Fraction Comparison Calculator
Compares two fractions by rewriting them over a common denominator. A denominator of 0 is not allowed.
Fraction Comparison Calculation Method
With a common denominator
Comparison
3/4 > 2/3
9/12 > 8/12
0.75 > 0.6667
About This Calculator
Fractions with different denominators cannot be compared at a glance. Rewrite both over the least common multiple of the denominators and compare the numerators, or cross-multiply and compare a·d with c·b, which avoids the division entirely.
So 3/4 = 0.75 against 2/3 ≈ 0.6667 already shows which is larger, and the common denominator confirms it: 9/12 versus 8/12. A denominator of zero, or a negative denominator, breaks the comparison.
The same idea works for more than two fractions: sort them by cross-multiplying pairwise, or convert each to a decimal and order those. Comparing against a percentage is also a fraction comparison in disguise — 7/8 = 0.875, so it is above 80 % (4/5 = 0.8) and below 90 % (9/10 = 0.9).
Key Formula:
a/b ⋚ c/d ⇔ a·d ⋚ c·b (b, d > 0)Frequently Asked Questions
Is there a way to compare without finding a common denominator?
Yes, cross-multiply: compute a·d and c·b and the larger product belongs to the larger fraction. For 3/4 and 2/3 that is 3 × 3 = 9 versus 2 × 4 = 8, so 3/4 is larger.
Where is fraction comparison useful in practice?
When comparing discounts (1/3 versus 3/10), splitting recipes, comparing part sizes or comparing probabilities. Ordering fractions without dividing avoids rounding errors and is faster to check by hand.
How do I compare a fraction with a percentage?
Turn the percentage into a fraction with denominator 100 and compare as usual, or convert the fraction to a decimal. 3/8 = 0.375, so it is smaller than 40 %; 2/5 = 0.4 is exactly 40 %.
How do I sort three fractions?
Bring all three to the least common multiple of the denominators and order the numerators. For 1/2, 2/3 and 3/5 the LCM is 30, giving 15/30, 20/30 and 18/30 — so the order is 1/2 < 3/5 < 2/3.