# 1.6.1 Rational Numbers (HOTS Questions), PT3 Practice

1.6.1 Rational Numbers (HOTS Questions), PT3 Practice
Question 1:
Complete the following calculation.
$\begin{array}{l}-4.6×\left(\frac{3}{5}-1\frac{3}{4}\right)=-4.6×\left(0.6-\overline{)x}\right)\\ \text{}=-4.6×\overline{)x}\\ \text{}=\overline{)x}\end{array}$

Solution:
$\begin{array}{l}-4.6×\left(\frac{3}{5}-1\frac{3}{4}\right)=-4.6×\left(0.6-\overline{)1.75}\right)\\ \text{}=-4.6×\overline{)-1.15}\\ \text{}=\overline{)5.29}\end{array}$

Question 2:
Complete the following calculation.
$\begin{array}{l}-43+35÷1\frac{1}{6}=-43+35÷\frac{7}{6}\\ \text{}=-43+35×\overline{)x}\\ \text{}=-43+\overline{)x}\\ \text{}=-13\end{array}$

Solution:
$\begin{array}{l}-43+35÷1\frac{1}{6}=-43+35÷\frac{7}{6}\\ \text{}=-43+35×\overline{)\frac{6}{7}}\\ \text{}=-43+\overline{)30}\\ \text{}=-13\end{array}$

Question 3:
Calculate each of the following.
(a) (–9) × 14
(b)   6.7 – 3.2 × (–0.5)
(c) –144 ÷ (–8) ÷ (–2)

Solution:
(a) (–9) × 14 = –126
(b)   6.7 – 3.2 × (–0.5) = 6.7 – (–1.6)
= 6.7 + 1.6
= 8.3
(c) –144 ÷ (–8) ÷ (–2) = –144 ÷ 4
= 36

Question 4:
Calculate the value of
$0.6+\left(-1\frac{2}{3}\right)÷\left(\frac{4}{15}\right)-2$

Solution:
$\begin{array}{l}0.6+\left(-1\frac{2}{3}\right)÷\left(\frac{4}{15}\right)-2\\ =0.6+\left[-\frac{5}{\overline{)3}}×\frac{{\overline{)15}}^{5}}{4}\right]-2\\ =0.6+\left[-\frac{25}{4}\right]-2\\ =0.6-6\frac{1}{4}-2\\ =0.6-6.25-2\\ =-7.65\end{array}$