# Examples

Today, weâ€™re going to walk through some examples ofÂ **adding fractions.**

Letâ€™s begin with the simplest of examples:

**Adding Fractions with the Same Denominator**

For example:

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

**Adding Numbers and a Fraction**

For example:

The 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:

When we have two fractions, we can start looking for theÂ **common denominator.**Â In this example, itâ€™s quite simple because the least common multiple of 1 and any number is that number. So:

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

â€¦and now we put it into our addition problem:

**Adding Fractions with Co-Prime Denominators**

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

The denominators are co-prime because:

These 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:

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

and

And the only thing thatâ€™s left to do is to add the two fractions together:

**Adding Fractions in General**

For example:

We need toÂ **calculate the least common multiple of the denominators**:

What do we have to do next? Letâ€™s break it down. First, letâ€™s look at the fraction:

To**Â find the numerator**, we need to divide the LCM by the fractionâ€™s denominator:

We need to multiply the fractionâ€™s numerator by 2. So:

And we can see that the new numerator is 6.

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

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

And multiply by the numerator:

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

**Now, all thatâ€™s left to do is to add the fractions together**Â â€¦

**And thatâ€™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**Â steps for adding fractions**Â are:

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

Good luck adding fractionsâ€”with a little practice, youâ€™ll see that theyâ€™re a snap and youâ€™ll get it in no time!