Add Fractions With Unlike Denominators

Ever struggle with those confusing math problems? A very difficult area for many people is fractions, especially when you begin adding. This can become even more complex when the fractions have different denominators, or bottom numbers. Still, adding fractions with unlike denominators is relatively easy, so don't worry.

Steps

  1. Write down the beginning fractions. Write them down side by side so that they're close to one another and easy to see. We'll give you examples below for each step that you read.
    • Ex. 1: 1/2 + 1/4
    • Ex. 2: 1/3 + 3/4
    • Ex. 3: 6/5 + 4/3
  2. 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.
    • Ex. 1: 2 x 4 = 8. Both of our fractions will have a denominator of 8.
    • Ex. 2: 3 x 4 = 12. Both of our fractions will have a denominator of 12.
    • Ex. 3: 5 x 3 = 15. Both of our fractions will have a denominator of 15.
  3. 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. 1: 1/2 x 4/4 = 4/8.
    • Ex. 2: 1/3 x 4/4 = 4/12.
    • Ex. 3: 6/5 x 3/3 = 18/15.
  4. 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. 1: 1/4 x 2/2 = 2/8.
    • Ex. 2: 3/4 x 3/3 = 9/12.
    • Ex. 3: 4/3 x 5/5 = 20/15.
  5. 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.
    • Ex. 1: instead of 1/2 + 1/4, we have 4/8 + 2/8
    • Ex. 2: instead of 1/3 + 3/4, we have 4/12 + 9/12
    • Ex. 3: instead of 6/5 + 4/3, we have 18/15 + 20/15
  6. Add together the numerators of the two fractions. The numerator is the top number of the fraction.
    • Ex. 1: 4 + 2 = 6. 6 will be our new numerator.
    • Ex. 2: 4 + 9 = 13. 13 will be our new numerator.
    • Ex. 3: 18 + 20 = 38. 38 will be our new numerator.
  7. Take the common denominator that you figured out in Step 2 and add it on the bottom of your new numerator.
    • Ex. 1: 8 will be our new denominator.
    • Ex. 2: 12 will be our new denominator.
    • Ex. 3: 15 will be our new denominator.
  8. Put the new numerator on top and the new denominator on bottom.
    • Ex. 1: 6/8 is our answer to 1/2 + 1/4 = ?
    • Ex. 2: 13/12 is our answer to 1/3 + 3/4 = ?
    • Ex. 3: 38/15 is our answer to 6/5 + 4/3 = ?
  9. Simplify and reduce. Simplify by dividing both the numerator and the denominator in the fraction by each number's greatest common factor.
    • Ex. 1: 6/8 can be simplified to 3/4.
    • Ex. 2: 13/12 can be reduced to 1 1/12.
    • Ex. 3: 38/15 can be reduced to 2 8/15.



Tips

  • Do not forget to multiply all numbers of the fraction by the same number.
  • Don't forget to simplify.
  • Always simplify at the end, the numbers are then easier to continue working with. Unless, of course, you are asked not to.
  • Denominators "must" be the same for the fractions to be added, that's why they are called "common" denominators. Don't attempt the problem until you have done all of the conversions - it's not a shortcut, and it will just mean more work for you.
  • You can use LCM to help you find the lowest common factor.
  • Simplify at the end by seeing if it is divisible by that number.

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