Associated Topics || Dr. Math Home || Search Dr. Math

```
Date: 03/19/99 at 23:53:21
From: demarie
Subject: Fractions

If you need to calculate 1/3 + 1/6, what do you do since the
denominators are different? Do you add the denominators?
```

```
Date: 03/20/99 at 09:24:13
From: Doctor Derrel
Subject: Re: Fractions

Remember that a fraction is composed of three things:

The first is the whole thing, also called the unit or the one. It
might be the distance from 0 to 1 on the number line. It might be a
whole square. It might be the kind of one cup measurement you use in
cooking.

The second is how many equal pieces the whole thing is divided into.
The number of equal pieces is the denominator. If you have a measuring
cup that you would use for flour, it holds one cup exactly. (This is
the type of measuring cup that you fill so the flour is heaped up, and
then you scrape off the stuff that is above the cup.) Some of these
cups are divided into four equal parts by lines that are drawn on the
inside or outside. Cups like these are divided into fourths, so the
denominator is 4. You might get one from your kitchen and see how many
parts it is divided into.

The third thing is how many of those equal pieces you are interested
in. That is the numerator. If you are interested in three of the four
parts in the cup, you would be interested in 3/4 of the cup. Now, it
is possible for the numerator to be larger than the denominator. This
happens when you are interested in more pieces than are in the whole
thing. For example, a pancake recipe might call for 3/2 cups of flour.
(But the cookbook would probably write it as 1 1/2 cups; 3/2 is what
is called an "improper fraction," while 1 1/2 cups is what is called a
"mixed number.")

So, does it make sense to add the denominator? Let me suggest
something to you. Go into your kitchen and get all of the measuring
cups you can find that have fractions marked on them, like 1/3 or 1/4
or 1/2. Next, write a fraction equation, like 1/4 + 1/2. Solve that by
putting a quarter cup (1/4) of water in a one-cup measure and then
pouring it in a glass, and then getting a half cup (1/2) of water and
pouring that in the same glass. Finally, pour the water in the glass
back into the measuring cup to see what you get.

Now make a table on paper and write down several equations and the
answers you get. Some of these might be kind of hard, so work on this
with a friend. Put these equations in a table in this order and figure
out how much the answer is. Then, look for patterns.

1/4 cup of water plus 1/4 cup of water = ?/? cup of water
1/4 cup of water plus 2/4 cup of water = ?/? cup of water
1/4 cup of water plus 3/4 cup of water = ?/? cup of water
1/4 cup of water plus 4/4 cup of water = ?/? cup of water

1/4 cup of water plus 1/3 cup of water = ?/? cup of water
1/4 cup of water plus 2/3 cup of water = ?/? cup of water
1/4 cup of water plus 3/3 cup of water = ?/? cup of water

1/4 cup of water plus 1/2 cup of water = ?/? cup of water
1/4 cup of water plus 2/2 cup of water = ?/? cup of water

1/3 cup of water plus 1/3 cup of water = ?/? cup of water
1/3 cup of water plus 2/3 cup of water = ?/? cup of water
1/3 cup of water plus 3/3 cup of water = ?/? cup of water

1/3 cup of water plus 1/2 cup of water = ?/? cup of water
1/3 cup of water plus 2/2 cup of water = ?/? cup of water

If you do not want to play with water, take strips of paper all the
same length and fold separate strips into 2 parts, 3 parts, 4 parts,
5 parts, 6 parts, 8 parts, 9 parts, 10 parts, or 12 parts. Make the
parts as equal as you can. You should have 9 strips, each representing
one type of fraction. Draw lines in the folds so that it is easy to
see each of the equal pieces that makes up the whole fraction strip.
Write on each strip what it is: for example, halves, thirds, fourths,
fifths, sixths, eighths, nineths, tenths, or twelfths. Then, try
adding various fractions by lining the strips up side by side. For
example,  1/4 + 1/2 would look like:

+---------+---------+---------+---------+
|||||||||||    1/4  |         |         |
+---------+---------+---------+---------+
+-------------------+-------------------+
|||||||||||||||||||||    1/2            |
+-------------------+-------------------+

You can see from the fraction strips that 1/4 + 1/2 is 3/4. So, rather
than trying to figure out how to add the fractions just by looking at
the numbers, use your fraction strips or draw little pictures to help
you.

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

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search