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Common Denominator: What Is A Denominator?

To add or subtract fractions, they must have a common denominator. This means the denominators must be the same. If the denominators are not the same, you can make them the same by multiplying the top and bottom of each fraction by the denominator of the other fraction. Once the fractions have a common denominator, you can add or subtract the numerators and keep the common denominator.

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109 views4 pages

Common Denominator: What Is A Denominator?

To add or subtract fractions, they must have a common denominator. This means the denominators must be the same. If the denominators are not the same, you can make them the same by multiplying the top and bottom of each fraction by the denominator of the other fraction. Once the fractions have a common denominator, you can add or subtract the numerators and keep the common denominator.

Uploaded by

yaki70
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Common Denominator

This is the easiest method we know to add or subtract fractions!

What is a Denominator?
The denominator is the bottom number in a fraction.
It shows how many equal parts the item is divided into.

What is a Common Denominator?


"Common" Denominator is when the
denominators
in two (or more) fractions are common, or the
same.

Why is it Important?
Adding and Subtracting Fractions
Before we can add or subtract fractions, the fractions need to have
a common denominator (in other words the denominators must be the
same).

Making The Denominators the Same


When the denominators are not the same, we can either use the Least
Common Denominator method to make them the same, or we can:

Multiply top and bottom of each fraction by the


denominator of the other.
o simplify a fraction, divide the top and bottom by the highest
number that
can divide into both numbers exactly.

Simplifying Fractions
Simplifying (or reducing) fractions means to make the fraction as simple
as possible.
Why say four-eighths (48) when we really mean half (12) ?
4

/8

==>

(Four-Eighths)

/4

(Two-Quarters)

How do I Simplify a Fraction ?


There are two ways to simplify a fraction:

Method 1

==>

/2

(One-Half)

Try to evenly divide (only whole number answers) both the top and
bottom of the fraction by 2, 3, 5, 7 ,... etc, until we can't go any further.

Example: Simplify the fraction 24/108 :


2

24

12
=

108

6
=

54

2
=

27

That is as far as we can go. The fraction simplifies to 29

Example: Simplify the fraction 1035 :


Dividing by 2 doesn't work because 35 can't be evenly divided by
2 (35/2 = 17)
Likewise we can't divide evenly by 3 (10/3 = 313 and also 35/3=1123)
No need to check 4 (we checked 2 already, and 4 is just 22).
But 5 does work!
5
10

2
=

35

7
5

That is as far as we can go. The fraction simplifies to 27


Notice that after checking 2 we didn't need to check 4 (4 is 22)?
We also don't need to check 6 when we have checked 2 and 3 (6 is 2x3).

What Did We Do?


1. We multiplied each fraction by the denominator of the other. Let's use
letters instead of numbers to show it:

2. And because they now have the same denominator, we can add them:

In One Step!
We could do those two things in one step like this:

Which we can use like this:

Example: What is
2

4
+

/3

/5

25 + 34
=

10 + 12
=

35

22
=

15

(Note: "a" was 2, "b" was 3, "c" was 4 and "d" was 5.)

15

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