Question

List five rational numbers between:

(i) $-1$ and $0$ (ii) $-2$ and $-1$

(iii) $\frac{-4}{5}$ and $\frac{-2}{3}$ (iv) $\frac{1}{2}$ and $\frac{2}{3}$

Answer 1

(i) -1 and 0

We can write the equivalent rational number of -1 and 0.

$-1=\frac{-1}{1}=\frac{-1\times 9}{1\times 9}=\frac{-9}{9}$​

$0=\frac{0}{1}=\frac{0\times 9}{1\times 9}=\frac{0}{9}$

$\frac{-9}{9}<\frac{-8}{9}<\frac{-7}{9}<\frac{-6}{9}<\frac{-5}{9}<\frac{-4}{9}<\frac{0}{9}$​

Five rational numbers between $-1$ and $0$ are

$\frac{-8}{9},\frac{-7}{9},\frac{-6}{9},\frac{-5}{9},\frac{-4}{9}$​

(ii) $-2$ and $-1$

We can write

$-2=\frac{-2\times 6}{1\times }=\frac{-12}{6}$ and $-1=\frac{-1\times 6}{1\times 6}=\frac{-6}{6}$​

$\frac{-12}{6}<\frac{-11}{6}<\frac{-10}{6}<\frac{-9}{6}<\frac{-8}{6}<\frac{-7}{6}<\frac{-6}{6}$​

Five rational numbers between -2 and -1 are

$\frac{-11}{6},\frac{-10}{6},\frac{-9}{6},\frac{-8}{6},\frac{-7}{6}$​

(iii) $\frac{-4}{5}$ and $\frac{-2}{3}$​

We can write the equivalent rational numbers of the given numbers as

$\frac{-4}{5}=\frac{-4\times 9}{5\times 9}=\frac{-36}{45}$​ and $\frac{-2}{3}=\frac{-2\times 15}{3\times 15}=\frac{-30}{45}$​

Five rational numbers between $\frac{-4}{5}$​ and $\frac{-2}{3}$​ are

$\frac{-35}{45},\frac{-34}{45},\frac{-33}{45},\frac{-32}{45},\frac{-31}{45}$

(iv) $\frac{1}{2}$ and $\frac{2}{3}$

$\frac{1}{2}=\frac{1\times 18}{2\times 18}=\frac{18}{36}$ and $\frac{2}{3}=\frac{2\times 12}{3\times 12}=\frac{24}{36}$

Five rational numbers between $\frac{1}{2}$ and $\frac{2}{3}$ are

$\frac{19}{36},\frac{20}{36},\frac{21}{36},\frac{22}{36},\frac{23}{36}$