To compare fractions, we need to figure out which one is bigger, smaller, or if they are the same size. Here is how we solve each problem step-by-step:
1. $\frac{2}{3}$ vs $\frac{1}{4}$
* Think about slices of a pie. $\frac{2}{3}$ is more than half. $\frac{1}{4}$ is less than half.
* So, $\frac{2}{3}$ is bigger.
* Answer:
>
2. $\frac{3}{4}$ vs $\frac{1}{3}$
* $\frac{3}{4}$ is almost a whole pie. $\frac{1}{3}$ is just a small slice.
* So, $\frac{3}{4}$ is bigger.
* Answer:
>
3. $\frac{3}{6}$ vs $\frac{6}{8}$
* $\frac{3}{6}$ is exactly half ($\frac{1}{2}$).
* $\frac{6}{8}$ simplifies to $\frac{3}{4}$, which is more than half.
* So, $\frac{3}{6}$ is smaller.
* Answer:
<
4. $\frac{1}{2}$ vs $\frac{3}{4}$
* $\frac{1}{2}$ is two quarters ($\frac{2}{4}$).
* $\frac{3}{4}$ is three quarters.
* 3 is bigger than 2, so $\frac{1}{2}$ is smaller.
* Answer:
<
5. $\frac{3}{8}$ vs $\frac{4}{6}$
* $\frac{3}{8}$ is less than half (because 4 would be half).
* $\frac{4}{6}$ is more than half (because 3 would be half).
* So, $\frac{3}{8}$ is smaller.
* Answer:
<
6. $\frac{2}{2}$ vs $\frac{5}{5}$
* $\frac{2}{2}$ means 2 out of 2 parts, which equals 1 whole.
* $\frac{5}{5}$ means 5 out of 5 parts, which also equals 1 whole.
* They are equal.
* Answer:
=
7. $\frac{4}{5}$ vs $\frac{6}{8}$
* Let's make the bottom numbers the same. The common number for 5 and 8 is 40.
* $\frac{4}{5} = \frac{32}{40}$
* $\frac{6}{8} = \frac{30}{40}$
* 32 is bigger than 30, so $\frac{4}{5}$ is bigger.
* Answer:
>
8. $\frac{1}{3}$ vs $\frac{4}{5}$
* $\frac{1}{3}$ is a small piece (less than half).
* $\frac{4}{5}$ is a big piece (almost the whole thing).
* So, $\frac{1}{3}$ is smaller.
* Answer:
<
9. $\frac{2}{4}$ vs $\frac{3}{8}$
* Change $\frac{2}{4}$ so it has an 8 on the bottom. Multiply top and bottom by 2.
* $\frac{2}{4} = \frac{4}{8}$.
* Now compare $\frac{4}{8}$ and $\frac{3}{8}$.
* 4 is bigger than 3, so $\frac{2}{4}$ is bigger.
* Answer:
>
10. $\frac{6}{10}$ vs $\frac{4}{9}$
* $\frac{6}{10}$ is more than half (half would be $\frac{5}{10}$).
* $\frac{4}{9}$ is less than half (half would be $\frac{4.5}{9}$).
* So, $\frac{6}{10}$ is bigger.
* Answer:
>
11. $\frac{2}{8}$ vs $\frac{3}{9}$
* Simplify both fractions.
* $\frac{2}{8}$ becomes $\frac{1}{4}$.
* $\frac{3}{9}$ becomes $\frac{1}{3}$.
* If you share a pizza with 3 people, you get more than if you share it with 4 people. So $\frac{1}{3}$ is bigger.
* Therefore, $\frac{2}{8}$ 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.
* So, $\frac{4}{4}$ is bigger.
* Answer:
>
Final Answer:
1. >
2. >
3. <
4. <
5. <
6. =
7. >
8. <
9. >
10. >
11. <
12. >
Parent Tip: Review the logic above to help your child master the concept of ordering fractions worksheet 4th grade.
