Working with fractions is not as easy as with whole numbers. Because whole numbers represent a certain number of the same size of unit (namely, 1) they can be added together with ease. Fractions require little more work so that we can work with the same size of units. Let’s look at a couple of examples and work through them.

¼ + ¼ =

The first step in adding or subtracting fractions is to make sure the denominators are the same. In this case they are, so all we need to do is add the numerators together, 1+1=2, and put them over the denominator, 4. We arrive at 2/4, which can be simplified by dividing both numerator and denominator by 2 and our answer is ½.

¾ + ½ =

You cannot add fractions that have different denominators because you are not adding the same size of units. ¼ of 1 is not the same size as ½ of 1, so we cannot just put the two together. When you add two whole numbers, 2 + 3, you are actually adding 2/1 + 3/1, units of the same size of 1. In our second example, we see that we have two different denominators. To make them the same so we are working with the same sized units, we need to find a common multiple of the two denominators. Two goes into 4, so we can use 4 as our common denominator in our example. In more complicated cases, the easiest way to find a common multiplier is to multiply the denominators.

As seen in example 1, if you multiply or divide both numerator and denominator by the same number, you have an equivalent fraction. We have a common multiplier of 4 in our second example, so we need to perform the same operation on the numerator as we perform on the denominator to determine our equivalent fraction. In the fraction ¾, we do not need to do anything because we already have a denominator of 4. For our second fraction, ½, we need to divide our common denominator (4) by the fraction’s denominator (2) and we get 2. Multiply the numerator by this number to achieve our equivalent fraction. 2*1=2 just as 2*2=4, so our equivalent is 2/4.

Now that we are adding the same size of unit, ¼, we add the numerators together (3 + 2) and get 5. Put that number on top of the denominator and we have our solution, 5/4. Because the numerator is larger than the denominator, we can make it into a mixed number by dividing the fraction. Five divided by four is 1¼ or 1.25. Adding fractions is just that easy. Subtracting is the same process except that you subtract nominators instead of adding!

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