Comparing Fractions with unlike denominators - SmartMathz - Free Printable

To compare fractions with different denominators, we can find a common denominator or convert them to decimals. Here is the step-by-step solution for each problem:

1. $\frac{1}{3}$ vs $\frac{1}{2}$
* Common denominator is 6.
* $\frac{1}{3} = \frac{2}{6}$
* $\frac{1}{2} = \frac{3}{6}$
* Since $2 < 3$, $\frac{1}{3} < \frac{1}{2}$.

2. $\frac{16}{20}$ vs $\frac{8}{50}$
* Simplify $\frac{16}{20}$ by dividing top and bottom by 4: $\frac{4}{5}$.
* Convert $\frac{4}{5}$ to denominator 50: $\frac{4 \times 10}{5 \times 10} = \frac{40}{50}$.
* Compare $\frac{40}{50}$ and $\frac{8}{50}$.
* Since $40 > 8$, $\frac{16}{20} > \frac{8}{50}$.

3. $\frac{1}{5}$ vs $\frac{3}{4}$
* Common denominator is 20.
* $\frac{1}{5} = \frac{4}{20}$
* $\frac{3}{4} = \frac{15}{20}$
* Since $4 < 15$, $\frac{1}{5} < \frac{3}{4}$.

4. $\frac{2}{14}$ vs $\frac{14}{32}$
* Simplify $\frac{2}{14}$ to $\frac{1}{7}$.
* Simplify $\frac{14}{32}$ to $\frac{7}{16}$.
* Cross-multiply: $1 \times 16 = 16$ and $7 \times 7 = 49$.
* Since $16 < 49$, $\frac{2}{14} < \frac{14}{32}$.

5. $\frac{7}{18}$ vs $\frac{4}{8}$
* Simplify $\frac{4}{8}$ to $\frac{1}{2}$.
* Convert $\frac{1}{2}$ to denominator 18: $\frac{9}{18}$.
* Compare $\frac{7}{18}$ and $\frac{9}{18}$.
* Since $7 < 9$, $\frac{7}{18} < \frac{4}{8}$.

6. $\frac{2}{4}$ vs $\frac{4}{5}$
* Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
* $\frac{1}{2}$ is equal to $0.5$. $\frac{4}{5}$ is equal to $0.8$.
* Since $0.5 < 0.8$, $\frac{2}{4} < \frac{4}{5}$.

7. $\frac{7}{10}$ vs $\frac{1}{16}$
* $\frac{7}{10}$ is close to 1 (it's 0.7). $\frac{1}{16}$ is very small (less than 0.1).
* Clearly, $\frac{7}{10} > \frac{1}{16}$.

8. $\frac{2}{4}$ vs $\frac{2}{3}$
* Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
* Compare $\frac{1}{2}$ and $\frac{2}{3}$. Common denominator 6.
* $\frac{1}{2} = \frac{3}{6}$, $\frac{2}{3} = \frac{4}{6}$.
* Since $3 < 4$, $\frac{2}{4} < \frac{2}{3}$.

9. $\frac{1}{5}$ vs $\frac{4}{36}$
* Simplify $\frac{4}{36}$ to $\frac{1}{9}$.
* Compare $\frac{1}{5}$ and $\frac{1}{9}$. When numerators are the same, the fraction with the smaller denominator is larger.
* Since $5 < 9$, $\frac{1}{5} > \frac{1}{9}$, so $\frac{1}{5} > \frac{4}{36}$.

10. $\frac{2}{5}$ vs $\frac{1}{3}$
* Common denominator is 15.
* $\frac{2}{5} = \frac{6}{15}$
* $\frac{1}{3} = \frac{5}{15}$
* Since $6 > 5$, $\frac{2}{5} > \frac{1}{3}$.

