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) $\frac{4}{25}$

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Solution

$(i) \frac{2}{12} HCF of 2 & 12 is 2 . Divide both the numerator & denominator by the HCF of 2 & 12 . \Rightarrow \frac{2 \div 2}{12 \div 2} = \frac{1}{6}$
$(ii) \frac{3}{15} HCF of 3 & 15 is 3 . Divide both the numerator & denominator by the HCF of 3 & 15 . \Rightarrow \frac{3 \div 3}{15 \div 3} = \frac{1}{5}$

$(iii) \frac{8}{50} HCF of 8 & 50 is 2 . Divide both the numerator & denominator by the HCF of 8 & 50 . \Rightarrow \frac{8 \div 2}{50 \div 2} = \frac{4}{25}$

$(iv) \frac{16}{100} HCF of 16 & 100 is 4 . Divide both the numerator & denominator by the HCF of 16 & 100 . \Rightarrow \frac{16 \div 4}{100 \div 4} = \frac{4}{25}$

$(v) \frac{10}{60} HCF of 10 & 60 is 10 . Divide both the numerator & denominator by the HCF of 10 & 60 . \Rightarrow \frac{10 \div 10}{60 \div 10} = \frac{1}{6}$

$(vi) \frac{15}{75} HCF of 15 & 75 is 15 . Divide both the numerator & denominator by the HCF of 15 & 75 . \Rightarrow \frac{15 \div 15}{75 \div 15} = \frac{1}{5}$

$(vii) \frac{12}{60} HCF of 12 & 60 is 12 . Divide both the numerator & denominator by the HCF of 12 & 60 . \Rightarrow \frac{12 \div 12}{60 \div 12} = \frac{1}{5}$

$(viii) \frac{16}{96} HCF of 16 & 96 is 16 . Divide both the numerator & denominator by the HCF of 16 & 96 . \Rightarrow \frac{16 \div 16}{96 \div 16} = \frac{1}{6}$

$(ix) \frac{12}{75} HCF of 12 & 75 is 3 . Divide both the numerator & denominator by the HCF of 12 & 75 . \Rightarrow \frac{12 \div 3}{75 \div 3} = \frac{4}{25}$

$(x) \frac{12}{72} HCF of 12 & 72 is 12 . Divide both the numerator & denominator by the HCF of 12 & 72 . \Rightarrow \frac{12 \div 12}{72 \div 12} = \frac{1}{6}$

$(xi) \frac{3}{18} HCF of 3 & 18 is 3 . Divide both the numerator & denominator by the HCF of 3 & 18 . \Rightarrow \frac{3 \div 3}{18 \div 3} = \frac{1}{6}$

$(xii) \frac{4}{25} HCF of 4 & 25 is 1 . Divide both the numerator & denominator by the HCF of 4 & 25 . \Rightarrow \frac{4 \div 1}{25 \div 1} = \frac{4}{25}$

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

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Similar questions

\frac{2}{12}

\frac{3}{15}

\frac{8}{50}

\frac{16}{100}

\frac{10}{60}

\frac{15}{75}

\frac{12}{60}

\frac{16}{96}

\frac{12}{75}

\frac{12}{72}

\frac{3}{18}

\frac{4}{25}

\frac{16}{96}

\frac{8}{50}

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