To find five fractions equivalent to each of the given fractions, we can multiply the numerator and denominator of each fraction by the same non-zero integer. Here’s how to do it step by step for each fraction:
### (i) For the fraction \( \frac{2}{3} \):
1. Multiply both the numerator and denominator by 2:
\[
\frac{2 \times 2}{3 \times 2} = \frac{4}{6}
\]
2. Multiply both by 3:
\[
\frac{2 \times 3}{3 \times 3} = \frac{6}{9}
\]
3. Multiply both by 4:
\[
\frac{2 \times 4}{3 \times 4} = \frac{8}{12}
\]
4. Multiply both by 5:
\[
\frac{2 \times 5}{3 \times 5} = \frac{10}{15}
\]
5. Multiply both by 6:
\[
\frac{2 \times 6}{3 \times 6} = \frac{12}{18}
\]
**Equivalent fractions for \( \frac{2}{3} \):** \( \frac{4}{6}, \frac{6}{9}, \frac{8}{12}, \frac{10}{15}, \frac{12}{18} \)
### (ii) For the fraction \( \frac{4}{5} \):
1. Multiply both by 2:
\[
\frac{4 \times 2}{5 \times 2} = \frac{8}{10}
\]
2. Multiply both by 3:
\[
\frac{4 \times 3}{5 \times 3} = \frac{12}{15}
\]
3. Multiply both by 4:
\[
\frac{4 \times 4}{5 \times 4} = \frac{16}{20}
\]
4. Multiply both by 5:
\[
\frac{4 \times 5}{5 \times 5} = \frac{20}{25}
\]
5. Multiply both by 6:
\[
\frac{4 \times 6}{5 \times 6} = \frac{24}{30}
\]
**Equivalent fractions for \( \frac{4}{5} \):** \( \frac{8}{10}, \frac{12}{15}, \frac{16}{20}, \frac{20}{25}, \frac{24}{30} \)
### (iii) For the fraction \( \frac{5}{8} \):
1. Multiply both by 2:
\[
\frac{5 \times 2}{8 \times 2} = \frac{10}{16}
\]
2. Multiply both by 3:
\[
\frac{5 \times 3}{8 \times 3} = \frac{15}{24}
\]
3. Multiply both by 4:
\[
\frac{5 \times 4}{8 \times 4} = \frac{20}{32}
\]
4. Multiply both by 5:
\[
\frac{5 \times 5}{8 \times 5} = \frac{25}{40}
\]
5. Multiply both by 6:
\[
\frac{5 \times 6}{8 \times 6} = \frac{30}{48}
\]
**Equivalent fractions for \( \frac{5}{8} \):** \( \frac{10}{16}, \frac{15}{24}, \frac{20}{32}, \frac{25}{40}, \frac{30}{48} \)
### (iv) For the fraction \( \frac{7}{10} \):
1. Multiply both by 2:
\[
\frac{7 \times 2}{10 \times 2} = \frac{14}{20}
\]
2. Multiply both by 3:
\[
\frac{7 \times 3}{10 \times 3} = \frac{21}{30}
\]
3. Multiply both by 4:
\[
\frac{7 \times 4}{10 \times 4} = \frac{28}{40}
\]
4. Multiply both by 5:
\[
\frac{7 \times 5}{10 \times 5} = \frac{35}{50}
\]
5. Multiply both by 6:
\[
\frac{7 \times 6}{10 \times 6} = \frac{42}{60}
\]
**Equivalent fractions for \( \frac{7}{10} \):** \( \frac{14}{20}, \frac{21}{30}, \frac{28}{40}, \frac{35}{50}, \frac{42}{60} \)
### (v) For the fraction \( \frac{3}{7} \):
1. Multiply both by 2:
\[
\frac{3 \times 2}{7 \times 2} = \frac{6}{14}
\]
2. Multiply both by 3:
\[
\frac{3 \times 3}{7 \times 3} = \frac{9}{21}
\]
3. Multiply both by 4:
\[
\frac{3 \times 4}{7 \times 4} = \frac{12}{28}
\]
4. Multiply both by 5:
\[
\frac{3 \times 5}{7 \times 5} = \frac{15}{35}
\]
5. Multiply both by 6:
\[
\frac{3 \times 6}{7 \times 6} = \frac{18}{42}
\]
**Equivalent fractions for \( \frac{3}{7} \):** \( \frac{6}{14}, \frac{9}{21}, \frac{12}{28}, \frac{15}{35}, \frac{18}{42} \)
### (vi) For the fraction \( \frac{6}{11} \):
1. Multiply both by 2:
\[
\frac{6 \times 2}{11 \times 2} = \frac{12}{22}
\]
2. Multiply both by 3:
\[
\frac{6 \times 3}{11 \times 3} = \frac{18}{33}
\]
3. Multiply both by 4:
\[
\frac{6 \times 4}{11 \times 4} = \frac{24}{44}
\]
4. Multiply both by 5:
\[
\frac{6 \times 5}{11 \times 5} = \frac{30}{55}
\]
5. Multiply both by 6:
\[
\frac{6 \times 6}{11 \times 6} = \frac{36}{66}
\]
**Equivalent fractions for \( \frac{6}{11} \):** \( \frac{12}{22}, \frac{18}{33}, \frac{24}{44}, \frac{30}{55}, \frac{36}{66} \)
### (vii) For the fraction \( \frac{7}{9} \):
1. Multiply both by 2:
\[
\frac{7 \times 2}{9 \times 2} = \frac{14}{18}
\]
2. Multiply both by 3:
\[
\frac{7 \times 3}{9 \times 3} = \frac{21}{27}
\]
3. Multiply both by 4:
\[
\frac{7 \times 4}{9 \times 4} = \frac{28}{36}
\]
4. Multiply both by 5:
\[
\frac{7 \times 5}{9 \times 5} = \frac{35}{45}
\]
5. Multiply both by 6:
\[
\frac{7 \times 6}{9 \times 6} = \frac{42}{54}
\]
**Equivalent fractions for \( \frac{7}{9} \):** \( \frac{14}{18}, \frac{21}{27}, \frac{28}{36}, \frac{35}{45}, \frac{42}{54} \)
### (viii) For the fraction \( \frac{5}{12} \):
1. Multiply both by 2:
\[
\frac{5 \times 2}{12 \times 2} = \frac{10}{24}
\]
2. Multiply both by 3:
\[
\frac{5 \times 3}{12 \times 3} = \frac{15}{36}
\]
3. Multiply both by 4:
\[
\frac{5 \times 4}{12 \times 4} = \frac{20}{48}
\]
4. Multiply both by 5:
\[
\frac{5 \times 5}{12 \times 5} = \frac{25}{60}
\]
5. Multiply both by 6:
\[
\frac{5 \times 6}{12 \times 6} = \frac{30}{72}
\]
**Equivalent fractions for \( \frac{5}{12} \):** \( \frac{10}{24}, \frac{15}{36}, \frac{20}{48}, \frac{25}{60}, \frac{30}{72} \)
