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### Understanding Common Denominators

```
Date: 07/16/97 at 09:30:53
From: eleanor Turino
Subject: Fractions

What is a common denominator?
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```
Date: 09/01/97 at 11:58:40
From: Doctor Sonya
Subject: Re: Fractions

Dear Eleanor,

Common denominators are the hardest and the most important things to
learn about when you are studying fractions. They can also be really
fun, because they allow you to take horribly complicated problems and
turn them into beautiful, neat fractions.

Let's start with an example in which you would need to use a common
denominator. If I told you to find 1 + 4, you would know how to add
them to get 5.  But what if I say:

What's 4/5 + 1/3 ?

How do we go about adding these two numbers?  The secret to doing this
is to use a common denominator.

The common denominator is just what it sounds like - a denominator
that is the same for both fractions (remember that the denominator is
the number on the bottom of the fraction). For example, what if I

1/5 + 2/5 ?

This is a much easier problem, because there is a common denominator.
Think of fifths like apples. If you add 1 apple and 2 apples, you get
three apples.  Similarly, one fifth and two fifths is three fifths.

Here are some other examples to make this a bit clearer:

1/6 + 2/6 = 3/6
2/7 + 4/7 = 6/7

Can you do these ?

1/5 + 4/5 = ?
1/4 + 2/4 = ?

The hard part comes in when the two fractions have different
denominators. Adding four fifths and one third is just like trying to
add apples and oranges. It can't be done. We need to give these
fractions the same denominator so we can add them.

The secret to this is realizing that we can always write one fraction
in many different ways. Let's say we have 1/2 of a pie. Draw a circle
to represent the pie, divide it in two, and color in half. But what if
we have 2/4 of a pie?  Again, draw a circle, divide it into four equal
parts, and color in two of them that are next to each other. This
should look suspiciously like 1/2, and it is true that 1/2 = 2/4.
Try the same thing with 4/8, or 8/16. These are all different ways to
write 1/2.

If we can write a fraction so many different ways, shouldn't we be
able to write two of them with a common denominator?

Here's an example that will begin to make things clearer:

1/4 + 1/2 = ?

Remember that 1/2 = 2/4, so we can replace 1/2 with 2/4 in the
problem.  Now we have:

1/4 + 2/4 = ?

These two fractions have the same denominator, and you can now add
them easily.

I hope this helps you understand what a common denominator is.

Finding the common denominator is also hard, but not as hard as just
understanding what it is. I hope your teacher will explain to you how
to find common denominators.  If you are still confused, just write us

-Doctor Sonya,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Fractions

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