Comparing Fractions Calculator
Our comparing fractions calculator can compare any two fractions in an instant.
Comparison3/4 > 5/7the first is larger
First as a decimal0.75
Second as a decimal0.71428571
Difference1/28
Working
| Cross-multiply | 3 × 7 = 21 and 5 × 4 = 20 |
| Common denominator | 28 |
| Decimals | 0.75 and 0.71428571 |
The method
cross-multiply: a/b vs c/d compares ad with cb
The rules in one place
- Adding and subtracting needs a common denominator first. The lowest common denominator keeps the numbers smallest, but any common denominator works.
- Multiplying needs no common denominator at all — multiply across the top and across the bottom.
- Dividing means multiplying by the reciprocal: flip the second fraction and multiply.
- Reducing divides top and bottom by their greatest common divisor. It never changes the value.
Why lowest terms matter
6/8 and 3/4 are the same number, but 3/4 is easier to compare, easier to check and conventional in an answer. Reducing also keeps later arithmetic small: multiplying unreduced fractions makes the numbers grow fast, and cancelling first avoids that.