11. $\frac{3}{4}$ vs $\frac{5}{10}$
* Simplify $\frac{5}{10}$ to $\frac{1}{2}$.
* $\frac{3}{4}$ is greater than $\frac{1}{2}$ (which is $\frac{2}{4}$).
* So, $\frac{3}{4} > \frac{5}{10}$.

12. $\frac{1}{2}$ vs $\frac{20}{100}$
* Simplify $\frac{20}{100}$ by dividing by 20: $\frac{1}{5}$.
* Compare $\frac{1}{2}$ and $\frac{1}{5}$.
* $\frac{1}{2} = 0.5$ and $\frac{1}{5} = 0.2$.
* So, $\frac{1}{2} > \frac{20}{100}$.

13. $\frac{2}{3}$ vs $\frac{3}{8}$
* Common denominator is 24.
* $\frac{2}{3} = \frac{16}{24}$
* $\frac{3}{8} = \frac{9}{24}$
* Since $16 > 9$, $\frac{2}{3} > \frac{3}{8}$.

14. $\frac{1}{12}$ vs $\frac{2}{6}$
* Simplify $\frac{2}{6}$ to $\frac{1}{3}$.
* Convert $\frac{1}{3}$ to denominator 12: $\frac{4}{12}$.
* Compare $\frac{1}{12}$ and $\frac{4}{12}$.
* Since $1 < 4$, $\frac{1}{12} < \frac{2}{6}$.

15. $\frac{16}{100}$ vs $\frac{6}{10}$
* Convert $\frac{6}{10}$ to denominator 100: $\frac{60}{100}$.
* Compare $\frac{16}{100}$ and $\frac{60}{100}$.
* Since $16 < 60$, $\frac{16}{100} < \frac{6}{10}$.

16. $\frac{1}{2}$ vs $\frac{9}{12}$
* Convert $\frac{1}{2}$ to denominator 12: $\frac{6}{12}$.
* Compare $\frac{6}{12}$ and $\frac{9}{12}$.
* Since $6 < 9$, $\frac{1}{2} < \frac{9}{12}$.

17. $\frac{6}{12}$ vs $\frac{18}{32}$
* Simplify $\frac{6}{12}$ to $\frac{1}{2}$.
* Simplify $\frac{18}{32}$ by dividing by 2: $\frac{9}{16}$.
* Convert $\frac{1}{2}$ to denominator 16: $\frac{8}{16}$.
* Compare $\frac{8}{16}$ and $\frac{9}{16}$.
* Since $8 < 9$, $\frac{6}{12} < \frac{18}{32}$.

18. $\frac{33}{50}$ vs $\frac{20}{90}$
* Simplify $\frac{20}{90}$ to $\frac{2}{9}$.
* $\frac{33}{50}$ is more than half ($\frac{25}{50}$). $\frac{2}{9}$ is less than half ($\frac{4.5}{9}$).
* So, $\frac{33}{50} > \frac{20}{90}$.

19. $\frac{150}{300}$ vs $\frac{6}{12}$
* Simplify $\frac{150}{300}$: divide by 150 gives $\frac{1}{2}$.
* Simplify $\frac{6}{12}$: divide by 6 gives $\frac{1}{2}$.
* They are equal. $\frac{150}{300} = \frac{6}{12}$.

20. $\frac{4}{5}$ vs $\frac{111}{150}$
* Convert $\frac{4}{5}$ to denominator 150. Multiply top and bottom by 30: $\frac{120}{150}$.
* Compare $\frac{120}{150}$ and $\frac{111}{150}$.
* Since $120 > 111$, $\frac{4}{5} > \frac{111}{150}$.

21. $\frac{10}{12}$ vs $\frac{9}{30}$
* Simplify $\frac{10}{12}$ to $\frac{5}{6}$.
* Simplify $\frac{9}{30}$ to $\frac{3}{10}$.
* $\frac{5}{6}$ is close to 1. $\frac{3}{10}$ is small (0.3).
* So, $\frac{10}{12} > \frac{9}{30}$.

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