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.
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.
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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