Question

Write five fractions equivalent to each of the following:
(i) $\frac{2}{3}$
(ii) $\frac{4}{5}$
(iii) $\frac{5}{8}$
(iv) $\frac{7}{10}$
(v) $\frac{3}{7}$
(vi) $\frac{6}{11}$
(vii) $\frac{7}{9}$
(viii) $\frac{5}{12}$

Answer 1

(i) $\frac{2}{3}=\frac{2\times 2}{3\times 2}=\frac{2\times 3}{3\times 3}=\frac{2\times 4}{3\times 4}=\frac{2\times 5}{3\times 5}=\frac{2\times 6}{3\times 6}$

∴ $\frac{2}{3}=\frac{4}{6}=\frac{6}{9}=\frac{8}{12}=\frac{10}{15}=\frac{12}{18}$

Hence, the five fractions equivalent to $\frac{2}{3}$ are $\frac{4}{6},\frac{6}{9},\frac{8}{12},\frac{10}{15}\mathrm{and}\frac{12}{18}$.


(ii) ​ $\frac{4}{5}=\frac{4\times 2}{5\times 2}=\frac{4\times 3}{5\times 3}=\frac{4\times 4}{5\times 4}=\frac{4\times 5}{5\times 5}=\frac{4\times 6}{5\times 6}$

∴ $\frac{4}{5}=\frac{8}{10}=\frac{12}{15}=\frac{16}{20}=\frac{20}{25}=\frac{24}{30}$

Hence, the five fractions equivalent to $\frac{4}{5}$ are $\frac{8}{10},\frac{12}{15},\frac{16}{20},\frac{20}{25}\mathrm{and}\frac{24}{30}$.


(iii) ​ $\frac{5}{8}=\frac{5\times 2}{8\times 2}=\frac{5\times 3}{8\times 3}=\frac{5\times 4}{8\times 4}=\frac{5\times 5}{8\times 5}=\frac{5\times 6}{8\times 6}$

∴ $\frac{5}{8}=\frac{10}{16}=\frac{15}{24}=\frac{20}{32}=\frac{25}{40}=\frac{30}{48}$

Hence, the five fractions equivalent to $\frac{5}{8}$ are $\frac{10}{16},\frac{15}{24},\frac{20}{32},\frac{25}{40}\mathrm{and}\frac{30}{48}$.



(iv) ​ $\frac{7}{10}=\frac{7\times 2}{10\times 2}=\frac{7\times 3}{10\times 3}=\frac{7\times 4}{10\times 4}=\frac{7\times 5}{10\times 5}=\frac{7\times 6}{10\times 6}$

∴ $\frac{7}{10}=\frac{14}{20}=\frac{21}{30}=\frac{28}{40}=\frac{35}{50}=\frac{42}{60}$

Hence, the five fractions equivalent to $\frac{7}{10}$ are $\frac{14}{20},\frac{21}{30},\frac{28}{40},\frac{35}{50}\mathrm{and}\frac{42}{60}$.


(v) ​​ $\frac{3}{7}=\frac{3\times 2}{7\times 2}=\frac{3\times 3}{7\times 3}=\frac{3\times 4}{7\times 4}=\frac{3\times 5}{7\times 5}=\frac{3\times 6}{7\times 6}$

∴ $\frac{3}{7}=\frac{6}{14}=\frac{9}{21}=\frac{12}{28}=\frac{15}{35}=\frac{18}{42}$

Hence, the five fractions equivalent to $\frac{3}{7}$ are $\frac{6}{14},\frac{9}{21},\frac{12}{28},\frac{15}{35}\mathrm{and}\frac{18}{42}$.


(vi) ​ $\frac{6}{11}=\frac{6\times 2}{11\times 2}=\frac{6\times 3}{11\times 3}=\frac{6\times 4}{11\times 4}=\frac{6\times 5}{11\times 5}=\frac{6\times 6}{11\times 6}$

∴ $\frac{6}{11}=\frac{12}{22}=\frac{18}{33}=\frac{24}{44}=\frac{30}{55}=\frac{36}{66}$

Hence, the five fractions equivalent to $\frac{6}{11}$ are $\frac{12}{22},\frac{18}{33},\frac{24}{44},\frac{30}{55}\mathrm{and}\frac{36}{66}$.


(vii) $\frac{7}{9}=\frac{7\times 2}{9\times 2}=\frac{7\times 3}{9\times 3}=\frac{7\times 4}{9\times 4}=\frac{7\times 5}{9\times 5}=\frac{7\times 6}{9\times 6}$

∴ $\frac{7}{9}=\frac{14}{18}=\frac{21}{27}=\frac{28}{36}=\frac{35}{45}=\frac{42}{54}$

Hence, the five fractions equivalent to $\frac{7}{9}$ are $\frac{14}{18},\frac{21}{27},\frac{28}{36},\frac{35}{45}\mathrm{and}\frac{42}{54}$.


(viii) $\frac{5}{12}=\frac{5\times 2}{12\times 2}=\frac{5\times 3}{12\times 3}=\frac{5\times 4}{12\times 4}=\frac{5\times 5}{12\times 5}=\frac{5\times 6}{12\times 6}$

∴ $\frac{5}{12}=\frac{10}{24}=\frac{15}{36}=\frac{20}{48}=\frac{25}{60}=\frac{30}{72}$

Hence, the five fractions equivalent to $\frac{5}{12}$ are $\frac{10}{24},\frac{15}{36},\frac{20}{48},\frac{25}{60}\mathrm{and}\frac{30}{72}$.