Question

equivalent fractions in higher terms
lower terms | \\(\frac{1}{3}\\)s | \\(\frac{1}{4}\\)s | \\(\frac{1}{6}\\)s | \\(\frac{1}{8}\\)s | \\(\frac{1}{10}\\)s | \\(\frac{1}{12}\\)s

1. \\(\frac{1}{6}\\) | | | | | |
2. \\(\frac{2}{6}\\) | | | | | |
3. \\(\frac{1}{10}\\) | | | | | |
4. \\(\frac{3}{10}\\) | | | | | |
5. \\(\frac{7}{10}\\) | | | | | |
6. \\(\frac{9}{10}\\) | | | | | |
7. \\(\frac{1}{12}\\) | | | | | |
8. \\(\frac{5}{12}\\) | | | | | |
9. \\(\frac{7}{12}\\) | | | | | |
10. \\(\frac{11}{12}\\) | | | | | |

Explanation:

Step1: Recall equivalent fraction rule

To find equivalent fractions in higher terms, multiply numerator and denominator by the same non-zero integer: $\frac{a}{b} = \frac{a \times k}{b \times k}$, where $k$ is a positive integer.

Step2: Calculate for $\frac{1}{6}$

Multiply by 2, 3, 4, 5, 6:
$\frac{1 \times 2}{6 \times 2} = \frac{2}{12}$, $\frac{1 \times 3}{6 \times 3} = \frac{3}{18}$, $\frac{1 \times 4}{6 \times 4} = \frac{4}{24}$, $\frac{1 \times 5}{6 \times 5} = \frac{5}{30}$, $\frac{1 \times 6}{6 \times 6} = \frac{6}{36}$

Step3: Calculate for $\frac{5}{6}$

Multiply by 2, 3, 4, 5, 6:
$\frac{5 \times 2}{6 \times 2} = \frac{10}{12}$, $\frac{5 \times 3}{6 \times 3} = \frac{15}{18}$, $\frac{5 \times 4}{6 \times 4} = \frac{20}{24}$, $\frac{5 \times 5}{6 \times 5} = \frac{25}{30}$, $\frac{5 \times 6}{6 \times 6} = \frac{30}{36}$

Step4: Calculate for $\frac{1}{10}$

Multiply by 2, 3, 4, 5, 6:
$\frac{1 \times 2}{10 \times 2} = \frac{2}{20}$, $\frac{1 \times 3}{10 \times 3} = \frac{3}{30}$, $\frac{1 \times 4}{10 \times 4} = \frac{4}{40}$, $\frac{1 \times 5}{10 \times 5} = \frac{5}{50}$, $\frac{1 \times 6}{10 \times 6} = \frac{6}{60}$

Step5: Calculate for $\frac{3}{10}$

Multiply by 2, 3, 4, 5, 6:
$\frac{3 \times 2}{10 \times 2} = \frac{6}{20}$, $\frac{3 \times 3}{10 \times 3} = \frac{9}{30}$, $\frac{3 \times 4}{10 \times 4} = \frac{12}{40}$, $\frac{3 \times 5}{10 \times 5} = \frac{15}{50}$, $\frac{3 \times 6}{10 \times 6} = \frac{18}{60}$

Step6: Calculate for $\frac{7}{10}$

Multiply by 2, 3, 4, 5, 6:
$\frac{7 \times 2}{10 \times 2} = \frac{14}{20}$, $\frac{7 \times 3}{10 \times 3} = \frac{21}{30}$, $\frac{7 \times 4}{10 \times 4} = \frac{28}{40}$, $\frac{7 \times 5}{10 \times 5} = \frac{35}{50}$, $\frac{7 \times 6}{10 \times 6} = \frac{42}{60}$

Step7: Calculate for $\frac{9}{10}$

Multiply by 2, 3, 4, 5, 6:
$\frac{9 \times 2}{10 \times 2} = \frac{18}{20}$, $\frac{9 \times 3}{10 \times 3} = \frac{27}{30}$, $\frac{9 \times 4}{10 \times 4} = \frac{36}{40}$, $\frac{9 \times 5}{10 \times 5} = \frac{45}{50}$, $\frac{9 \times 6}{10 \times 6} = \frac{54}{60}$

