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### Dividing Fractions

```
Date: 09/08/99 at 22:29:38
From: Olivia Baker
Subject: Dividing Fractions

How do you divide fractions? I love math and I am good at it. This is
the only thing slowing me down. I've tried and cannot find a way.

Thanks.
```

```
Date: 09/09/99 at 09:29:02
From: Doctor Rick
Subject: Re: Dividing Fractions

Hi, Olivia.

Let's think about a few simple examples. Once you understand them, you
will be able to put them together to make harder problems.

What is 2 divided by 1/5? Here are 2 blocks:

+---------+---------+
|         |         |
|         |         |
|         |         |
|         |         |
|         |         |
|         |         |
|         |         |
|         |         |
|         |         |
+---------+---------+

Here is 1/5 of a block (the shaded part):

+---------+
|XXXXXXXXX|
+.........+
|         |
+.........+
|         |
+.........+
|         |
+.........+
|         |
+---------+

To divide 2 by 1/5, we divide 2 blocks into pieces the size of the 1/5
block.

+---------+---------+
|         |         |
+.........+.........+
|         |         |
+.........+.........+
|         |         |
+.........+.........+
|         |         |
+.........+.........+
|         |         |
+---------+---------+

There are 10 pieces this size in the 2 blocks. In other words,

2 divided by 1/5 = 10

That's the same as

2 x 5 = 10

Do you see why? To make 1/5 size blocks, we had to make each whole
block into 5 pieces. In other words, we multiplied the number of
pieces by 5.

Next problem:

2 divided by 2/5 = ?

Here is 2/5 of a block (the shaded part):

+---------+
|XXXXXXXXX|
+.........+
|XXXXXXXXX|
+.........+
|         |
+.........+
|         |
+.........+
|         |
+---------+

Let's divide the 2 blocks into pieces this size.

+---------+---------+
|         |         |
+         +         +
|         |         |
+.........+.........+
|         |         |
+         +         +
|         |         |
+.........+.........+
|                   |
+---------+---------+

The bottom block is a different shape, but it's the same size, because
it's made of 2 1/5-size pieces. Since the pieces we want are twice as
big, there are only 1/2 as many of them. The answer is

2 divided by 2/5 = 10/2 = 5

This is the same as

2 x 5/2 = 5

Do you see how the two equations are related? You take the fraction,
2/5, and "turn it upside down" (in math words, we say "invert the
fraction," or "take its reciprocal"). Then replace the division sign
by a multiplication sign.

Now we can tackle harder problems. The same method always works, even
if the answer isn't a whole number as in the simple examples. For
instance,

5 divided by 3/8 = ?

Invert the fraction 3/8; you get 8/3. Then multiply by this fraction:

5 x 8/3 = 40/3 = 13 1/3

We can even replace the whole number in the problem with a fraction,
like this:

5/7 divided by 3/8 = ?

5/7 x 8/3 = ?

5     8     40       19
--- x --- = ---- = 1 ----
7     3     21       21

If you are comfortable with multiplying fractions, then you will have
no trouble dividing fractions. Just remember: invert the fraction you
are dividing by (the divisor), and multiply instead of dividing.

If you still have trouble, write back and tell me just what you don't
understand; if you can do some problems but you have trouble with
others, give some examples of the ones you have trouble with. I want
to give you just the help you need, so the more you can tell me, the
better.

dividing fractions. Go to our Search Dr. Math page:

http://mathforum.org/mathgrepform.html

Type in "divide fractions" (no quotes), select "that exact phrase"
and click on "Search." You will see half a dozen or more answers.

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Division
Elementary Fractions

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