Fraction comparison worksheet with 20 problems requiring students to write the correct comparison symbol between pairs of fractions.

Explanation:
We need to compare two fractions in each problem and write the correct symbol: <, >, or =.

To compare fractions, we can:
- Convert them to decimals (easy with a calculator, but let’s avoid that for accuracy),
- Or find a common denominator and compare numerators,
- Or use cross-multiplication:
For fractions $ \frac{a}{b} $ and $ \frac{c}{d} $, compare $ a \cdot d $ vs $ c \cdot b $.
- If $ a \cdot d > c \cdot b $, then $ \frac{a}{b} > \frac{c}{d} $
- If $ a \cdot d < c \cdot b $, then $ \frac{a}{b} < \frac{c}{d} $
- If equal, then the fractions are equal.

Let’s go one by one:

1) $ \frac{1}{2} $ vs $ \frac{2}{3} $
Cross-multiply: $ 1 \cdot 3 = 3 $, $ 2 \cdot 2 = 4 $ → 3 < 4 → so $ \frac{1}{2} < \frac{2}{3} $

2) $ \frac{6}{8} $ vs $ \frac{2}{3} $
Simplify $ \frac{6}{8} = \frac{3}{4} $. Compare $ \frac{3}{4} $ and $ \frac{2}{3} $:
$ 3 \cdot 3 = 9 $, $ 2 \cdot 4 = 8 $ → 9 > 8 → $ \frac{3}{4} > \frac{2}{3} $ → So $ \frac{6}{8} > \frac{2}{3} $

3) $ \frac{1}{2} $ vs $ \frac{1}{2} $ → obviously equal → =

4) $ \frac{1}{4} $ vs $ \frac{4}{5} $
$ 1 \cdot 5 = 5 $, $ 4 \cdot 4 = 16 $ → 5 < 16 → $ \frac{1}{4} < \frac{4}{5} $

5) $ \frac{3}{5} $ vs $ \frac{1}{6} $
$ 3 \cdot 6 = 18 $, $ 1 \cdot 5 = 5 $ → 18 > 5 → $ \frac{3}{5} > \frac{1}{6} $

6) $ \frac{1}{3} $ vs $ \frac{6}{8} = \frac{3}{4} $
$ 1 \cdot 4 = 4 $, $ 3 \cdot 3 = 9 $ → 4 < 9 → $ \frac{1}{3} < \frac{3}{4} $ → so <

7) $ \frac{4}{8} = \frac{1}{2} $ vs $ \frac{1}{4} $
$ \frac{1}{2} > \frac{1}{4} $ → >

8) $ \frac{3}{6} = \frac{1}{2} $ vs $ \frac{3}{8} $
$ 1 \cdot 8 = 8 $, $ 3 \cdot 2 = 6 $ → Wait! Better: compare $ \frac{1}{2} $ and $ \frac{3}{8} $:
$ 1 \cdot 8 = 8 $, $ 3 \cdot 2 = 6 $ → 8 > 6 → $ \frac{1}{2} > \frac{3}{8} $ → >

9) $ \frac{5}{6} $ vs $ \frac{7}{8} $
$ 5 \cdot 8 = 40 $, $ 7 \cdot 6 = 42 $ → 40 < 42 → $ \frac{5}{6} < \frac{7}{8} $

10) $ \frac{3}{5} $ vs $ \frac{2}{8} = \frac{1}{4} $
$ 3 \cdot 4 = 12 $, $ 1 \cdot 5 = 5 $ → 12 > 5 → $ \frac{3}{5} > \frac{1}{4} $ → >

11) $ \frac{2}{4} = \frac{1}{2} $ vs $ \frac{2}{6} = \frac{1}{3} $
$ \frac{1}{2} > \frac{1}{3} $ → >

12) $ \frac{7}{8} $ vs $ \frac{1}{2} $
$ 7 \cdot 2 = 14 $, $ 1 \cdot 8 = 8 $ → 14 > 8 → >

13) $ \frac{1}{2} $ vs $ \frac{1}{4} $ → >

14) $ \frac{1}{4} $ vs $ \frac{4}{6} = \frac{2}{3} $
$ 1 \cdot 3 = 3 $, $ 2 \cdot 4 = 8 $ → 3 < 8 → <

15) $ \frac{3}{5} $ vs $ \frac{4}{6} = \frac{2}{3} $
$ 3 \cdot 3 = 9 $, $ 2 \cdot 5 = 10 $ → 9 < 10 → <

16) $ \frac{1}{3} $ vs $ \frac{3}{5} $
$ 1 \cdot 5 = 5 $, $ 3 \cdot 3 = 9 $ → 5 < 9 → <

17) $ \frac{4}{8} = \frac{1}{2} $ vs $ \frac{1}{3} $
$ 1 \cdot 3 = 3 $, $ 1 \cdot 2 = 2 $ → 3 > 2 → >

18) $ \frac{1}{2} $ vs $ \frac{1}{4} $ → >

19) $ \frac{1}{4} $ vs $ \frac{1}{2} $ → <

20) $ \frac{2}{3} $ vs $ \frac{2}{3} $ → =

Now let’s list all answers clearly:

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

Double-check a few tricky ones:

- #15: $ \frac{3}{5} = 0.6 $, $ \frac{4}{6} ≈ 0.666 $ → yes, < ✔
- #16: $ \frac{1}{3} ≈ 0.333 $, $ \frac{3}{5} = 0.6 $ → < ✔
- #17: $ \frac{4}{8} = 0.5 $, $ \frac{1}{3} ≈ 0.333 $ → > ✔
- #19: $ \frac{1}{4} = 0.25 $, $ \frac{1}{2} = 0.5 $ → < ✔

All correct.

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