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.

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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