Mathematics 3.
March 25, 2012
Lesson #19. Classwork.
Fractions. A fraction is a part of a whole
1
/2
1
One-Half
3
/4 One-Quarter
/8 Three-Eighths
The top number tells how many slices you have
The bottom number tells how many slices the pizza was cut into.
Numerator / Denominator
We call the top number the Numerator, it is the number of
Numerator
parts you have.
---
We call the bottom number the Denominator, it is the
Denominator
number of parts the whole is divided into. You just have to
remember those names! (If you forget just think "Down"-Dominator)
Equivalent Fractions
Some fractions may look different, but are really the same, for example:
4
/8
(Four-Eighths)
=
2
/4
Two-Quarters)
=
1
/2
(One-Half)
It is usually best to show an answer using the simplest fraction ( 1/2 in this case ).
That is called Simplifying, or Reducing the Fraction
Three Types of Fractions
There are three types of fraction:
So we can define the three types of fractions like this:
The numerator is less than the denominator
Proper Fractions:
Examples: 1/3, 3/4, 2/7
The numerator is greater than (or equal to) the denominator
Improper Fractions:
Examples: 4/3, 11/4, 7/7
A whole number and proper fraction together
Mixed Fractions:
Examples: 1 1/3, 2 1/4, 16 2/5
Proper Fractions
So, a proper fraction is just a fraction where the numerator (the top number) is less than the
denominator (the bottom number). Here are some examples of proper fractions:
1
/2
(One-Half)
1
/4
(One-Quarter)
3
/8
(Three-Eighths)
Improper Fractions
An Improper fraction has a top number
larger than (or equal to) the bottom number
Examples
3
7
/2
7
/4
16
/15
15
/15
99
/5
/4 (seven-fourths or seven-quarters)
It is "top-heavy"
See how the top number is bigger than (or equal to) the bottom number?
So, an improper fraction is just a fraction where the top number (numerator) is greater
than or equal to the bottom number (denominator). In other words, it is top-heavy.
Can be Equal. What about when the numerator is equal to the
denominator? For example 4/4 ? Well, it is obviously the same as a
whole, but it is written as a fraction, so most people agree it is a type of
improper fraction.
Mixed Fractions
A Mixed Fraction is a whole number
and a proper fraction combined.
such as 1 3/4.
1 3/4
(one and three-quarters)
Examples
You can use either an improper fraction or a mixed fraction to show the same amount. For
example 1 3/4 = 7/4, shown here:
1 3/ 4
7
/4
=
See how each example is made up of a whole number and a proper fraction together? That
is why it is called a "mixed" fraction (or mixed number).
Converting Mixed Fractions to Improper Fractions
To convert a mixed fraction to an improper fraction, follow these steps:
•
•
•
Multiply the whole number part by the fraction's denominator.
Add that to the numerator
Write that result on top of the denominator.
Example: Convert 3 2/5 to an improper fraction.
Multiply the whole number by the denominator: 3 × 5 = 15
Add the numerator to that: 15 + 2 = 17
Then write that down above the denominator, like this: 17/5
Converting Improper Fractions to Mixed Fractions
To convert an improper fraction to a mixed fraction, follow these steps:
•
•
Divide the numerator by the denominator.
Write down the whole number answer
Example: Convert 11/4 to a mixed fraction. Divide:
11 ÷ 4 = 2 with a remainder of 3
Write down the 2 and then write down the remainder (3) above the denominator (4), like
this: 2 3/4
When to Use Improper Fractions or Mixed Fractions
For everyday use, people understand mixed fractions better:
Example: It is easier to say "I ate 2 1/4 sausages", than "I ate 9/4 sausages"
But for mathematics improper fractions are actually better than mixed fractions.
write down any remainder above the denominator
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