How to Find the Difference Between Fractions


Fractions represent a part of a total number. For instance, 2/5 represents two parts out of a total of five parts and can also be written as 40 percent. The percentage is found by dividing the numerator, 2, by the denominator, 5. You calculate the difference between multiple fractions by subtracting one fraction from another. To keep the difference in fraction form instead of changing it into a percentage, you must find a common denominator between the two fractions.

  • Multiply the denominators of each fraction. For this example, consider the following the fractions: 8/12 and 20/35. Multiply 35 times 12, which equals 420.

  • Multiply each numerator by the opposite denominator. For instance, multiply 8 times 35 to get a total of 280. Meanwhile, multiply 20 times 12 to get a total of 240.

  • Subtract the two new numerators to get the difference between the two fractions. This is only possible once each fraction has a common denominator. The actual value or percentage of each fraction is exactly the same as before; they are simply represented as larger numbers. Continuing the example, 280 minus 240 equals 40. Your new fraction is 40/420. This represents the difference between the original two fractions.

  • Simplify the new fraction by finding the greatest common factor. This is the largest number that is divisible by both the numerator and denominator. Divide the numerator and denominator by the same positive numbers until they cannot both be divided any further by the same number. For instance, both 40 and 420 are divisible by 20. So 40 divided by 20 equals 2, and 420 divided by 20 equals 21. The new fraction, 2/21, cannot be simplified any further. So the difference between 8/12 and 20/35 is 2/21.


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