Printable Grade 3 math worksheet for comparing fractions with different denominators.

To compare fractions with different denominators, we need to make the bottom numbers (denominators) the same. This is called finding a common denominator. Once the denominators are the same, we can just look at the top numbers (numerators) to see which fraction is bigger.

Here is the step-by-step solution for each problem:

1. $\frac{8}{20}$ ___ $\frac{3}{6}$
* Simplify $\frac{3}{6}$ to $\frac{1}{2}$.
* Convert $\frac{1}{2}$ to have a denominator of 20: $\frac{1 \times 10}{2 \times 10} = \frac{10}{20}$.
* Compare $\frac{8}{20}$ and $\frac{10}{20}$. Since $8 < 10$, then $\frac{8}{20} < \frac{3}{6}$.
* Answer: <

2. $\frac{1}{10}$ ___ $\frac{1}{4}$
* The least common multiple for 10 and 4 is 20.
* $\frac{1}{10} = \frac{2}{20}$
* $\frac{1}{4} = \frac{5}{20}$
* Since $2 < 5$, then $\frac{1}{10} < \frac{1}{4}$.
* Answer: <

3. $\frac{1}{5}$ ___ $\frac{5}{10}$
* Simplify $\frac{5}{10}$ to $\frac{1}{2}$.
* Convert $\frac{1}{5}$ to tenths: $\frac{1 \times 2}{5 \times 2} = \frac{2}{10}$.
* Compare $\frac{2}{10}$ and $\frac{5}{10}$. Since $2 < 5$, then $\frac{1}{5} < \frac{5}{10}$.
* Answer: <

4. $\frac{5}{15}$ ___ $\frac{7}{12}$
* Simplify $\frac{5}{15}$ to $\frac{1}{3}$.
* Common denominator for 3 and 12 is 12.
* $\frac{1}{3} = \frac{4}{12}$.
* Compare $\frac{4}{12}$ and $\frac{7}{12}$. Since $4 < 7$, then $\frac{5}{15} < \frac{7}{12}$.
* Answer: <

5. $\frac{2}{4}$ ___ $\frac{10}{40}$
* Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
* Simplify $\frac{10}{40}$ to $\frac{1}{4}$.
* Convert $\frac{1}{2}$ to fourths: $\frac{2}{4}$.
* Compare $\frac{2}{4}$ and $\frac{1}{4}$. Since $2 > 1$, then $\frac{2}{4} > \frac{10}{40}$.
* Answer: >

6. $\frac{2}{6}$ ___ $\frac{20}{50}$
* Simplify $\frac{2}{6}$ to $\frac{1}{3}$.
* Simplify $\frac{20}{50}$ to $\frac{2}{5}$.
* Common denominator for 3 and 5 is 15.
* $\frac{1}{3} = \frac{5}{15}$.
* $\frac{2}{5} = \frac{6}{15}$.
* Since $5 < 6$, then $\frac{2}{6} < \frac{20}{50}$.
* Answer: <

7. $\frac{4}{5}$ ___ $\frac{7}{10}$
* Convert $\frac{4}{5}$ to tenths: $\frac{4 \times 2}{5 \times 2} = \frac{8}{10}$.
* Compare $\frac{8}{10}$ and $\frac{7}{10}$. Since $8 > 7$, then $\frac{4}{5} > \frac{7}{10}$.
* Answer: >

8. $\frac{5}{12}$ ___ $\frac{1}{2}$
* Convert $\frac{1}{2}$ to twelfths: $\frac{1 \times 6}{2 \times 6} = \frac{6}{12}$.
* Compare $\frac{5}{12}$ and $\frac{6}{12}$. Since $5 < 6$, then $\frac{5}{12} < \frac{1}{2}$.
* Answer: <

9. $\frac{4}{6}$ ___ $\frac{42}{48}$
* Simplify $\frac{4}{6}$ to $\frac{2}{3}$.
* Simplify $\frac{42}{48}$ (divide both by 6) to $\frac{7}{8}$.
* Common denominator for 3 and 8 is 24.
* $\frac{2}{3} = \frac{16}{24}$.
* $\frac{7}{8} = \frac{21}{24}$.
* Since $16 < 21$, then $\frac{4}{6} < \frac{42}{48}$.
* Answer: <

