Fraction comparison worksheet for students to practice identifying the correct symbol between pairs of fractions.

To solve these problems, we need to compare two fractions and decide which one is bigger, smaller, or if they are equal. We will use the symbols:
* > (greater than)
* < (less than)
* = (equal to)

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

1) $\frac{1}{3}$ vs $\frac{7}{8}$
* $\frac{1}{3}$ is a small part (about 0.33).
* $\frac{7}{8}$ is almost a whole (0.875).
* So, $\frac{1}{3} < \frac{7}{8}$.

2) $\frac{1}{6}$ vs $\frac{3}{4}$
* Find a common denominator (12).
* $\frac{1}{6} = \frac{2}{12}$
* $\frac{3}{4} = \frac{9}{12}$
* 2 is less than 9, so $\frac{1}{6} < \frac{3}{4}$.

3) $\frac{3}{8}$ vs $\frac{2}{4}$
* Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
* Compare $\frac{3}{8}$ and $\frac{1}{2}$ ($\frac{4}{8}$).
* 3 is less than 4, so $\frac{3}{8} < \frac{2}{4}$.

4) $\frac{4}{5}$ vs $\frac{4}{8}$
* The numerators are the same (4). When numerators are the same, the fraction with the *smaller* denominator is bigger because the pieces are larger.
* 5 is smaller than 8, so fifths are bigger than eighths.
* $\frac{4}{5} > \frac{4}{8}$.

5) $\frac{1}{4}$ vs $\frac{1}{2}$
* Common denominator is 4.
* $\frac{1}{4}$ stays $\frac{1}{4}$.
* $\frac{1}{2} = \frac{2}{4}$.
* 1 is less than 2, so $\frac{1}{4} < \frac{1}{2}$.

6) $\frac{1}{6}$ vs $\frac{4}{5}$
* $\frac{1}{6}$ is very small.
* $\frac{4}{5}$ is very large (close to 1).
* $\frac{1}{6} < \frac{4}{5}$.

7) $\frac{1}{2}$ vs $\frac{2}{6}$
* Simplify $\frac{2}{6}$ to $\frac{1}{3}$.
* Compare $\frac{1}{2}$ and $\frac{1}{3}$. Half of a pizza is bigger than a third of a pizza.
* $\frac{1}{2} > \frac{2}{6}$.

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

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

10) $\frac{2}{3}$ vs $\frac{2}{4}$
* Numerators are the same (2).
* Denominator 3 is smaller than 4, so thirds are bigger.
* $\frac{2}{3} > \frac{2}{4}$.

11) $\frac{1}{8}$ vs $\frac{3}{4}$
* Convert $\frac{3}{4}$ to eighths: $\frac{3 \times 2}{4 \times 2} = \frac{6}{8}$.
* Compare $\frac{1}{8}$ and $\frac{6}{8}$.
* $\frac{1}{8} < \frac{3}{4}$.

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 than a third.
* $\frac{2}{4} > \frac{1}{3}$.

13) $\frac{1}{6}$ vs $\frac{3}{5}$
* Cross multiply: $1 \times 5 = 5$ and $6 \times 3 = 18$.
* 5 is less than 18.
* $\frac{1}{6} < \frac{3}{5}$.

14) $\frac{5}{8}$ vs $\frac{4}{8}$
* Denominators are the same. Look at the top numbers.
* 5 is greater than 4.
* $\frac{5}{8} > \frac{4}{8}$.

15) $\frac{1}{3}$ vs $\frac{2}{3}$
* Denominators are the same.
* 1 is less than 2.
* $\frac{1}{3} < \frac{2}{3}$.

16) $\frac{3}{5}$ vs $\frac{1}{2}$
* Common denominator is 10.
* $\frac{3}{5} = \frac{6}{10}$.
* $\frac{1}{2} = \frac{5}{10}$.
* 6 is greater than 5.
* $\frac{3}{5} > \frac{1}{2}$.

17) $\frac{2}{5}$ vs $\frac{2}{3}$
* Numerators are the same (2).
* Smaller denominator (3) means bigger pieces.
* $\frac{2}{5} < \frac{2}{3}$.

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

19) $\frac{1}{6}$ vs $\frac{2}{5}$
* Cross multiply: $1 \times 5 = 5$ and $6 \times 2 = 12$.
* 5 is less than 12.
* $\frac{1}{6} < \frac{2}{5}$.

20) $\frac{1}{8}$ vs $\frac{1}{2}$
* Numerators are the same (1).
* Denominator 2 is smaller than 8, so halves are much bigger.
* $\frac{1}{8} < \frac{1}{2}$.

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