Adding fractions (if they have different denominators) is not something you can easily work out how to do. You have to know a method. The method is not difficult and becomes second nature with practice.

Fractions with different denominators are incompatible, you cannot add them before you have made them compatible by converting them so that have the same (common) denominator. A foolproof way to find a common denominator is to multiply them. You could say that, to make fractions compatible, go forth and multiply the denominators!

For example:-

5/4 + 4/6 — a common denominator is 4 x 6 = 24

You will have possibly noticed that 4 & 6 have a lower common denominator, namely 12. If you notice a lower common denominator, go ahead and use it; it will save you having to simplify your answer at the end. BUT don’t get hung up about finding the lowest common denominator. Just be assured that by multiplying the denominators you have a secure way to find a common denominator. You can always simplify your answer at the end.

Adding Fractions — Some Definitions

**Mixed number **- a whole number and a fraction. For example 1¼.

**Improper Fraction– **a fraction where the top number (the numerator) is greater than the bottom number (the denominator). For example 5/4.

**Numerator**- The **top** number of a fraction. For example, the numerator of 5/4 is 5.

**Denominator**- The **bottom **number of a fraction. For example, the denominator of 5/4 is 4.

Here is a video that walks you through the 5 simple steps to add any two fractions. I suggest you read the rest of this article first and then use the video to make sure you understand and, more importantly, remember the 5 steps to add fractions:

### Video Tutorial: Adding Fractions

## Adding Fractions in 5 Simple Steps

We know now the underlying principles of adding fractions and have defined some key terms. Here’s an addition of fractions question to show the 5 simple steps that can be used to add any two fractions.

Question: 1¼ + 4/6

### Step 1 Convert Any Mixed Numbers to Improper Fractions

In this question 1¼ is a mixed number. To convert a mixed number to improper fractions, multiply the whole units (in this case, 1) by the denominator of the fraction (in this case, 4). Add the answer to the numerator of the fraction (in this case, 1) and place this answer over the denominator:

((1 x4 ) + 1 ) / 4 = 5/4

So we have revised the fractions to add to:-

5/4 + 4/6

### Step 2 Find a Common Denominator

5/4 + 4/6

To find a common denominator simply multiply the 2 denominators:

4 x 6 =24

### Step 3 Convert the Numerators

To do this multiply the numerators by the same amount as you multiplied the denominators.

Taking the first fraction 5/4

to get the common denominator we multiplied by 6:- 4 x 6 =24

So we need to multiply the numerator by the same amount:-

5 x 6 = 30

So our first fraction becomes (5 x 6)/(4 x 6) = 30/24

Similarly for the second fraction 4/6

to get the common denominator we multiplied by 4:- 6 x 4 =24

So we need to multiply the numerator by the same amount:-

4 x 4 = 16

So our second fraction becomes (4 x 4)/(6 x 4) = 16/24

And we now have compatible fractions to add:-

30/24 + 16/24

### Step 4 Add the Numerators

We can now simply add the numerators:

30/24 + 16/24 = 46/24

### Step 5– If Possible Simplify the Fraction and If Answer is an Improper Fraction Convert to a Mixed Number

So from step 4 we have 30/24 + 16/24 = 46/24

First simplify 46/24 = 23/12

Now we have an improper fraction (the numerator is greater than the denominator) so we need to convert to a mixed number. To do this divide the numerator by the denominator (23 ÷ 12) and show the answer as a whole number with the remainder as a fraction:-

23/12 = 1 11/12

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