Download fractions

Intro: Using fractions is something that is very common in all
levels of math and statistics. If you are planning to take statistics
in college, you will do yourself a big favor by learning how to
manipulate fractions now! For more help, please see the online resources that I've listed at the bottom of this document.
Definitions
Fraction: a number that names part of a whole thing.
Numerator: the number on the top and tells how many parts are
being referred to
Denominator: the bottom number and shows how many equal
parts there are in all.
Whole Number: a number with no fractional (or left over)
parts. A whole number is also called an integer. All whole
numbers can be expressed as a fraction with that number over 1.
For example: the whole number 8 = 8/1, the whole number 52 =
52/1.
Equivalent fractions: are fractions that name the same amount
(i.e., maintain the same ratio or proportion). For example, the
whole number 8 = 8/1, 16/2, 24/3, 32/4, etc. The fraction 2/3 =
4/6, 6/9, 8/12, etc. To tell if fractions are equivalent, reduce each
fraction to its simplest form by dividing both the numerator and
denominator by the same, largest possible number.
Mixed Fractions: contain both a whole number and fraction
(sometimes called mixed numbers). Examples: 1¼, 16½, etc.
Improper Fraction: a fraction that has a numerator larger than
or equal to its denominator.
Example A: In shape A, the whole pizza is cut into 8 equal
parts. Even though the pizza is cut into 8 pieces, there are no
pieces missing. This pizza has 8 possible pieces (denominator)
and of the possible pieces, 8 are present (numerator). Shape A,
then has 8 pieces out of 8 possible pieces, or 8/8. So, Shape A
can be written as the fraction 8/8 which can be reduced to 1/1 or
just 1.
1 pizza = 8 pieces remain/8 pieces possible
Shape A
Example B: The pizza has had a visitor! 2 of the 8 pieces are
missing. The portion of the pizza that is missing is 2/8. 2/8 can
be reduced to an equivalent fraction. First, I should look at the
factors of my numerator and denominator. 2/8 = (21)/(24)
Then, I can reduced the numerator and denominator by any
common terms (in this case 2). When I divide the numerator and
denominator by 2, I am left with (11)/(14) or ¼. 2/8 is an
equivalent fraction to ¼.
In simplest form, the fraction of pizza missing is ¼.
Shape B
Example C: The game has gone into overtime and you only
have ½ of your pizza left! Luckily, you friend just showed up
with 3 whole pizzas! As luck would have it, the new pizzas are
also cut into 8 slices! How much pizza do you have now?
You have 3 whole + ½ or 3½ pizzas. 3½ is a mixed fraction.
Example D: Let's say you have seven (7) people at your house
now and you want to know how much pizza each person gets.
1½ might be a difficult number to use. Another way that you can
look at 1½ is to make it an improper fraction. You can do this by
finding the denominator of the fraction.
In this case, our denominator will be 2. You will need to
convert the "wholes" into "halves" by multiplying the whole
number (in this case 3/1) by the equivalent fraction of 1 (in
this case 2/2) that uses the denominator of the fraction. That
last sentence is probably pretty confusing, but remember above,
we said that the number 1 can be written as 4/4 or 8/8 or
2048/2048. It's still 1. Math rules say that you can multiply any
number times 1 and it's OK.
So if I have 3 whole pizzas and 1 half pizza, I need to multiply
my whole pizzas (remember whole numbers are really a number
over a denominator of 1) by 2/2.
{(3/1)(2/2)}+ ½= {(32) /(12)}+ ½= 6/2 +½= 7/2
In this case, each person, will conveniently get ½ of a pizza.
Example E: So Example D told what portion of a whole pizza
each person will get. Each person will get ½ of the pizza. How
many slices will each person get? Since a whole pizza is divided
into 8 pieces, we will need to convert ½ into its equivalent
fraction that has a denominator of 8. To do this, we need to find
the factor of 8 that will convert the denominator of ½ to 8th's.
Luckily, we know that 42 = 8. Since 2 is in our current
denominator of ½, we will need to multiply ½ by 4/4.
½ 4/4 = 4/8 or 4 slices = ½ pizza. Each person gets 4 slices.
To check that this is an equivalent fraction, we can factor a 4
from both the numerator and denominator and end up back
where we started – ½.
Remember when multiplying fractions, we multiply the
numerators together and the denominators together. You do
not need a common denominator to multiply fractions
together.
Example F: So now, everyone has left and you have uneaten
pizza. You have ½ of a pizza in a box and 3/4 of a pizza in a
second box. How much pizza do you have?
You must have a common denominator to add or subtract
fractions.
I want to add ½ to 3/4. First I find my common denominator. It
will be 8. I will need to convert both the ½ and the ¾ to 8th's. To
do this, I will multiply the ½ by 4/4 and the ¾ by 2/2.
{(1/2)(4/4)}+{(3/4)(2/2)} = 4/8 +6/8 = 10/8. 10 slices of pizza, but I
want to convert this into a mixed fraction so I will divide 10 by
8 and put the remainder over the denominator.
10
/8 = 1 whole and the fraction 2/8. 2/8 can be reduced by factoring
a 2 from both the numerator and denominator.
2/8 is equivalent to ¼
I have 1¼ pizzas remaining.
I hope this has helped! There will be time for questions on
this handout and fractions in general in class Monday,
November 30.
For more explanation, please see the following online resources:
http://www.math.com/homeworkhelp/HotSubjects_fractions.html
http://www.mathsisfun.com/fractions.html