Question 11:
Table below shows the types of fruit tree planted by Azmi in his orchard.


(a) Calculate the number of guava trees.
(b) 100 mangosteen trees died due to fungus.
Find the total number of the remaining trees.

Solution:
(a)
$\begin{array}{l}\text{Number of Guava trees}\\ =\frac{1}{3}\times 180\\ =60\end{array}$

(b)
$\begin{array}{l}\text{Number of mangosteen and guava trees}\\ =180+60\\ =240\\ \\ \text{Fraction of mangosteen and guava trees}=\frac{3}{5}\\ \text{Total number of trees}\\ =\frac{5}{3}\times 240\\ =400\\ \\ \text{Total number of remaining trees}\\ =400-100\\ =300\end{array}$

Question 12:
A palm oil processing factory has a number of workers. $\frac{4}{7}$ of the workers are skilled workers. If $\frac{3}{5}$ of the general workers are 18 females, find the total number of workers in the factory.

Solution:
$\begin{array}{l}\frac{3}{5}\text{ of the general workers are 18 females}\text{.}\\ \text{Let the number of general workers }=w\\ \frac{3}{5}\times w=18\\ w=18\times \frac{5}{3}\\ =30\\ \text{Hence the total number of workers in the factory}\\ =30÷\left(\frac{7}{7}-\frac{4}{7}\right)\\ =30÷\frac{3}{7}\\ =30\times \frac{7}{3}\\ =70\end{array}$

Question 13:
In a fruit basket, $\frac{2}{5}$ are mangoes and the rest are kiwis.
If $\frac{2}{3}$ of the mangoes or 12 of them are in good condition, calculate the number of kiwis in the basket.

Solution:
$\begin{array}{l}\text{Let the number of mangos}\\ \text{in the basket}=x\\ \frac{2}{3}\times x=12\\ x=12\times \frac{3}{2}\\ x=18\text{ mangoes}\\ \\ \text{Total number of mangoes and }\\ \text{kiwis in the basket}\\ =18\times \frac{5}{2}\\ =45\\ \\ \text{Hence, the number of kiwis}\\ \text{in the basket}\\ =\left(1-\frac{2}{5}\right)\times 45\\ =\left(\frac{5}{5}-\frac{2}{5}\right)\times 45\\ =\frac{3}{5}\times 45\\ =27\end{array}$

Question 6:
$1\frac{1}{2}÷\frac{1}{4}\times \frac{4}{5}=$

Solution:
$\begin{array}{l}1\frac{1}{2}÷\frac{1}{4}\times \frac{4}{5}\\ =\frac{3}{\cancel{2}}\times \frac{{\cancel{4}}^2}{1}\times \frac{4}{5}\\ =\frac{24}{5}\\ =4\frac{4}{5}\end{array}$

Question 7:
$4\frac{1}{5}÷1\frac{1}{6}\times 2\frac{2}{9}=$

Solution:
$\begin{array}{l}4\frac{1}{5}÷1\frac{1}{6}\times 2\frac{2}{9}\\ =\frac{{\cancel{21}}^{\cancel{3}}}{\cancel{5}}\times \frac{{\cancel{6}}^2}{\cancel{7}}\times \frac{{\cancel{20}}^4}{{\cancel{9}}^{\cancel{3}}}\\ =8\end{array}$

Question 8:
$2\frac{3}{4}\times 1\frac{1}{3}÷7\frac{1}{3}=$

Solution:
$\begin{array}{l}2\frac{3}{4}\times 1\frac{1}{3}÷7\frac{1}{3}\\ =\frac{11}{4}\times \frac{4}{3}÷\frac{22}{3}\\ =\frac{\cancel{11}}{\cancel{4}}\times \frac{\cancel{4}}{\cancel{3}}\times \frac{\cancel{3}}{{\cancel{22}}^2}\\ =\frac{1}{2}\end{array}$

