How to Subtract Common Fractions
- 1). Check if the denominators of the fractions in your subtraction problem are the same. If they are not, you must take steps to find the least common denominator. For example, in the problem 2/3 - 3/9, you cannot perform subtraction because the denominators are different.
- 2). Find the greatest common factor of the denominators. This is the first step in finding the least common denominator. In the example, 2/3 - 3/9, the largest whole number that divides into denominators 3 and 9 is the number 3.
- 3). Multiply the denominators in your problem (the second step in determining the east common denominator). In the example 2/3 - 3/9, the denominators are 3 and 9. So 3 x 9 = 27.
- 4). Divide the product of the denominators by the greatest common factor, which is 3 in this example. So 27/3 = 9. The number 9 is the least common denominator for the fractions 2/3 and 3/9 and can be used to convert the fractions into a form that makes subtraction possible. (Both denominators are the same.)
- 5). Divide the denominators by the least common denominator and then multiply both the numerator and denominator of the original fraction by the answer. In the problem 2/3 - 3/9, convert 2/3 by dividing 9 (the least common denominator) by denominator 3: 9/3 = 3. The fraction 2/3 becomes 6/9 (2 x 3 = 6 and 3 x 3 = 9). Repeat this process until all denominators in the subtraction problem are equal.
- 6). Subtract the numerators and leave the denominator the same. For example, 6/9 - 3/9 = 3/9.
- 7). Simply the fraction, if possible, by finding the greatest common factor. The greatest common factor is the largest number that you can divide into both the numerator and denominator. For example, 4/12 is divisible by 2 and 4; however, the number 4 is the greatest common factor, so this is the number to use. So 4 divided by 4 equals 1 and 12 divided by 4 equals 3; 4/12 simplifies to 1/3. In the example, 3/9 also simplifies to 1/3.
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