Today we’re walk to find out why, **when we’re adding and subtracting fractions, they require to have actually the very same denominator.You are watching: Why do fractions need to have a common denominator**

If you didn’t already know, once we’re including and individually fractions, they need to be **homogeneous**. You deserve to read more about homogeneous and also heterogeneous fractions in this post.

It’s really straightforward to know using intuitive aids, which we’ll take it a look at below. The real reason is due to the an interpretation of the portion itself, i beg your pardon is a depiction of components of a total which have to be **the same size**.

When you add or subtract fractions, girlfriend can’t to express the result as a portion if you perform not divide the complete into equal parts.

### Adding fractions

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

We have:

1 that 2 equal components of a whole unit (in eco-friendly in the image).1 that 3 equal components of a unit (purple in the image).To perform the addition, we need to take the colored parts right into account. Due to the fact that each part is a various size, us can’t express this amount in the kind of a fraction.

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

So what can we do? We can express the fountain we desire to add in the form of a fraction that permits us to think about them parts **of the exact same size**.

As you have the right to see in the complying with images, you deserve to express the fraction 1/2 together 3/6 and also the fraction 1/3 as 2/6.

Now we’ve obtained the quantities that we want to add expressed in the type of fractions that have **parts that the exact same size**!

Now we deserve to count the fancy parts and also express them in the kind of a fraction. There are five equal parts: 5/6.

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

### Subtracting fractions

Now, if we to try subtract, for example, 1/2 and 1/3, we get the exact same problem. To subtract 1/3 native 1/2, **we need to take away components that space the exact same size as the ones us have**.

So, we have to express both fountain homogeneously, and then we have the right to take far the parts shown by the subtraction.

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If us express 1/2 as 3/6 and 1/3 as 2/6, to subtract 1/2 – 1/3, us take far 2 the the 3 equal parts of 3/6, and we get 1 part, or 1/6. So, we uncover that 1/2 – 1/3 = 1/6.

It’s simple to know why the denominators have to be the same once we’re adding and subtracting fractions, isn’t it?

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