Subtract Fractions

Subtracting fractions with like denominators is easy, but when the fractions have unlike denominators, it can take a few steps to make them have the same denominator so that you can subtract them. These few steps can take a little while, but once you get the hang of it, you'll be able to subtract fractions in no time at all. If you want to know how to do it, just follow these steps.

Steps

  1. Find the denominators of the fractions. If you want to subtract fractions, then the first thing you have to do is to make sure that they have like denominators. The numerator is the number on the top of the fraction and the denominator is the number on the bottom. In the example, 3/4 - 1/3, the two denominators of the fractions are 4 and 3. Circle them.
    • If the denominators of the fractions are the same, then you can just subtract the numerators and keep the denominator the same. For example, 4/5 - 3/5 = 1/5. If the fraction is in simplified form, as this one is, then you're done.
  2. Find the least common multiple (LCM) of the denominators. The LCM of two numbers is the smallest number that is evenly divisible by both numbers. You'll need to find the LCM of 4 and 3, which will give you the lowest common denominator (LCD) of the fraction. Here's the best method to use for small numbers:
    • List the first few multiples of 4: 4 x 1 = 4, 4 x 2 = 8, 4 x 3 = 12, 4 x 4 =16
    • List the first few multiples of 3: 3 x 1 =3, 3 x 2 = 6, 3 x 3 = 9, 3 x 4 = 12
    • Stop when you have found a common multiple. You can see that 12 is a multiple of both 4 and 3. Since it's the smallest, you can stop there.
      • Note that you can do this for all numbers, including whole numbers and mixed numbers. For whole numbers, think of the denominator as 1. (Thus, 2 = 2/1.) For mixed numbers, rewrite the mixed number as an improper fraction. (Thus, 2 1/2 = 5/2.)
  3. Make the numerators of the fractions match their new denominators. Now that you know that the LCM of 4 and 3 is 12, you can think of 12 as the new denominator of the fractions. But to make the fractions equivalent, you'll have to multiply their numerators by a number that would give them the same value with their new denominators. Here's how you do it:
    • With the fraction 3/4, you know the new denominator is 12, so you'll have to find the number that 4 multiplies with to get 12. 4 x 3 = 12, so you'll essentially be multiplying 3/4 x 3/3 for the numerator and denominator to retain the original value of the fraction. You know that 4 x 3 is 12, and that's the denominator, and 3 x 3 is 9, so the new numerator of the fraction is 9. 3/4 can be rewritten as 9/12.
    • With the fraction 1/3, you know the new denominator is 12, so you'll have to find the number that 3 multiplies with to get 12. 3 x 4 = 12, so you'll essentially be multiplying 1/3 x 4/4 for the numerator and denominator to retain the original value of the fraction. You know that 3 x 4 is 12, and that's the denominator, and 1 x 4 is 4, so the new numerator of the fraction is 4. 1/3 can be rewritten as 4/12.
  4. Write the new numerators over the lowest common denominator. Now that you know that the lowest common multiple of 4 and 3 is 12, you can say that the lowest common denominator of the fractions 1/3 and 3/4 is 12. Now that you know the new numerators, you can just write them over the same denominator as one fraction with subtracted numerators. Make sure to write the new numerators in the appropriate order, since changing the order in a subtraction problem will give you the wrong answer. Here's what you can write:
    • 3/4 - 1/3 = 9/12 - 4/12
    • 9/12 - 4/12 = (9-4)/12
  5. Subtract the numerators. Once you have written the new numerators over the LCD, you are ready to subtract. Simply subtract the numerators in the appropriate order; do not do anything to the denominator.
    • 9-4 = 5, so 9/12 - 4/12 = 5/12
  6. Simplify your answer. Once you have your answer, check to see if you can simplify it. If the numerator and denominator can be divided by the same number, divide them by that number. Remember that fractions are proportions, so whatever you do to the numerator, you must also do to the denominator. Do not divide one without dividing the other by the same number. 5/12 remains as it is because it cannot be simplified further.
    • For example, the fraction 6/8 can be simplified because both 6 and 8 are divisible by 2. Just divide 6 and 8 by 2 for a new simplified answer: 6/2 = 3, 8/2 = 4, so 6/8 = 3/4.



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