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### Multiplying a Fraction by a Decimal

```
Date: 9/5/96 at 13:8:48
From: Glenn Hill
Subject: Fraction Times a Number

How do I simplify and multiply:

40
----- x 78.5
360
```

```
Date: 9/6/96 at 4:20:55
From: Doctor Mike
Subject: Re: Fraction Times a Number

Hi Glenn,

There are several ways to do this.  If you have a calculator, you
could do  40/360  first, and then multiply that by 78.5 .

If you are doing it by hand, then the easiest way is to first reduce
the fraction to lowest terms.  The numerator 40 and the denominator
360 are both multiples of 10, so you could divide both numerator and
denominator by 10 to get the equivalent fraction 4/36 .  Since 4 times
9 is 36, this fraction is equivalent to 1/9 .

Your original problem is now

1
--- x 78.5
9

That is the same as 78.5/9 which you can do on paper with long
division.  Either way the answer is an infinitely repeating decimal
8.722222222... .  A good approximate value is 8.722.

I hope this helps.

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

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