How to add and subtract fractions having different denominators

Fractions are something that scare many people. But they're not really as tough as you think. In this article, I'll show you how to add and subtract fractions having different denominators. And as a skilled instructor, I'll walk you through every step in the process!

Instructions

1. **Fraction parts**

   A fraction consists of 2 numbers, a numerator and a denominator. The numerator is the number on top. And the denominator is the number on the bottom.

   So 3/5 has a numerator of 3 and a denominator of 5.

2. Now that you understand the two parts of a fraction, we can begin to discuss how to add and subtract fractions when the denominators are not the same.

   For example, 1/5 + 2/3.

   1/5 has a denominator of 5 and 2/3 has a denominator of 3. So what we need to do is find a denominator that they both have in common.

   TIP: Many teachers and books will have you find the lowest common denominator first. However, I suggest not doing this unless you immediately know what that denominator is. Instead, I say to get your answer first and then reduce afterwards.

   By doing it this way, I find my students get an answer quicker and have a correct one to compare the reduced one to. So I suggest reducing at the very end, after you've done your addition or subtraction.

   In other words, if you reduce incorrectly, then your addition or subtraction will be off too! My way helps you get a right answer to begin with. All you have to do is properly reduce it afterwards. So you're beginning with a correct answer instead of a possible wrong one.

3. **Finding a common denominator**

   The easiest and fastest way to find a common denominator is to multiply the denominators together. So going back to my example, 1/5 + 2/3, you'd multiply 5 times 3. That would give you 15.

4. Now we raise both fractions to the new denominator, which in my example would be 15.

   So we'd take 1/5 and turn it into 15ths. And we'd take 2/3 and turn it in to 15ths.

   To do this, you take the new denominator (15 in my example) and divide it by the current deonominator. Then multiply that result by the numerator.

5. So to convert 1/5, we'd:

   a) Ask ourselves, what is 15 divided by 5? Answer, 3.
   b) Take our answer (3) from part a, and multiply that by the numerator (1). Doing this gives us 3x1 or 3.

   So 1/5 becomes 3/15.

   To convert 2/3, we'd:

   a) Ask ourselves, what is 15 divided by 3? Answer, 5.
   b) Take our answer (5) from part a, and multiply that by the numerator (1). Doing this gives us 5x2 or 10.

   So 2/3 becomes 10/15.

6. Now that we have our fractions in the same denominator, 15 in my example, we can do our addition or subtraction.

   In other words, we took 1/5 + 2/3 and turned it into 3/15 + 10/15.

   To add or subtract fractions with the same denominator, all you do is add or subtract the numerators and put that over the denominator.

   Since we're adding in my example, you'd add 3 and 10 to get 13. And putting that over the denominator 15 gives us 13/15.

   So 1/5 + 2/3 = 13/15.

   And if you needed to reduce your answer to lowest terms, you'd do that now.

Tips & Warnings

• Find a common denominator--doesn't have to be the lowest!

• Convert the fractions to that new denominator]

• Reduce at the end. Just makes things easier and gives you an answer faster!

• If you reduce first, be sure you do it correctly!

• If you don't reduce properly, then your addition or subtraction will also be off!

• That's why I suggest doing the addition or subtraction first, and then reducing afterwards. Less chance of errors and quicker!