How to compare fractions
To compare two fractions, bring them to a common denominator and compare the numerators. The fraction with the larger numerator is the greater one.
Steps for comparing fractions
- If either fraction is a mixed number, convert it to an improper fraction (multiply the whole part by the denominator and add the numerator).
- Reduce each fraction by dividing numerator and denominator by their GCD.
- Find the LCM of the denominators — this is the common denominator.
- Scale each fraction to the common denominator by multiplying numerator and denominator by the appropriate factor.
- Compare the numerators: the fraction with the larger numerator is greater.
Example 1. Compare 1/2 and 3/4
- Find LCM(2, 4) = 4
- Scale to common denominator: 12 = 24
- Compare numerators: 2 < 3
12
<
34
Example 2. Compare 2/3 and 3/5
- Find LCM(3, 5) = 15
- Scale to common denominator: 23 = 1015 35 = 915
- Compare numerators: 10 > 9
23
>
35