10. $\frac{3}{6}$ ___ $\frac{2}{4}$
* Simplify $\frac{3}{6}$ to $\frac{1}{2}$.
* Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
* They are equal.
* Answer: =

11. $\frac{3}{9}$ ___ $\frac{10}{50}$
* Simplify $\frac{3}{9}$ to $\frac{1}{3}$.
* Simplify $\frac{10}{50}$ to $\frac{1}{5}$.
* When numerators are the same, the fraction with the smaller denominator is larger. $3 < 5$, so $\frac{1}{3} > \frac{1}{5}$.
* Answer: >

12. $\frac{10}{20}$ ___ $\frac{4}{8}$
* Simplify $\frac{10}{20}$ to $\frac{1}{2}$.
* Simplify $\frac{4}{8}$ to $\frac{1}{2}$.
* They are equal.
* Answer: =

13. $\frac{5}{8}$ ___ $\frac{2}{6}$
* Simplify $\frac{2}{6}$ to $\frac{1}{3}$.
* Common denominator for 8 and 3 is 24.
* $\frac{5}{8} = \frac{15}{24}$.
* $\frac{1}{3} = \frac{8}{24}$.
* Since $15 > 8$, then $\frac{5}{8} > \frac{2}{6}$.
* Answer: >

14. $\frac{5}{60}$ ___ $\frac{15}{20}$
* Simplify $\frac{5}{60}$ to $\frac{1}{12}$.
* Simplify $\frac{15}{20}$ to $\frac{3}{4}$.
* Common denominator for 12 and 4 is 12.
* $\frac{3}{4} = \frac{9}{12}$.
* Compare $\frac{1}{12}$ and $\frac{9}{12}$. Since $1 < 9$, then $\frac{5}{60} < \frac{15}{20}$.
* Answer: <

15. $\frac{6}{24}$ ___ $\frac{2}{10}$
* Simplify $\frac{6}{24}$ to $\frac{1}{4}$.
* Simplify $\frac{2}{10}$ to $\frac{1}{5}$.
* Common denominator for 4 and 5 is 20.
* $\frac{1}{4} = \frac{5}{20}$.
* $\frac{1}{5} = \frac{4}{20}$.
* Since $5 > 4$, then $\frac{6}{24} > \frac{2}{10}$.
* Answer: >

16. $\frac{20}{24}$ ___ $\frac{3}{9}$
* Simplify $\frac{20}{24}$ (divide by 4) to $\frac{5}{6}$.
* Simplify $\frac{3}{9}$ to $\frac{1}{3}$.
* Convert $\frac{1}{3}$ to sixths: $\frac{2}{6}$.
* Compare $\frac{5}{6}$ and $\frac{2}{6}$. Since $5 > 2$, then $\frac{20}{24} > \frac{3}{9}$.
* Answer: >

17. $\frac{18}{48}$ ___ $\frac{10}{30}$
* Simplify $\frac{18}{48}$ (divide by 6) to $\frac{3}{8}$.
* Simplify $\frac{10}{30}$ to $\frac{1}{3}$.
* Common denominator for 8 and 3 is 24.
* $\frac{3}{8} = \frac{9}{24}$.
* $\frac{1}{3} = \frac{8}{24}$.
* Since $9 > 8$, then $\frac{18}{48} > \frac{10}{30}$.
* Answer: >

18. $\frac{2}{10}$ ___ $\frac{1}{2}$
* Simplify $\frac{2}{10}$ to $\frac{1}{5}$.
* Convert $\frac{1}{2}$ to tenths: $\frac{5}{10}$.
* Convert $\frac{1}{5}$ to tenths: $\frac{2}{10}$.
* Since $2 < 5$, then $\frac{2}{10} < \frac{1}{2}$.
* Answer: <

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