Here are the correct comparison symbols for each problem, followed by the answers to the fill-in-the-blank questions at the bottom.
Step-by-step Logic:
*
Same Denominator (bottom number): Look at the top numbers (numerators). The bigger top number means the bigger fraction.
* Example: $6/7$ vs $2/7$. Since 6 is bigger than 2, $6/7$ is bigger.
*
Same Numerator (top number): Look at the bottom numbers (denominators). The smaller bottom number means the bigger fraction (because the pieces are larger).
* Example: $1/3$ vs $1/10$. Cutting a pizza into 3 pieces makes bigger slices than cutting it into 10 pieces. So, $1/3$ is bigger.
Solutions:
1) $\frac{6}{7} > \frac{2}{7}$ (Same bottom, 6 is bigger than 2)
2) $\frac{1}{3} > \frac{1}{10}$ (Same top, 3 is smaller than 10, so pieces are bigger)
3) $\frac{8}{12} > \frac{1}{12}$ (Same bottom, 8 is bigger than 1)
4) $\frac{1}{4} > \frac{1}{7}$ (Same top, 4 is smaller than 7)
5) $\frac{2}{6} > \frac{2}{8}$ (Same top, 6 is smaller than 8)
6) $\frac{4}{6} > \frac{3}{6}$ (Same bottom, 4 is bigger than 3)
7) $\frac{5}{7} > \frac{2}{7}$ (Same bottom, 5 is bigger than 2)
8) $\frac{3}{6} > \frac{3}{8}$ (Same top, 6 is smaller than 8)
9) $\frac{3}{5} > \frac{2}{5}$ (Same bottom, 3 is bigger than 2)
10) $\frac{1}{8} < \frac{1}{5}$ (Same top, 8 is bigger than 5, so pieces are smaller)
11) $\frac{1}{3} > \frac{1}{4}$ (Same top, 3 is smaller than 4)
12) $\frac{2}{3} > \frac{1}{3}$ (Same bottom, 2 is bigger than 1)
13) $\frac{2}{8} < \frac{2}{5}$ (Same top, 8 is bigger than 5, so pieces are smaller)
14) $\frac{2}{4} < \frac{3}{4}$ (Same bottom, 2 is smaller than 3)
15) $\frac{1}{9} < \frac{1}{4}$ (Same top, 9 is bigger than 4, so pieces are smaller)
16) $\frac{7}{11} < \frac{10}{11}$ (Same bottom, 7 is smaller than 10)
Fill in the blanks:
* When the denominators are the same, the fraction with the
larger numerator is the largest fraction.
* When the numerators are the same, the fraction with the
smaller denominator is the largest fraction.
Final Answer:
1) >
2) >
3) >
4) >
5) >
6) >
7) >
8) >
9) >
10) <
11) >
12) >
13) <
14) <
15) <
16) <
Blank 1: larger numerator
Blank 2: smaller denominator
Parent Tip: Review the logic above to help your child master the concept of fractions for 4th grade worksheet.