Question 9:
$4\frac{5}{6}-2\frac{1}{3}÷\frac{5}{9}=$

Solution:
$\begin{array}{l}4\frac{5}{6}-2\frac{1}{3}÷\frac{5}{9}\\ =4\frac{5}{6}-\left(\frac{7}{3}÷\frac{5}{9}\right)\\ =4\frac{5}{6}-\left(\frac{7}{\cancel{3}}\times \frac{{\cancel{9}}^3}{5}\right)\\ =4\frac{5}{6}-\frac{21}{5}\\ =4\frac{5}{6}-4\frac{1}{5}\\ =\frac{25}{30}-\frac{6}{30}\\ =\frac{19}{30}\end{array}$

Question 10:
$\left(\frac{7}{9}+\frac{11}{15}\right)÷\left(7\frac{8}{15}-4\frac{1}{5}\right)=$

Solution:
$\begin{array}{l}\left(\frac{7}{9}+\frac{11}{15}\right)÷\left(4\frac{8}{15}-3\frac{1}{5}\right)\\ =\left(\frac{35}{45}+\frac{33}{45}\right)÷\left(4\frac{8}{15}-3\frac{3}{15}\right)\\ =\frac{68}{45}÷1\frac{5}{15}\\ =\frac{68}{45}÷1\frac{1}{3}\\ =\frac{68}{45}÷\frac{4}{3}\\ =\frac{{\cancel{68}}^{17}}{{\cancel{45}}^{15}}\times \frac{\cancel{3}}{\cancel{4}}\\ =\frac{17}{15}\\ =1\frac{2}{15}\end{array}$

Question 1:
$3\frac{2}{5}+1\frac{5}{6}-\frac{1}{5}=$

Solution:
$\begin{array}{l}3\frac{2}{5}+1\frac{5}{6}-\frac{1}{5}\\ =3\frac{12}{30}+1\frac{25}{30}-\frac{6}{30}\\ =4\frac{37}{30}-\frac{6}{30}\\ =4\frac{31}{30}\\ =5\frac{1}{30}\end{array}$

Question 2:
$6\frac{1}{12}-3\frac{2}{3}-1\frac{5}{6}=$

Solution:
$\begin{array}{l}6\frac{1}{12}-3\frac{2}{3}-1\frac{5}{6}\\ =6\frac{1}{12}-3\frac{8}{12}-1\frac{10}{12}\\ =\left(5\frac{13}{12}-3\frac{8}{12}\right)-1\frac{10}{12}\\ =2\frac{5}{12}-1\frac{10}{12}\\ =1\frac{17}{12}-1\frac{10}{12}\\ =\frac{7}{12}\end{array}$

Question 3:
$30-\left(\frac{2}{7}÷\frac{2}{21}\right)=$

Solution:
$\begin{array}{l}30-\left(\frac{2}{7}÷\frac{2}{21}\right)\\ =30-\left(\frac{\cancel{2}}{\cancel{7}}\times \frac{{\cancel{21}}^3}{\cancel{2}}\right)\\ =30-3\\ =27\end{array}$

Question 4:
$\left(7\frac{1}{2}-3\frac{2}{3}\right)\times \frac{12}{69}=$

Solution:
$\begin{array}{l}\left(7\frac{1}{2}-3\frac{2}{3}\right)\times \frac{12}{69}\\ =\left(7\frac{3}{6}-3\frac{4}{6}\right)\times \frac{12}{69}\\ =\left(6\frac{9}{6}-3\frac{4}{6}\right)\times \frac{12}{69}\\ =3\frac{5}{6}\times \frac{12}{69}\\ =\frac{\cancel{23}}{\cancel{6}}\times \frac{{\cancel{12}}^2}{{\cancel{69}}^3}\\ =\frac{2}{3}\end{array}$

Question 5:
$1\frac{1}{5}÷\left(4-2\frac{1}{2}\right)=$

Solution:
$\begin{array}{l}1\frac{1}{5}÷\left(4-2\frac{1}{2}\right)\\ =1\frac{1}{5}÷\left(3\frac{2}{2}-2\frac{1}{2}\right)\\ =\frac{6}{5}÷\left(1\frac{1}{2}\right)\\ =\frac{6}{5}÷\frac{3}{2}\\ =\frac{{\cancel{6}}^2}{5}\times \frac{2}{\cancel{3}}\\ =\frac{4}{5}\end{array}$