How to add fractions

How to add fractions

Examples

Today, we’re going to walk through some examples of adding fractions.

Let’s begin with the simplest of examples:

Adding Fractions with the Same Denominator

For example:

Adding Fractions

The only thing we need to do is add the numerators and leave the denominator alone. The answer is:

Adding Fractions

Adding Numbers and a Fraction

For example:

Adding FractionsThe first thing that we need to do in this case is to convert the 2 into a fraction. As you already know, we can simply put a 1 in the denominator of any number without changing its value:

Adding FractionsWhen we have two fractions, we can start looking for the common denominator. In this example, it’s quite simple because the least common multiple of 1 and any number is that number. So:

Adding FractionsNow, we only need to multiply 2 x 4 and we get:

adding…and now we put it into our addition problem:

Adding Fractions

Adding Fractions with Co-Prime Denominators

Remember that two numbers are co-prime if their greatest common divisor is 1. For example, in the problem:

addingThe denominators are co-prime because:

Adding FractionsThese kinds of problems are simple to solve because the only thing that we need to do to find the new numerators is to multiply each numerator by the denominator of the other fraction, as shown below:

addingAnd we simply multiply the denominators together. So, we get:

addingand

Adding FractionsAnd the only thing that’s left to do is to add the two fractions together:

adding

Adding Fractions in General

For example:

adding

We need to calculate the least common multiple of the denominators:

addingWhat do we have to do next? Let’s break it down. First, let’s look at the fraction:

adding

To find the numerator, we need to divide the LCM by the fraction’s denominator:

addingWe need to multiply the fraction’s numerator by 2. So:

addingAnd we can see that the new numerator is 6.

For the denominator, we just need to use the GCM (18):

addingNow, we just do the same thing with the other fraction. To solve for the numerator, we need to divide:

addingAnd multiply by the numerator:

addingThen, we put in the GCM as the denominator, which gives us:

adding

Now, all that’s left to do is to add the fractions together …

addingAnd that’s it!

We actually add all fractions this way, the first examples were simpler thanks to the GCM that was easier to work with. The way of solving the problems, however, always stayed the same.

To summarize, the steps for adding fractions are:

  • Find the GCM of the two denominators.
  • Divide the GCM by the denominator and multiply that by the numerator to convert each fraction into a fraction that has the GCM as the new denominator.
  • When we’ve done the two previous steps with all the fractions, put them all in order and add their numerators.

 

Good luck adding fractions—with a little practice, you’ll see that they’re a snap and you’ll get it in no time!

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