Use common denominators and benchmark fractions to decide which fraction is larger — and put a list of fractions in order.
Two methods to compare fractions:
Method 1 — Common denominator: rewrite both fractions so they have the same bottom number, then compare the numerators.
Method 2 — Benchmark: decide if each fraction is less than 1/2, equal to 1/2, or greater than 1/2 and reason from there.
1. Which symbol makes this true? 3/4 ___ 2/3
LCD of 4 and 3 is 12. 3/4 = 9/12. 2/3 = 8/12. Since 9 > 8, we have 3/4 > 2/3.
2. Which fraction is the smallest?
Convert to a common denominator of 12: 5/6=10/12, 3/4=9/12, 1/3=4/12, 2/3=8/12. Smallest numerator = 4/12 = 1/3.
3. Compare 5/8 and 1/2. Which is greater?
1/2 = 4/8. Compare 5/8 and 4/8. Since 5 > 4, we have 5/8 > 1/2.
4. Order these fractions from least to greatest: 3/4, 1/6, 1/2. Which list is correct?
LCD = 12. 3/4=9/12, 1/6=2/12, 1/2=6/12. Order the numerators: 2, 6, 9 → fractions: 1/6, 1/2, 3/4.
5. Which fraction is between 1/2 and 1 on the number line?
1/2 = 4/8. 3/4 = 6/8. Since 4/8 < 6/8 < 8/8, yes 3/4 is between 1/2 and 1.
6. Which is greater: 2/5 or 3/8?
LCD of 5 and 8 is 40. 2/5 = 16/40. 3/8 = 15/40. Since 16 > 15, we have 2/5 > 3/8.
7. Which list shows 1/3, 3/4, 1/2 ordered from least to greatest?
LCD = 12. 1/3=4/12, 1/2=6/12, 3/4=9/12. Numerators in order: 4, 6, 9 → 1/3, 1/2, 3/4.