Question

(a) Arrange the rational numbers $\frac{-7}{10}$, $\frac{5}{-8}$, $\frac{2}{-3}$ in ascending order.

(b) Arrange the rational numbers $\frac{4}{3}$, $\frac{17}{2}$, $\frac{5}{18}$ in ascending order.

[4 MARKS]

Answer 1

Each part: 2 Marks

(a) First write the rational numbers with positive denominator = $\frac{-7}{10}$, $\frac{5}{-8}$, $\frac{2}{-3}$.

LCM of denominators (LCM of 10, 8, 3 is 120)

$\frac{-7}{10}$ = $\frac{(-7\times 12)}{(10\times 12)}=\frac{-84}{120}$

$\frac{-5}{8}$ = $\frac{(-5\times 15)}{(8\times 15)}=\frac{-75}{120}$

$\frac{-2}{3}$ = $\frac{(2\times 40)}{(3\times 40)}=\frac{-80}{120}$

Comparing the numerators of these numbers, we get:

- 84 < - 80 < - 75

∴ $\frac{-84}{120}$ < $\frac{-80}{120}$ < $\frac{-75}{120}$;
$\frac{-7}{10}$ < $\frac{-2}{3}$ < $\frac{-5}{8}$.

(b) $\frac{4}{3}$, $\frac{17}{2}$, $\frac{5}{18}$

LCM of denominators (LCM of 3, 2, 18 is 18)

$\frac{4}{3}$ = $\frac{(4\times 6)}{(3\times 6)}=\frac{24}{18}$

$\frac{17}{2}$ = $\frac{(17\times 9)}{(2\times 9)}=\frac{153}{18}$

$\frac{5}{18}$ = $\frac{(5\times 1)}{(18\times 1)}=\frac{5}{18}$

Comparing the numerators of these numbers, we get:

5 < 24 < 153

∴ $\frac{5}{18}$ < $\frac{24}{18}$ < $\frac{153}{18}$;
$\frac{5}{18}$ < $\frac{4}{3}$ < $\frac{17}{2}$.