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• To step
• Method 1 of 2: Part One: Adding Fractions with the Same Denominator
• Method 2 of 2: Part Two: Adding Fractions with Unequal Denominators
• Tips

Being able to add fractions is a very useful skill. Not only for primary and secondary school, it is also a very practical skill. Read more about adding fractions here. You will be amazed at what you can learn in a few minutes.

To step

Method 1 of 2: Part One: Adding Fractions with the Same Denominator

1. Check the denominators (the numbers below the line) of each fraction. If they have the same number, you are dealing with fractions with like denominators. If not, skip the next section.
2. Here are two examples of problems we'll work on in this section. When you get to the last step you should understand how addition works.
   
   • Ex. 1: 1/4 + 2/4
   • Ex. 2: 3/8 + 2/8 + 4/8
3. Take the two counters (the numbers above the line) and add them together. It doesn't matter how many fractions you have, if they have the same denominator you can just add all the numerators together.
   • Ex. 1: 1/4 + 2/4 is our equation. "1" and "2" are the counters. That means 1 + 2 = 3.
   • Ex. 2: 3/8 + 2/8 + 4/8 is our equation. "3" and "2" and "4" are the counters. That means 3 + 2 + 4 = 9.
4. Construct the new fraction. Take the sum of the numerators you obtained in Step 2; this sum becomes the new counter. Use the denominator of the fractions from the previous step. This will be the new denominator; this denominator always remains the same if you add fractions with the same denominator
   • Ex. 1: 3 is our new numerator, and 4 the "new" denominator. This gives the answer: 3/4. 1/4 + 2/4 = 3/4.
   • Ex. 2: 9 is our new numerator, and 8 the "new" denominator. This gives the answer: 9/8. 3/8 + 2/8 + 4/8 = 9/8.
5. Simplify if possible. Simplify the new fraction to make sure the numbers are as small as possible.
   • If the numerator is greater than the denominator, as in eg. 2, then at least one integer can be removed from the fraction. Divide the numerator by the denominator. If we divide 9 by 8, we get 1 whole number and a remainder of 1. Place the whole number in front of the fraction and the remainder as the numerator of the new fraction, while the denominator remains the same. 9/8 = 1 1/8.

Method 2 of 2: Part Two: Adding Fractions with Unequal Denominators

1. Check the denominators (numbers below the fraction) of each fraction. If the denominators are unequal then you have to find a way to make them equal. Read on to learn how.
2. Here are two examples of exercises we will work on in this section. When we get to the last step, you know how to add fractions with unlike denominators.
   
   • Ex. 3: 1/3 + 3/5
   • Ex. 4: 2/7 + 2/14
3. Find a suitable denominator. You can do this by looking for the common multiple of the denominators. An easy way to find it is to simply multiply both denominators. If one of the denominators is a multiple of the other, all you have to do is multiply that other fraction.
   • Ex. 3: 3 x 5 = 15. Both fractions get 8 as the denominator.
   • Ex. 4: 14 is a multiple of 7. So we just need to multiply 7 by 2 to get 14. Both fractions then have a denominator of 14.
4. Multiply both numbers of the first fraction by the denominator of the second fraction. There is no change in 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, all we need to do is multiply the first fraction by 2, because this way we can get the common denominator.
     • 2/7 x 2/2 = 4/14.
5. Multiply both numbers of the second fraction by the denominator of the first fraction. Again, we don't change the value of the fraction, just how it looks. It's still the same fraction.
   • Ex. 3: 3/5 x 3/3 = 9/15.
   • Ex. 4: The second fraction does not need to be multiplied because both fractions already have the same denominator.
6. Place both fractions next to each other with their new numbers. They have not been added together yet, please be patient! What we've done is multiply each fraction by an appropriate number, with the goal of making both denominators equal.
   • 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 the numerators of both fractions.
   • Ex. 3: 5 + 9 = 14.14 will be the new counter.
   • Ex. 4: 4 + 2 = 6.6 will be the new counter.
8. Take the equal denominator you calculated in Step 2 and use it as the denominator of the new fraction. By the way, this is of course the same denominator that you already see in the changed fraction.
   • Ex. 3: 15 will be our new denominator.
   • Ex. 4: 14 will be our new denominator.
   • Ex. 3: 14/15 is our new answer to 1/3 + 3/5 =?
   • Ex. 4: 6/14 is our answer to 2/7 + 2/14 =?
9. Simplify the fraction. Simplify the fraction by dividing both the numerator and denominator by the greatest common divisor.
   • Ex. 3: 14/15 cannot be simplified.
   • Ex. 4: 6/14 can be reduced to 3/7 by dividing both the numerator and denominator by 2, the greatest common divisor.

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