \frac{-1}{1}=-1 \\ \frac{-2}{1}=-2 \\ \frac{-3}{2}=\frac{-3}{2} \\ \frac{-4}{2}=-2 \\ \frac{-5}{2}=\frac{-5}{2} \\ \frac{-6}{2}=-3 \end{gathered}$$

Hence, the rational number from the given list which are also the integers are:

$$\begin{gathered} \frac{\mathbf{8}}{\mathbf{4}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{2} \\ \frac{\mathbf{9}}{\mathbf{3}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{3} \\ \frac{\mathbf{6}}{\mathbf{3}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{2} \\ \frac{\mathbf{4}}{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{2} \\ \frac{\mathbf{3}}{\mathbf{1}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{3} \\ \frac{\mathbf{1}}{\mathbf{1}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1} \\ \frac{\mathbf{0}}{\mathbf{1}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0} \\ \frac{\mathbf{-}\mathbf{1}}{\mathbf{1}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{1} \\ \frac{\mathbf{-}\mathbf{2}}{\mathbf{1}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{2} \\ \frac{\mathbf{-}\mathbf{4}}{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{2} \\ \frac{\mathbf{-}\mathbf{6}}{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{3} \end{gathered}$$