Comparing Fractions With Different Denominators Worksheet for 3rd ... - Free Printable

To compare fractions, we need to figure out which one is bigger, smaller, or if they are equal. Here is the step-by-step logic for each problem:

1. $\frac{2}{3}$ vs $\frac{1}{4}$
* Think about pizza slices. $\frac{2}{3}$ is more than half a pizza. $\frac{1}{4}$ is less than half.
* Therefore, $\frac{2}{3}$ is greater.
* Answer: $>$

2. $\frac{3}{4}$ vs $\frac{1}{3}$
* $\frac{3}{4}$ is almost a whole (it's 0.75). $\frac{1}{3}$ is small (about 0.33).
* Therefore, $\frac{3}{4}$ is greater.
* Answer: $>$

3. $\frac{3}{6}$ vs $\frac{6}{8}$
* Simplify $\frac{3}{6}$: It equals $\frac{1}{2}$.
* Look at $\frac{6}{8}$: Half of 8 is 4. Since 6 is bigger than 4, $\frac{6}{8}$ is bigger than half.
* Therefore, $\frac{3}{6}$ is less than $\frac{6}{8}$.
* Answer: $<$

4. $\frac{1}{2}$ vs $\frac{3}{4}$
* Imagine a dollar. $\frac{1}{2}$ is 50 cents. $\frac{3}{4}$ is 75 cents.
* 50 is less than 75.
* Answer: $<$

5. $\frac{3}{8}$ vs $\frac{4}{6}$
* $\frac{3}{8}$ is less than half (because half of 8 is 4, and 3 is less than 4).
* $\frac{4}{6}$ is greater than half (because half of 6 is 3, and 4 is more than 3).
* Therefore, $\frac{3}{8}$ is less.
* Answer: $<$

6. $\frac{2}{2}$ vs $\frac{5}{5}$
* Any fraction where the top number and bottom number are the same equals 1 whole.
* $1 = 1$.
* Answer: $=$

7. $\frac{4}{5}$ vs $\frac{6}{8}$
* Let's find a common denominator or use cross-multiplication.
* Cross-multiply: $4 \times 8 = 32$ and $5 \times 6 = 30$.
* Since 32 is bigger than 30, the first fraction ($\frac{4}{5}$) is bigger.
* Answer: $>$

8. $\frac{1}{3}$ vs $\frac{4}{5}$
* $\frac{1}{3}$ is a small piece. $\frac{4}{5}$ is almost a whole thing.
* Clearly, $\frac{1}{3}$ is smaller.
* Answer: $<$

9. $\frac{2}{4}$ vs $\frac{3}{8}$
* Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
* Convert $\frac{1}{2}$ to eighths so we can compare: $\frac{1}{2} = \frac{4}{8}$.
* Now compare $\frac{4}{8}$ and $\frac{3}{8}$. 4 is bigger than 3.
* Answer: $>$

10. $\frac{6}{10}$ vs $\frac{4}{9}$
* $\frac{6}{10}$ is more than half (half of 10 is 5).
* $\frac{4}{9}$ is less than half (half of 9 is 4.5).
* Therefore, $\frac{6}{10}$ is greater.
* Answer: $>$

11. $\frac{2}{8}$ vs $\frac{3}{9}$
* Simplify both fractions.
* $\frac{2}{8}$ simplifies to $\frac{1}{4}$.
* $\frac{3}{9}$ simplifies to $\frac{1}{3}$.
* Compare $\frac{1}{4}$ and $\frac{1}{3}$. If you share a candy bar among 4 people, you get less than if you share it among 3 people. So $\frac{1}{4}$ is smaller.
* Answer: $<$

12. $\frac{4}{4}$ vs $\frac{3}{5}$
* $\frac{4}{4}$ equals 1 whole.
* $\frac{3}{5}$ is less than 1 whole.
* Answer: $>$

13. $\frac{5}{10}$ vs $\frac{6}{6}$
* $\frac{5}{10}$ simplifies to $\frac{1}{2}$.
* $\frac{6}{6}$ equals 1 whole.
* Half is less than one whole.
* Answer: $<$

14. $\frac{1}{6}$ vs $\frac{2}{12}$
* If you multiply the top and bottom of $\frac{1}{6}$ by 2, you get $\frac{2}{12}$.
* They are exactly the same amount.
* Answer: $=$

15. $\frac{3}{12}$ vs $\frac{1}{4}$
* Simplify $\frac{3}{12}$. Both numbers can be divided by 3.
* $3 \div 3 = 1$ and $12 \div 3 = 4$. So, $\frac{3}{12} = \frac{1}{4}$.
* They are equal.
* Answer: $=$

16. $\frac{3}{4}$ vs $\frac{1}{4}$
* The bottoms are the same (4). Just look at the tops.
* 3 is bigger than 1.
* Answer: $>$

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