Improper Fractions Worksheets | Maths Resources - Free Printable

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

1) $\frac{1}{3}$ vs $\frac{7}{8}$
* Think about size: $\frac{1}{3}$ is a small piece (less than half). $\frac{7}{8}$ is almost a whole pizza.
* $\frac{7}{8}$ is much bigger.
* Answer: $<$

2) $\frac{1}{6}$ vs $\frac{3}{4}$
* $\frac{1}{6}$ is a very small slice. $\frac{3}{4}$ is three big slices (most of the pie).
* Answer: $<$

3) $\frac{3}{8}$ vs $\frac{2}{4}$
* Let's make them easy to compare. $\frac{2}{4}$ is the same as $\frac{1}{2}$.
* $\frac{1}{2}$ is the same as $\frac{4}{8}$.
* Is $\frac{3}{8}$ bigger or smaller than $\frac{4}{8}$? It is smaller.
* Answer: $<$

4) $\frac{4}{5}$ vs $\frac{4}{8}$
* The top numbers (numerators) are the same (4).
* When the top numbers are the same, look at the bottom. A smaller bottom number means bigger pieces.
* 5ths are bigger than 8ths. So $\frac{4}{5}$ is bigger.
* Answer: $>$

5) $\frac{1}{4}$ vs $\frac{1}{2}$
* Imagine cutting a cake into 4 pieces vs 2 pieces. The 2 pieces are huge.
* $\frac{1}{2}$ is bigger.
* Answer: $<$

6) $\frac{1}{6}$ vs $\frac{4}{5}$
* $\frac{1}{6}$ is tiny. $\frac{4}{5}$ is almost the whole thing.
* Answer: $<$

7) $\frac{1}{2}$ vs $\frac{2}{6}$
* Simplify $\frac{2}{6}$. If you divide top and bottom by 2, it becomes $\frac{1}{3}$.
* Compare $\frac{1}{2}$ and $\frac{1}{3}$. Half is bigger than a third.
* Answer: $>$

8) $\frac{3}{4}$ vs $\frac{2}{6}$
* Simplify $\frac{2}{6}$ to $\frac{1}{3}$.
* $\frac{3}{4}$ is almost 1. $\frac{1}{3}$ is small.
* Answer: $>$

9) $\frac{1}{3}$ vs $\frac{1}{3}$
* They are exactly the same.
* Answer: $=$

10) $\frac{2}{3}$ vs $\frac{2}{4}$
* Top numbers are the same (2).
* Bottom number 3 is smaller than 4, so 3rds are bigger pieces than 4ths.
* Answer: $>$

11) $\frac{1}{8}$ vs $\frac{3}{4}$
* Change $\frac{3}{4}$ to eighths so they match. Multiply top and bottom by 2: $\frac{3 \times 2}{4 \times 2} = \frac{6}{8}$.
* Compare $\frac{1}{8}$ and $\frac{6}{8}$. 1 is less than 6.
* Answer: $<$

12) $\frac{2}{4}$ vs $\frac{1}{3}$
* Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
* Compare $\frac{1}{2}$ and $\frac{1}{3}$. Half is bigger.
* Answer: $>$

13) $\frac{1}{6}$ vs $\frac{3}{5}$
* $\frac{1}{6}$ is very small. $\frac{3}{5}$ is more than half.
* Answer: $<$

14) $\frac{5}{8}$ vs $\frac{4}{8}$
* Bottom numbers are the same (8). Just look at the top.
* 5 is bigger than 4.
* Answer: $>$

15) $\frac{1}{3}$ vs $\frac{2}{3}$
* Bottom numbers are the same. Look at the top.
* 1 is less than 2.
* Answer: $<$

16) $\frac{3}{5}$ vs $\frac{1}{2}$
* To compare with halves, think: what is half of 5? It's 2.5.
* $\frac{2.5}{5}$ would be exactly half. Since we have $\frac{3}{5}$, and 3 is bigger than 2.5, this fraction is bigger than half.
* Answer: $>$

17) $\frac{2}{5}$ vs $\frac{2}{3}$
* Top numbers are the same (2).
* Smaller bottom number (3) means bigger pieces. So $\frac{2}{3}$ is bigger.
* Therefore, $\frac{2}{5}$ is smaller.
* Answer: $<$

18) $\frac{1}{2}$ vs $\frac{5}{6}$
* Change $\frac{1}{2}$ to sixths. $\frac{1 \times 3}{2 \times 3} = \frac{3}{6}$.
* Compare $\frac{3}{6}$ and $\frac{5}{6}$. 3 is less than 5.
* Answer: $<$

19) $\frac{1}{6}$ vs $\frac{2}{5}$
* Find a common bottom number. $6 \times 5 = 30$.
* $\frac{1}{6} = \frac{5}{30}$.
* $\frac{2}{5} = \frac{12}{30}$.
* 5 is less than 12.
* Answer: $<$

20) $\frac{1}{8}$ vs $\frac{1}{2}$
* Change $\frac{1}{2}$ to eighths. $\frac{1 \times 4}{2 \times 4} = \frac{4}{8}$.
* Compare $\frac{1}{8}$ and $\frac{4}{8}$. 1 is less than 4.
* Answer: $<$

Final Answer:
1) <
2) <
3) <
4) >
5) <
6) <
7) >
8) >
9) =
10) >
11) <
12) >
13) <
14) >
15) <
16) >
17) <
18) <
19) <
20) <