Question

The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing each one to its simplest form:

(i) $\frac{2}{12}$
(ii) $\frac{3}{15}$
(iii) $\frac{8}{50}$
(iv) $\frac{16}{100}$
(v) $\frac{10}{60}$
(vi) $\frac{15}{75}$
(vii) $\frac{12}{60}$
(viii) $\frac{16}{96}$
(ix) $\frac{12}{75}$
(x) $\frac{12}{72}$
(xi) $\frac{3}{18}$
(xii) $\frac{4}{25}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\frac{2}{12} \\ \mathrm{HCF}\mathrm{of}2\&12\mathrm{is}2. \\ \mathrm{Divide}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCF}\mathrm{of}2\&12. \\ \Rightarrow \frac{2÷2}{12÷2}=\frac{1}{6} \end{gathered}$$
$$\begin{gathered} \left(\mathrm{ii}\right)\frac{3}{15} \\ \mathrm{HCF}\mathrm{of}3\&15\mathrm{is}3. \\ \mathrm{Divide}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCF}\mathrm{of}3\&15. \\ \Rightarrow \frac{3÷3}{15÷3}=\frac{1}{5} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iii}\right)\frac{8}{50} \\ \mathrm{HCF}\mathrm{of}8\&50\mathrm{is}2. \\ \mathrm{Divide}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCF}\mathrm{of}8\&50. \\ \Rightarrow \frac{8÷2}{50÷2}=\frac{4}{25} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iv}\right)\frac{16}{100} \\ \mathrm{HCF}\mathrm{of}16\&100\mathrm{is}4. \\ \mathrm{Divide}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCF}\mathrm{of}16\&100. \\ \Rightarrow \frac{16÷4}{100÷4}=\frac{4}{25} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{v}\right)\frac{10}{60} \\ \mathrm{HCF}\mathrm{of}10\&60\mathrm{is}10. \\ \mathrm{Divide}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCF}\mathrm{of}10\&60. \\ \Rightarrow \frac{10÷10}{60÷10}=\frac{1}{6} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{vi}\right)\frac{15}{75} \\ \mathrm{HCF}\mathrm{of}15\&75\mathrm{is}15. \\ \mathrm{Divide}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCF}\mathrm{of}15\&75. \\ \Rightarrow \frac{15÷15}{75÷15}=\frac{1}{5} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{vii}\right)\frac{12}{60} \\ \mathrm{HCF}\mathrm{of}12\&60\mathrm{is}12. \\ \mathrm{Divide}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCF}\mathrm{of}12\&60. \\ \Rightarrow \frac{12÷12}{60÷12}=\frac{1}{5} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{viii}\right)\frac{16}{96} \\ \mathrm{HCF}\mathrm{of}16\&96\mathrm{is}16. \\ \mathrm{Divide}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCF}\mathrm{of}16\&96. \\ \Rightarrow \frac{16÷16}{96÷16}=\frac{1}{6} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ix}\right)\frac{12}{75} \\ \mathrm{HCF}\mathrm{of}12\&75\mathrm{is}3. \\ \mathrm{Divide}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCF}\mathrm{of}12\&75. \\ \Rightarrow \frac{12÷3}{75÷3}=\frac{4}{25} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{x}\right)\frac{12}{72} \\ \mathrm{HCF}\mathrm{of}12\&72\mathrm{is}12. \\ \mathrm{Divide}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCF}\mathrm{of}12\&72. \\ \Rightarrow \frac{12÷12}{72÷12}=\frac{1}{6} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{xi}\right)\frac{3}{18} \\ \mathrm{HCF}\mathrm{of}3\&18\mathrm{is}3. \\ \mathrm{Divide}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCF}\mathrm{of}3\&18. \\ \Rightarrow \frac{3÷3}{18÷3}=\frac{1}{6} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{xii}\right)\frac{4}{25} \\ \mathrm{HCF}\mathrm{of}4\&25\mathrm{is}1. \\ \mathrm{Divide}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCF}\mathrm{of}4\&25. \\ \Rightarrow \frac{4÷1}{25÷1}=\frac{4}{25} \end{gathered}$$

$\mathrm{Three}\mathrm{groups}\mathrm{of}\mathrm{equal}\mathrm{fractions}:\frac{2}{12},\frac{10}{60},\frac{16}{96},\frac{12}{72},\frac{3}{18};\frac{3}{15},\frac{15}{75},\frac{12}{60};\frac{8}{50},\frac{16}{100},\frac{12}{75},\frac{4}{25}$