Today we’re going to find out why, **when we’re including and individually fractions, they need to have the same denominator.You are watching: Why is it necessary to have common denominators when adding fractions**

If you didn’t currently know, as soon as we’re including and subtracting fractions, they have to be **homogeneous**. You have the right to read more about homogeneous and also heterogeneous fractions in this post.

It’s really simple to understand using visual aids, which we’ll take it a look at below. The actual reason is because of the definition of the portion itself, which is a representation of parts of a complete which need to be **the exact same size**.

When you include or subtract fractions, girlfriend can’t to express the an outcome as a fraction if you execute not divide the total into equal parts.

### Adding fractions

For example, if you want to include 1/2 + 1/3

We have:

1 of 2 equal parts of a entirety unit (in environment-friendly in the image).1 that 3 equal parts of a unit (purple in the image).To execute the addition, we have to take the colored parts right into account. Due to the fact that each part is a various size, we can’t refer this amount in the kind of a fraction.

We have **3 parts** (1 stood for by a environment-friendly rectangle and 2 represented by violet rectangles), but they are **not the very same size**.

So what can we do? We can express the fractions we want to include in the form of a fraction that permits us to consider them parts **of the same size**.

As you have the right to see in the adhering to images, you can express the fraction 1/2 as 3/6 and the fraction 1/3 together 2/6.

Now we’ve obtained the amounts that we desire to include expressed in the type of fractions the have **parts that the very same size**!

Now we have the right to count the colored parts and also express them in the kind of a fraction. Over there are 5 equal parts: 5/6.

So 1/2 + 1/3 = 5/6.

### Subtracting fractions

Now, if us to try subtract, for example, 1/2 and also 1/3, we get the same problem. Come subtract 1/3 native 1/2, **we should take away parts that space the exact same size together the ones us have**.

So, we should express both fractions homogeneously, and also then we deserve to take far the parts suggested by the subtraction.

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If us express 1/2 as 3/6 and 1/3 as 2/6, come subtract 1/2 – 1/3, us take far 2 of the 3 equal components of 3/6, and we obtain 1 part, or 1/6. So, we find that 1/2 – 1/3 = 1/6.

It’s straightforward to recognize why the denominators should be the same as soon as we’re adding and subtracting fractions, isn’t it?

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