Question

Match the equivalent fractions and write another 2 form each:

(i) $\frac{250}{400}$ (a) $\frac{2}{3}$
(ii) $\frac{180}{200}$ (b) $\frac{2}{5}$
(iii) $\frac{660}{990}$ (c) $\frac{1}{2}$
(iv) $\frac{180}{360}$ (d) $\frac{5}{8}$
(v) $\frac{220}{550}$ (e) $\frac{9}{10}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\frac{250}{400} \\ \mathrm{Dividing}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCFs}\mathrm{of}250\&400,\mathrm{we}\mathrm{get}: \\ =\left(\frac{{\displaystyle \frac{250}{50}}}{{\displaystyle \frac{400}{50}}}\right) \\ =\frac{5}{8} \end{gathered}$$
$$\begin{gathered} \left(\mathrm{ii}\right)\frac{180}{200} \\ \mathrm{Dividing}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCFs}\mathrm{of}180\&200,\mathrm{we}\mathrm{get}: \\ =\left(\frac{{\displaystyle \frac{180}{20}}}{{\displaystyle \frac{200}{20}}}\right) \\ =\frac{9}{10} \end{gathered}$$
$$\begin{gathered} \left(\mathrm{iii}\right)\frac{660}{990} \\ \mathrm{Dividing}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCFs}\mathrm{of}660\&990,\mathrm{we}\mathrm{get}: \\ =\left(\frac{{\displaystyle \frac{660}{30}}}{{\displaystyle \frac{990}{30}}}\right) \\ =\frac{\left({\displaystyle \frac{22}{11}}\right)}{\left({\displaystyle \frac{33}{11}}\right)} \\ =\frac{2}{3} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iv}\right)\frac{180}{360} \\ \mathrm{Dividing}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCFs}\mathrm{of}180\&360,\mathrm{we}\mathrm{get}: \\ =\left(\frac{{\displaystyle \frac{180}{180}}}{{\displaystyle \frac{360}{180}}}\right) \\ =\frac{1}{2} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{v}\right)\frac{220}{550} \\ \mathrm{Dividing}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCFs}\mathrm{of}220\&550,\mathrm{we}\mathrm{get}: \\ =\left(\frac{{\displaystyle \frac{220}{11}}}{{\displaystyle \frac{550}{11}}}\right) \\ =\left(\frac{20}{50}\right) \\ =\left(\frac{{\displaystyle \frac{20}{10}}}{{\displaystyle \frac{50}{10}}}\right) \\ =\frac{2}{5} \end{gathered}$$

(i) - (d)
(ii) - (e)
(iii) - (a)
(iv) -(c)
(v)- (b)