At first, fractions can be really hard to understand. However, it is a fundamental skill to have. Essentially, fractions represent parts or pieces of a total. The easiest way to grasp this concept would be to think about pies. Now, don’t think about eating them :D, think about the portion or part of the total pie that your slice covers. For example, if you were to take a piece of pie and 3/4 remained afterwards, how big was your pie slice? Well, the total is 1 and the remaining is 3/4. So, let’s subtract! 1-3/4 = 1/1 – 3/4. Let’s convert 1/1 into 4/4 so that we can have the same denominator and continue with our solution: = 4/4 – 3/4 = 1/4. Meaning, your pie slice represented 1/4 of the pie.

When we have two fractions like 2/3 and 4/5 and we need to add them, it is very tempting to just add the numerators (or the numbers on top of the line) and put that over the sum of the denominators (or the numbers underneath the line). Unfortunately, it’s not that easy. Luckily, there is a simple way to add and subtract fractions! Here’s how it works:

Now, we know that the LCM of the denominators is 15. Thus, we have to convert our fractions to match that value. Here’s how it’s done:

Finally, since the fractions have been properly converted, we can add them together like this:

Overall, we saw how 2/3 + 4/5 eventually became 10/15 + 12/15 allowing us to easily get 27/15. Moreover, now that we have actually gone through the whole process, let’s make a simpler kind of formula to add or subtract fractions:

Before we apply this concept to some problems, it is important to realize that this will not always give you the answer in reduced terms. For instance, if our answer was 1/2 using the traditional lcm approach, it is possible that we get something like 2/4 using this one. Alas, make sure that you put the fraction into reduced terms for a correct solution. Anyways, let’s apply this to: 5/7 + 3/8, and 3/5 – 2/7:

So, as you can tell, this method is pretty efficient as it makes dealing with fractions very easy. Before moving on to multiplication and division of fractions, I would like to show you a little fraction trick:

Although this is being derived from the formula above, this simplification can make these types of fraction sums or differences very efficient. For example, with 1/2 + 1/9, immediately you can tell it’s 11/18. Similarly, with 1/2 – 1/9, you can get 7/18 in an instant. Finally, let’s go over the multiplication and addition of fractions:

Luckily for us, multiplication and division are WAY easier! With multiplication, it’s just the product of the numerators over the product of the denominators. Division is similar to that, with one exception. We take the reciprocal of the second fraction (AKA: the divisor) and multiply that with the quotient. Here is an easier way to remember:

Lastly, let’s practice these new concepts with some questions: