Question

for 1 - 16, find equivalent fractions to compare. then write >, <, or =.

1. $\frac{5}{6}$ $\bigcirc$ $\frac{2}{3}$
2. $\frac{1}{5}$ $\bigcirc$ $\frac{2}{8}$
3. $\frac{9}{10}$ $\bigcirc$ $\frac{3}{4}$
4. $\frac{3}{4}$ $\bigcirc$ $\frac{2}{8}$
5. $\frac{7}{8}$ $\bigcirc$ $\frac{1}{2}$
6. $\frac{2}{5}$ $\bigcirc$ $\frac{2}{6}$
7. $\frac{1}{3}$ $\bigcirc$ $\frac{3}{8}$
8. $\frac{2}{10}$ $\bigcirc$ $\frac{3}{5}$
9. $\frac{8}{10}$ $\bigcirc$ $\frac{3}{4}$
10. $\frac{3}{8}$ $\bigcirc$ $\frac{9}{12}$
11. $\frac{2}{3}$ $\bigcirc$ $\frac{10}{12}$
12. $\frac{7}{8}$ $\bigcirc$ $\frac{3}{4}$
13. $\frac{3}{4}$ $\bigcirc$ $\frac{7}{8}$
14. $\frac{2}{4}$ $\bigcirc$ $\frac{4}{8}$
15. $\frac{6}{8}$ $\bigcirc$ $\frac{8}{12}$
16. $\frac{1}{3}$ $\bigcirc$ $\frac{4}{8}$

Explanation:

Step1: Get common denominators

For each pair, find a common denominator.

Step2: Convert fractions

Rewrite fractions with the common denominator.

Step3: Compare numerators

Larger numerator means larger fraction.

1. $\frac{5}{6}$ vs $\frac{2}{3}$

Common denominator: 6. $\frac{2}{3}=\frac{4}{6}$. $5>4$, so $\frac{5}{6}>\frac{2}{3}$.

2. $\frac{1}{5}$ vs $\frac{2}{8}$

Simplify $\frac{2}{8}=\frac{1}{4}$. Common denominator: 20. $\frac{1}{5}=\frac{4}{20}$, $\frac{1}{4}=\frac{5}{20}$. $4<5$, so $\frac{1}{5}<\frac{2}{8}$.

3. $\frac{9}{10}$ vs $\frac{3}{4}$

Common denominator: 20. $\frac{9}{10}=\frac{18}{20}$, $\frac{3}{4}=\frac{15}{20}$. $18>15$, so $\frac{9}{10}>\frac{3}{4}$.

4. $\frac{3}{4}$ vs $\frac{2}{8}$

Simplify $\frac{2}{8}=\frac{1}{4}$. $3>1$, so $\frac{3}{4}>\frac{2}{8}$.

5. $\frac{7}{8}$ vs $\frac{1}{2}$

Common denominator: 8. $\frac{1}{2}=\frac{4}{8}$. $7>4$, so $\frac{7}{8}>\frac{1}{2}$.

6. $\frac{2}{5}$ vs $\frac{2}{6}$

Same numerator: smaller denominator = larger fraction. $5<6$, so $\frac{2}{5}>\frac{2}{6}$.

7. $\frac{1}{3}$ vs $\frac{3}{8}$

Common denominator: 24. $\frac{1}{3}=\frac{8}{24}$, $\frac{3}{8}=\frac{9}{24}$. $8<9$, so $\frac{1}{3}<\frac{3}{8}$.

8. $\frac{2}{10}$ vs $\frac{3}{5}$

Common denominator: 10. $\frac{3}{5}=\frac{6}{10}$. $2<6$, so $\frac{2}{10}<\frac{3}{5}$.

9. $\frac{8}{10}$ vs $\frac{3}{4}$

Simplify $\frac{8}{10}=\frac{4}{5}$. Common denominator: 20. $\frac{4}{5}=\frac{16}{20}$, $\frac{3}{4}=\frac{15}{20}$. $16>15$, so $\frac{8}{10}>\frac{3}{4}$.

10. $\frac{3}{8}$ vs $\frac{9}{12}$

Simplify $\frac{9}{12}=\frac{3}{4}$. Common denominator: 8. $\frac{3}{4}=\frac{6}{8}$. $3<6$, so $\frac{3}{8}<\frac{9}{12}$.

11. $\frac{2}{3}$ vs $\frac{10}{12}$

Simplify $\frac{10}{12}=\frac{5}{6}$. Common denominator: 6. $\frac{2}{3}=\frac{4}{6}$. $4<5$, so $\frac{2}{3}<\frac{10}{12}$.

12. $\frac{7}{8}$ vs $\frac{3}{4}$

Common denominator: 8. $\frac{3}{4}=\frac{6}{8}$. $7>6$, so $\frac{7}{8}>\frac{3}{4}$.

13. $\frac{3}{4}$ vs $\frac{7}{8}$

Common denominator: 8. $\frac{3}{4}=\frac{6}{8}$. $6<7$, so $\frac{3}{4}<\frac{7}{8}$.

14. $\frac{2}{4}$ vs $\frac{4}{8}$

Simplify both to $\frac{1}{2}$. $\frac{2}{4}=\frac{1}{2}$, $\frac{4}{8}=\frac{1}{2}$. So $\frac{2}{4}=\frac{4}{8}$.

15. $\frac{6}{8}$ vs $\frac{8}{12}$

Simplify $\frac{6}{8}=\frac{3}{4}$, $\frac{8}{12}=\frac{2}{3}$. Common denominator: 12. $\frac{3}{4}=\frac{9}{12}$, $\frac{2}{3}=\frac{8}{12}$. $9>8$, so $\frac{6}{8}>\frac{8}{12}$.

16. $\frac{1}{3}$ vs $\frac{4}{8}$

Simplify $\frac{4}{8}=\frac{1}{2}$. Common denominator: 6. $\frac{1}{3}=\frac{2}{6}$, $\frac{1}{2}=\frac{3}{6}$. $2<3$, so $\frac{1}{3}<\frac{4}{8}$.

Answer:

1. $\frac{5}{6} > \frac{2}{3}$
2. $\frac{1}{5} < \frac{2}{8}$
3. $\frac{9}{10} > \frac{3}{4}$
4. $\frac{3}{4} > \frac{2}{8}$
5. $\frac{7}{8} > \frac{1}{2}$
6. $\frac{2}{5} > \frac{2}{6}$
7. $\frac{1}{3} > \frac{3}{8}$
8. $\frac{2}{10} < \frac{3}{5}$
9. $\frac{8}{10} < \frac{3}{4}$
10. $\frac{3}{8} < \frac{9}{12}$
11. $\frac{2}{3} < \frac{10}{12}$
12. $\frac{7}{8} > \frac{3}{4}$
13. $\frac{3}{4} < \frac{7}{8}$
14. $\frac{2}{4} = \frac{4}{8}$
15. $\frac{6}{8} > \frac{8}{12}$
16. $\frac{1}{3} < \frac{4}{8}$