Answer key for comparing fractions worksheet.

To solve these problems, we need to compare two fractions in each box and decide if the first fraction is greater than ($>$), less than ($<$), or equal to ($=$) the second fraction.

Here is the step-by-step logic for comparing them:
1. Same Denominator (bottom number): If the bottom numbers are the same, just look at the top numbers. The bigger top number means the bigger fraction.
* *Example:* $\frac{5}{8}$ vs $\frac{3}{8}$. Since $5 > 3$, then $\frac{5}{8} > \frac{3}{8}$.
2. Same Numerator (top number): If the top numbers are the same, look at the bottom numbers. The *smaller* bottom number means the pieces are bigger, so the fraction is larger.
* *Example:* $\frac{1}{4}$ vs $\frac{1}{6}$. Cutting a pizza into 4 pieces makes bigger slices than cutting it into 6. So, $\frac{1}{4} > \frac{1}{6}$.
3. Different Numbers: If both numbers are different, you can think about how close they are to 1 (a whole) or use cross-multiplication.
* *Cross-multiplication trick:* Multiply the top of the first by the bottom of the second, and vice versa. Compare those results.

Let's go through each problem on the sheet:

Column 1:

1. $\frac{1}{8}$ [ ] $\frac{1}{10}$
* Same top number (1). Bottom number 8 is smaller than 10, so the pieces are bigger.
* Answer: $>$

2. $\frac{10}{3}$ [ ] $\frac{9}{3}$
* Same bottom number (3). Top number 10 is bigger than 9.
* Answer: $>$

3. $\frac{3}{7}$ [ ] $\frac{4}{7}$
* Same bottom number (7). Top number 3 is smaller than 4.
* Answer: $<$

4. $\frac{8}{5}$ [ ] $\frac{3}{5}$
* Same bottom number (5). Top number 8 is bigger than 3.
* Answer: $>$

5. $\frac{10}{6}$ [ ] $\frac{8}{6}$
* Same bottom number (6). Top number 10 is bigger than 8.
* Answer: $>$

6. $\frac{6}{4}$ [ ] $\frac{8}{4}$
* Same bottom number (4). Top number 6 is smaller than 8.
* Answer: $<$

7. $\frac{10}{4}$ [ ] $\frac{1}{4}$
* Same bottom number (4). Top number 10 is bigger than 1.
* Answer: $>$

8. $\frac{1}{8}$ [ ] $\frac{1}{8}$
* Both numbers are exactly the same.
* Answer: $=$

9. $\frac{10}{5}$ [ ] $\frac{10}{5}$
* Both numbers are exactly the same.
* Answer: $=$

10. $\frac{3}{6}$ [ ] $\frac{8}{6}$
* Same bottom number (6). Top number 3 is smaller than 8.
* Answer: $<$

Column 2:

11. $\frac{8}{7}$ [ ] $\frac{3}{7}$
* Same bottom number (7). Top number 8 is bigger than 3.
* Answer: $>$

12. $\frac{8}{8}$ [ ] $\frac{1}{8}$
* Same bottom number (8). Top number 8 is bigger than 1. (Note: $\frac{8}{8}$ equals 1 whole).
* Answer: $>$

13. $\frac{7}{7}$ [ ] $\frac{1}{7}$
* Same bottom number (7). Top number 7 is bigger than 1.
* Answer: $>$

14. $\frac{2}{4}$ [ ] $\frac{3}{4}$
* Same bottom number (4). Top number 2 is smaller than 3.
* Answer: $<$

15. $\frac{1}{7}$ [ ] $\frac{5}{7}$
* Same bottom number (7). Top number 1 is smaller than 5.
* Answer: $<$

16. $\frac{1}{5}$ [ ] $\frac{1}{5}$
* Both numbers are exactly the same.
* Answer: $=$

17. $\frac{1}{4}$ [ ] $\frac{1}{6}$
* Same top number (1). Bottom number 4 is smaller than 6, so the piece is bigger.
* Answer: $>$

18. $\frac{7}{7}$ [ ] $\frac{7}{7}$
* Both numbers are exactly the same.
* Answer: $=$

19. $\frac{8}{7}$ [ ] $\frac{1}{7}$
* Same bottom number (7). Top number 8 is bigger than 1.
* Answer: $>$

20. $\frac{5}{7}$ [ ] $\frac{1}{7}$
* Same bottom number (7). Top number 5 is bigger than 1.
* Answer: $>$

Final Answer:
Column 1:
1. $>$
2. $>$
3. $<$
4. $>$
5. $>$
6. $<$
7. $>$
8. $=$
9. $=$
10. $<$

Column 2:
11. $>$
12. $>$
13. $>$
14. $<$
15. $<$
16. $=$
17. $>$
18. $=$
19. $>$
20. $>$