How to Add Fractions in Five Easy Steps

Adding fractions can seem an impossible challenge. How can you add something as different as, for example, thirds (1/3) and sevenths (1/7)? That is the crux of the problem. The key to conquering the addition of fractions, is to realize that you need to first make the fractions compatible (by finding a common denominator). Then you need a dependable, easy method to make the fractions compatible. This article will walk you through some examples and also includes a video demonstration. For best results, I would recommend reading this article and then watching the video (see link to YouTube video, below).

There's an added bonus, the technique for adding fractions is virtually identical to the technique for subtracting fractions.

Half (or is it five-eighths?) the battle with fractions is knowing the terminology. Here are some basics:-

Mixed Number = 1¼ - i.e a mixture of a whole number and a fraction.

Improper number = 5/4 - i.e a fraction where the top number (the numerator) is greater than the bottom number (the denominator).

Numerator and Denominator Defined:-

As with all math and numeracy lessons, the best way is to use an example. Here are the 5 easy steps to add 1¼ + 3/7

Example 1¼ + 3/7

In this example 1¼ is a mixed number. Before we can complete the addition we need to convert this mixed number into an improper fraction (remember an improper fraction is one where the numerator is greater than the denominator). To convert a mixed number into an improper fraction multiply the whole number by the denominator of the fraction (in this case 1 x 4) and add to the numerator of the fraction (in this case 1). This gives a new numerator to place over the denominator:-

1¼ - Numerator = (1 x 4) + 1 = 5. Denominator = 4. Improper fraction = 5/4.

So 1¼ + 3/7 becomes 5/4 + 3/7

Again using our example 1¼ + 3/7 = 5/4 + 3/7.

So we need to find a common denominator for 5/4 + 3/7. For more straightforward fractions, you may just know the common denominator. However we need a foolproof method that will work with the addition of any fractions. All we need to do is multiply the existing denominators, in our example denominators are 4 and 7, so we know that a common denominator will be:

4 x 7 = 28

Multiply the numerators by the same amount you multiplied the denominators:-

1¼ x 3/7 = 5/4 x 3/7 =

(5 x 7)/(4 x 7) + (3 x 4)/(7 x 4) =

35/28 + 12/28

To be honest this is the most difficult part to do (and to explain!) - look at the illustrated example here and answer a few questions yourself and it will soon become second nature.

First a recap:-

Step 1 = 1¼ + 3/7 = 5/4 + 3/7

Step 2 = Common denominator = 4 x 7 = 28

Step 3 = 5/4 + 3/7 = 35/28 + 12/28

Step 4 is the easiest part, we just add the numerators:

Step 4 = 35/28 + 12/28 = 47/28

In reality step 4 gave us an answer BUT depending on how fussy your teacher, or more importantly, your exam board is, you may lose marks for not simplifying fractions or converting improper fractions to mixed numbers. Step 5 is the final step where we tidy our answer up by simplifying, if possible and if we have an improper fraction (i.e. where the numerator is greater than the denominator) converting to a mixed number.

In our case our preliminary answer from step 4 is: 47/28 - this fraction cannot be simplified but it is an improper number so we need to turn into a mixed number. To do this we divide the numerator by the denominator to give the number of whole units. The remainder over the denominator gives the fraction.

In our case 47 ÷ 28 = 1 remainder 19 so our final answer is :-