Add Fractions

Adding fractions is a very handy skill to know. Not only is it an important part of school — from elementary school all the way up to high school — it's also a really practical skill to know. Read on for more information about adding fractions. You'll be spinning with knowledge in just a few minutes.

Steps

Adding Fractions With Like Denominators

  1. Check the denominators (bottom numbers) of each fraction. If they are the same number, then you're dealing with fractions that have the same denominator. If not, skip to the section down below.
  2. Here are two example problems we'll work on in this section. By the last step, you should understand how they were added together.
    • Ex. 1: 1/4 + 2/4
    • Ex. 2: 3/8 + 2/8 + 4/8
  3. Take the two numerators (top numbers) and add them up. The numerator is the number on top of the fraction. However many fractions you have, if they have the same bottom numbers, add up all the top numbers.
    • Ex. 1: 1/4 + 2/4 is our equation. "1" and "2" are the numerators. That means 1 + 2 = 3.
    • Ex. 2: 3/8 + 2/8 + 4/8 is our equation. "3" and "2" and "4" are the numerators. That means 3 + 2 + 4 = 9.
  4. Start putting together your new fraction. Take the sum of the numerators you got in Step 2; that sum will be your new numerator. Take the denominator that was the same for each fraction. Don't do anything to it. This is your new denominator; it will always be the same as the old denominator when you add fractions with the same denominators.
    • Ex. 1: 3 is our new numerator, and 4 is our new denominator. This gives us an answer of 3/4. 1/4 + 2/4 = 3/4.
    • Ex. 2: 9 is our new numerator, and 8 is our new denominator. This gives us an answer of 9/8. 3/8 + 2/8 + 4/8 = 9/8.
  5. Simplify if necessary. Simplify the new fraction to make sure it's written as simply as possible.
    • If the numerator is bigger than the denominator, like it is in Ex. 2, that means we can take out at least one whole number. Divide the top number by the bottom number. When we divide 9 by 8, we get 1 whole number and a remainder of 1. Put the whole number out in front of the fraction and the remainder in the numerator of the new fraction, leaving the denominator the same.
      9/8 = 1 1/8.

Adding Fractions With Unlike Denominators

  1. Check the denominators (bottom numbers) of each fraction. If the denominators are different numbers, then you're dealing with unlike denominators. You're going to have to find a way to make the unlike denominators be the same. This guide will help you do that.
  2. Here are two example problems we'll work on in this section. By the last step, you should understand how they were added together.
    • Ex. 3: 1/3 + 3/5
    • Ex. 4: 2/7 + 2/14
  3. Find a common denominator. Do this by finding a "multiple" of the two denominators. An easy way to find one is to simply multiply the two denominators together. If one of the numbers multiplies into the other numbers, you may only need to multiply one of the fractions.
    • Ex. 3: 3 x 5 = 15. Both of our fractions will have a denominator of 15.
    • Ex. 4: 14 is a multiple of 7. So all we have to do is multiply 7 by 2 to get 14. Both of our fractions will have a denominator of 14.
  4. Multiply both numbers on the first fraction by the bottom number of the second fraction. We're not changing the value of the fraction; we're just changing how the fraction looks. It's still the same fraction.
    • Ex. 3: 1/3 x 5/5 = 5/15.
    • Ex. 4: For this fraction, we only have to multiply the first fraction by 2, because that's what gives us our common denominator.
      • 2/7 x 2/2 = 4/14.
  5. Multiply both numbers on the second fraction by the bottom number of the first fraction. Again, we're not changing the value of the fraction; we're just changing how the fraction looks. It's still the same fraction.
    • Ex. 3: 3/5 x 3/3 = 9/15.
    • Ex. 4: We don't need to multiply the second fraction because both fractions already have their common denominators.
  6. Line both fractions up side by side with their new numbers. We haven't added them yet, but that will come soon! What we've done is multiple each fraction by the number 1. Our goal here was to get the denominators to look exactly the same.
    • Ex. 3: instead of 1/3 + 3/5, we have 5/15 + 9/15
    • Ex. 4: instead of 2/7 + 2/14, we have 4/14 + 2/14
  7. Add together the numerators of the two fractions. The numerator is the top number of the fraction.
    • Ex. 3: 5 + 9 = 14. 14 will be our new numerator.
    • Ex. 4: 4 + 2 = 6. 6 will be our new numerator.
  8. Take the common denominator that you figured out in Step 2 and add it on the bottom of your new numerator. Or, just keep the denominator that's on the changed fractions already — it's the same number.
    • Ex. 3: 15 will be our new denominator.
    • Ex. 4: 14 will be our new denominator.
  9. Put the new numerator on top and the new denominator on bottom.
    • Ex. 3: 14/15 is our answer to 1/3 + 3/5 = ?
    • Ex. 4: 6/14 is our answer to 2/7 + 2/14 = ?
  10. Simplify and reduce. Simplify by dividing both the numerator and the denominator in the fraction by each number's greatest common factor.
    • Ex. 3: 14/15 cannot be simplified.
    • Ex. 4: 6/14 can be reduced to 3/7 by dividing both the top and the bottom numbers by 2, the greatest common factor.

Tips

  • Always make sure the denominators are the same before adding the numerators.
  • Don't add the denominators. Once you've found a common denominator, keep it the same.
  • If a proper or improper fraction is added with a mixed number, it is easier to convert the mixed number first into an improper fraction then use the steps and conditions mentioned above.

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