... Common Denominator?

When the denominators of two or an ext fractions are the same, they have Common Denominators.

You are watching: Common denominator of 6 and 9


... Least common Denominator?

it is the smallest of all the common denominators.

Why?

Why do we want common denominators?

Because we can"t add fractions with various denominators:

13+16=?
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Before us can add them we should make the denominators the same.

Finding a common Denominator

But what should the new denominator be?

One simple answer is to multiply the existing denominators together:

3 × 6 = 18

So rather of having actually 3 or 6 slices, we will certainly make both that them have actually 18 slices.

The pizzas currently look favor this:

618+318=918
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They now have common denominators (but no the least usual denominator)

(Read more about typical Denominators.)

Least usual Denominator

That is all fine, yet 18 is a lot of slices ... Can we execute it with fewer slices?

Here is exactly how to find out:

13List multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...
16List multiples the 6: 6, 12, 18, 24, ...

Now discover the smallest number the is the same:

multiples the 3: 3, 6, 9, 12, 15, 18, 21, ...
multiples of 6: 6, 12, 18, 24, ...

The answer is 6, and that is the Least typical Denominator.

So allow us shot using it!

We desire both fountain to have actually 6 slices:

When us multiply top and bottom that 13 through 2 we acquire 26 16 already has a denominator the 6

And our question now looks like:

26+16=36
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One last action is to simplify the portion (if possible). In this case 3/6 is less complicated as 1/2:

26+16=36=12
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And that is what the Least typical Denominator is all about.

It allows us include (or subtract) fractions using the least variety of slices.


What Did we Do?

The trick to be to list the multiples of each denominator, then find the Least typical Multiple

In the previous example the Least typical Multiple of 3 and also 6 to be 6.

In various other words the Least usual Denominator that 13 and also 16 is 6.

Here room the procedures to follow:

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Find the Least typical Multiple of the denominators (which is referred to as the Least usual Denominator).Then add (or subtract) the fractions, together we wish!

Example: What is 16 + 715 ?

The Denominators room 6 and also 15:

multiples that 6: 6, 12, 18, 24, 30, 36, ...
multiples 15: 15, 30, 45, 60, ...

So the Least common Multiple the 6 and 15 is 30.

Now let"s try to do the denominators the same.

Note: what we carry out to the bottom that the fraction, we must also do come the top

For the very first fraction we can multiply top and also bottom by 5 to acquire a denominator the 30:

× 5
16=530
× 5

For the second fraction we deserve to multiply top and bottom by 2 to acquire a denominator that 30:

× 2
715=1430
× 2

Now we can do the enhancement by including the top numbers:

530 + 1430 = 1930

The portion is currently as straightforward as it deserve to be, so the is the answer.


Least usual Multiple Tool

To find the least usual denominator automatically use the Least common Multiple Tool. Simply put in the denominators, push the button, and also the least usual denominator is shown.

One an ext Example


Example: What is 38 + 512?

List the multiples that 8 and also 12

multiples the 8: 8, 16, 24, 32, 40, ...

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multiples 12: 12, 24, 36, 48, ...

The Least typical Multiple is 24

For the very first fraction we deserve to multiply top and bottom by 3 to acquire a denominator the 24:

× 3


38=924


× 3

For the second portion we can multiply top and bottom by 2 to get a denominator the 24: