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Date: 10/25/1999 at 08:45:58
From: Kevin Balandin
Subject: Fractions

I am in grade 7 and (can you believe it?) I can't add or subtract
fractions!

Kevin
```

```
Date: 10/25/1999 at 15:44:27
From: Doctor Rick
Subject: Re: Fractions

Hi, Kevin.

Let's just go over some basics; if you have a problem with a
particular part of this process, write again and we can work through
it.

dimes, does it? If I have 2 quarters and 3 dimes, then I have 5 coins,
but this doesn't tell you anything about how much money I have.

What you could do instead is to convert the quarters and dimes to
cents:

2 quarters + 3 dimes =
2 * 25 cents + 3 * 10 cents =
50 cents + 30 cents =
80 cents

Another way would be to convert the quarters and dimes into nickels.
Each quarter becomes 5 nickels, and each dime becomes 2 nickels. So

2 quarters + 3 dimes =
2*5 nickels + 3*2 dimes =
10 nickels + 6 nickels =
16 nickels

I can rewrite the problem as a sum of fractions, because a quarter is
1/4 dollar, a dime is 1/10 dollar, and a nickel is 1/20 dollar.

2     3    16
--- + --- = --
4    10    20

Before you can add two fractions, you need to rewrite one or both
fractions so they have the same denominator. This is the same thing as
converting different coins into the same kind of coin. You have
learned about equivalent fractions, right? If you multiply the
numerator and denominator of a fraction by the same number, you get
another name for the same fraction - an equivalent fraction.

3     3*2     6
--- = ---- = ----
10    10*2    20

If you want to add, say, 3/10 and 5/6, you need to find a pair of
fractions that are equivalent to these but that have the same
denominator. Let's write out some equivalent fractions:

3/10 = 6/20 = 9/30 = 12/40 = 15/50 = ...

5/6 = 10/12 = 15/18 = 20/24 = 25/30 = ...

You can see a pair of fractions that have the same denominator: 9/30

3     5      9     25     34
---- + --- = ---- + ---- = ----
10     6     30     30     30

Now we can simplify the answer, by reducing it to lowest terms. Both
34 and 30 are divisible by 2, so a fraction equivalent to 34/30 is
17/15 (dividing the numerator and denominator by 2). Finally, because
17 is greater than 15, this is an improper fraction, so we can convert
it into a mixed number:

17   15    2      2
-- = -- + -- = 1 --
15   15   15     15

Subtraction works the same way. Here is an example:

5     3    25    9   16    8
--- - --- = -- - -- = -- = --
6     10   30   30   30   15

You can find some further help with fractions in the links at the
bottom of our Dr. Math FAQ on "Fractions, Decimals, Percentages":

http://mathforum.org/dr.math/faq/faq.fractions.html

In particular, you can find techniques for finding the smallest
denominator that will work -- the Lowest Common Denominator (LCD),
also called the Least Common Multiple (LCM). That's the trickiest part
of adding fractions. You will find more help with this if you go to
our Dr. Math Search page,

http://mathforum.org/mathgrepform.html

and search for   LCD LCM   selecting "At least one of your keywords".

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

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