1.6.2 Rational Numbers (HOTS Questions), PT3 Practice

1.6.2 Rational Numbers (HOTS Questions), PT3 Practice

Question 5:
Calculate the value of
$\left(-0.6×1\frac{1}{4}\right)-\left[-1.6×\left(-1.5\right)\right]÷0.4$

Solution:
$\begin{array}{l}\left(-0.6×1\frac{1}{4}\right)-\left[-1.6×\left(-1.5\right)\right]÷0.4\\ =\left({\overline{)-0.6}}^{-0.3}×\frac{5}{{\overline{)4}}^{2}}\right)-\left[\frac{{\overline{)-1.6}}^{-4}×\left(-1.5\right)}{{\overline{)0.4}}^{1}}\right]\\ =-\frac{1.5}{2}-6\\ =-0.75-6\\ =-6.75\end{array}$

Question 6:
Calculate the value of
$1-\left(-2+7×0.15\right)÷2\frac{1}{2}$

Solution:
$\begin{array}{l}1-\left(-2+7×0.15\right)÷2\frac{1}{2}\\ =1-\left(-2+1.05\right)×\frac{2}{5}\\ =1-\left(-0.95\right)×\frac{2}{5}\\ =1-\left(-0.38\right)\\ =1.38\end{array}$

Question 7:
Calculate the value of   $1\frac{1}{8}×\left(\frac{4}{5}-\frac{2}{3}\right)$  and express the answer as a fraction in its lowest terms.

Solution:
$\begin{array}{l}1\frac{1}{8}×\left(\frac{4}{5}-\frac{2}{3}\right)\\ =1\frac{1}{8}×\left(\frac{12}{15}-\frac{10}{15}\right)\\ =\frac{{\overline{)9}}^{3}}{{\overline{)8}}_{4}}×\frac{{\overline{)2}}^{1}}{{\overline{)15}}_{5}}\\ =\frac{3}{20}\end{array}$