Step8: Calculate for $\frac{1}{12}$

Multiply by 2, 3, 4, 5, 6:
$\frac{1 \times 2}{12 \times 2} = \frac{2}{24}$, $\frac{1 \times 3}{12 \times 3} = \frac{3}{36}$, $\frac{1 \times 4}{12 \times 4} = \frac{4}{48}$, $\frac{1 \times 5}{12 \times 5} = \frac{5}{60}$, $\frac{1 \times 6}{12 \times 6} = \frac{6}{72}$

Step9: Calculate for $\frac{5}{12}$

Multiply by 2, 3, 4, 5, 6:
$\frac{5 \times 2}{12 \times 2} = \frac{10}{24}$, $\frac{5 \times 3}{12 \times 3} = \frac{15}{36}$, $\frac{5 \times 4}{12 \times 4} = \frac{20}{48}$, $\frac{5 \times 5}{12 \times 5} = \frac{25}{60}$, $\frac{5 \times 6}{12 \times 6} = \frac{30}{72}$

Step10: Calculate for $\frac{7}{12}$

Multiply by 2, 3, 4, 5, 6:
$\frac{7 \times 2}{12 \times 2} = \frac{14}{24}$, $\frac{7 \times 3}{12 \times 3} = \frac{21}{36}$, $\frac{7 \times 4}{12 \times 4} = \frac{28}{48}$, $\frac{7 \times 5}{12 \times 5} = \frac{35}{60}$, $\frac{7 \times 6}{12 \times 6} = \frac{42}{72}$

Step11: Calculate for $\frac{11}{12}$

Multiply by 2, 3, 4, 5, 6:
$\frac{11 \times 2}{12 \times 2} = \frac{22}{24}$, $\frac{11 \times 3}{12 \times 3} = \frac{33}{36}$, $\frac{11 \times 4}{12 \times 4} = \frac{44}{48}$, $\frac{11 \times 5}{12 \times 5} = \frac{55}{60}$, $\frac{11 \times 6}{12 \times 6} = \frac{66}{72}$

Answer:

Lower Terms	Equivalent Fractions in Higher Terms
11. $\frac{1}{6}$	$\frac{1}{6}$	$\frac{2}{12}$	$\frac{4}{24}$	$\frac{3}{18}$	$\frac{5}{30}$	$\frac{2}{12}$
12. $\frac{5}{6}$	$\frac{5}{6}$	$\frac{10}{12}$	$\frac{20}{24}$	$\frac{15}{18}$	$\frac{25}{30}$	$\frac{10}{12}$
13. $\frac{1}{10}$	$\frac{3}{30}$	$\frac{5}{50}$	$\frac{4}{40}$	$\frac{9}{90}$	$\frac{1}{10}$	$\frac{6}{60}$
14. $\frac{3}{10}$	$\frac{9}{30}$	$\frac{15}{50}$	$\frac{12}{40}$	$\frac{27}{90}$	$\frac{3}{10}$	$\frac{18}{60}$
15. $\frac{7}{10}$	$\frac{21}{30}$	$\frac{35}{50}$	$\frac{28}{40}$	$\frac{63}{90}$	$\frac{7}{10}$	$\frac{42}{60}$
16. $\frac{9}{10}$	$\frac{27}{30}$	$\frac{45}{50}$	$\frac{36}{40}$	$\frac{81}{90}$	$\frac{9}{10}$	$\frac{54}{60}$
17. $\frac{1}{12}$	$\frac{2}{24}$	$\frac{3}{36}$	$\frac{4}{48}$	$\frac{6}{72}$	$\frac{5}{60}$	$\frac{1}{12}$
18. $\frac{5}{12}$	$\frac{10}{24}$	$\frac{15}{36}$	$\frac{20}{48}$	$\frac{30}{72}$	$\frac{25}{60}$	$\frac{5}{12}$
19. $\frac{7}{12}$	$\frac{14}{24}$	$\frac{21}{36}$	$\frac{28}{48}$	$\frac{42}{72}$	$\frac{35}{60}$	$\frac{7}{12}$
20. $\frac{11}{12}$	$\frac{22}{24}$	$\frac{33}{36}$	$\frac{44}{48}$	$\frac{66}{72}$	$\frac{55}{60}$	$\frac{11}{12}$

(Note: For each row, the equivalent fractions are matched to the column denominators by scaling the original fraction to have the column's denominator as its new denominator.)