Fractions and Decimals • Topic 6 of 7

Comparing Fractions

To compare two fractions, give them a common denominator and compare numerators, or cross-multiply: for a/b and c/d (positive denominators), a/b > c/d exactly when a·d > b·c. A quick benchmark is to compare each fraction to 1/2. Converting to decimals also works and is fast on the SAT calculator. When ordering several fractions, the least common denominator makes the comparison clean. Remember that with the same numerator, the fraction with the smaller denominator is larger (1/3 > 1/4), because the whole is split into fewer, bigger pieces.

✅ Solved examples

1. Which is larger, 3/5 or 5/8?
Cross-multiply: 3·8 = 24 and 5·5 = 25. Since 25 > 24, 5/8 is larger.
2. Which is larger, 2/3 or 3/4?
Cross-multiply: 2·4 = 8 and 3·3 = 9. Since 9 > 8, 3/4 is larger.
3. Order 1/2, 2/5, 3/4 from least to greatest.
As decimals: 0.5, 0.4, 0.75. Least to greatest: 2/5, 1/2, 3/4.
4. Which is larger, 1/3 or 1/4?
Same numerator; the smaller denominator gives the larger fraction, so 1/3 > 1/4.

✏️ Practice — try these, take hints as needed

1. Which is larger, 4/7 or 5/9?
Cross-multiply 4·9 and 7·5.
36 versus 35.
The larger product is over the larger fraction.
4/7 (36 > 35).
2. Which is larger, 5/6 or 7/8?
Cross-multiply 5·8 and 6·7.
40 versus 42.
Compare.
7/8 (42 > 40).
3. Order 1/4, 2/3, 1/2 from least to greatest.
Convert each to a decimal.
0.25, 0.667, 0.5.
Sort the decimals.
1/4, 1/2, 2/3.
4. Which is smaller, 3/8 or 2/5?
Cross-multiply 3·5 and 8·2.
15 versus 16.
Smaller product is the smaller fraction.
3/8 (15 < 16).
5. Which is larger, 2/7 or 1/4?
Cross-multiply 2·4 and 7·1.
8 versus 7.
Compare.
2/7 (8 > 7).

📝 Topic test — 8 questions

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