Question

(1) Simplify:

(i) $\frac{8}{11}-\frac{7}{11}$
(ii) $-\frac{9}{13}+\frac{2}{13}$
(iii) $\frac{15}{3}\times \frac{9}{8}$
(iv) $14÷\frac{2}{7}$
(v) $\frac{-12}{0}\times 0$
(vi) $\frac{7}{9}\times \frac{3}{5}+\frac{2}{7}\times \frac{7}{5}$
(vii) $\frac{5}{3}+\frac{13}{2}\times \frac{2}{15}$

Answer 1

(i) $\frac{8}{11}-\frac{7}{11}$

$$\begin{gathered} =\frac{8-7}{11} \\ =\frac{1}{11} \end{gathered}$$

(ii) $-\frac{9}{13}+\frac{2}{13}$

$$\begin{gathered} =\frac{-9+2}{13} \\ =\frac{-7}{13} \end{gathered}$$

(iii) $\frac{15}{3}\times \frac{9}{8}$

$$\begin{gathered} =\frac{3\times 5}{3}\times \frac{3\times 3}{2\times 2\times 2} \\ =\frac{5}{1}\times \frac{9}{8} \\ =\frac{5\times 9}{1\times 8} \\ =\frac{45}{8} \\ =5\frac{5}{8} \end{gathered}$$

(iv) $14÷\frac{2}{7}$

$$\begin{gathered} =\frac{14}{1}\times \frac{7}{2} \\ =\frac{2\times 7}{1}\times \frac{7}{2} \\ =\frac{7}{1}\times \frac{7}{1} \\ =\frac{49}{1} \\ =49 \end{gathered}$$

(v) $\frac{-12}{0}\times 0$
= 0

(vi) $\frac{7}{9}\times \frac{3}{5}+\frac{2}{7}\times \frac{7}{5}$

$$\begin{gathered} =\frac{7}{3\times 3}\times \frac{3}{5}+\frac{2}{7}\times \frac{7}{5} \\ =\frac{7}{3}\times \frac{1}{5}+\frac{2}{1}\times \frac{1}{5} \\ =\frac{7}{15}+\frac{2}{5} \\ =\frac{7}{15}+\frac{2\times 3}{5\times 3} \\ =\frac{7}{15}+\frac{6}{15} \\ =\frac{7+6}{15} \\ =\frac{13}{15} \end{gathered}$$

(vii) $\frac{5}{3}+\frac{13}{2}\times \frac{2}{15}$

$$\begin{gathered} =\frac{5}{3}+\frac{13}{15} \\ =\frac{5\times 5}{3\times 5}+\frac{13}{15} \\ =\frac{25}{15}+\frac{13}{15} \\ =\frac{25+13}{15} \\ =\frac{38}{15} \end{gathered}$$