5th Grade Math Help: Subtracting Fractions

Now that you're in 5th grade, you've probably spent a lot of time learning to write and compare fractions, and you may have learned to find equivalent fractions, too. The next step is learning to perform operations, like subtraction, with fractions. Keep reading to learn how!

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Math Help for Subtracting Fractions

Keep in mind that every fraction has a numerator, which is the top number, and a denominator, which is the bottom number. When your two fractions have the same denominator, subtract the numerators, and leave the denominator the same. For example, 7/9 - 5/9 = 2/9, because 7 - 5 = 2.

Different Denominators

If you're subtracting fractions that have different denominators, you need to find equivalent fractions that have the same denominator. For instance, here's how you would solve the problem 3/4 - 2/3:

  1. List a few of the multiples of both denominators. Some multiples of four are eight, 12 and 16. Multiples of three are six, nine, 12 and 15.
  2. Find the lowest number that's on both lists of multiples. This number is called the least common multiple (LCM). In this example, the LCM is 12.
  3. For each fraction, figure out what number you need to multiply the denominator by to get the LCM. For four, that number is three, since 4 x 3 = 12. For three, it's four, because 3 x 4 = 12.
  4. Multiply the numerator and denominator of each fraction by that number, so each fraction has the LCM as its denominator. For instance, 3/4 x 3/3 = 9/12, and 2/3 x 4/4 = 8/12.

Now, you have an equivalent fraction for each of the original fractions. All that's left to do is subtract the numerator of 8/12 from the numerator of 9/12. Since 9/12 - 8/12 = 1/12, the solution is 1/12.

Mixed Numbers

To subtract mixed numbers, the first step is to change them into improper fractions. If these fractions have the same denominator, you can subtract them right away. If not, find equivalent fractions for them that have the same denominator, and then subtract. Here's an example of how to solve 3 1/5 - 1 3/4:

  1. First, change both mixed numbers to improper fractions. The mixed number 3 1/5 equals 16/5, and 1 3/4 = 7/4.
  2. Now, to solve 16/5 - 7/4, you need to find equivalent fractions that have the same denominator. Following the steps described in the last section, the equivalent fractions are 64/20 and 35/20.
  3. Next, subtract the numerators: 64/20 - 35/20 = 29/20.

For some problems, your teacher may ask you to reduce the fraction or convert it back into a mixed fraction. The improper fraction 29/20 can't be reduced, but it's equal to the mixed fraction 1 9/20.

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