This document provides an introduction to fractions. It begins by defining what a fraction is and using circles to represent whole numbers and fractions. It then covers addition and subtraction of fractions by explaining how to find common denominators. Multiplication of fractions is explained as multiplying the numerators and denominators. Division of fractions is described as equivalent to multiplying by the inverse fraction. Examples are provided for addition, subtraction, multiplication and division of fractions.

1. Outline
What is a fraction?
Addition and Subtraction
Multiplication
Division
An Introduction to fractions
January 21, 2010
An Introduction to fractions

2. Outline
What is a fraction?
Addition and Subtraction
Multiplication
Division
What is a fraction?
Whole Numbers
Halves, Quarters and Eighths
Addition and Subtraction
Multiplication
Division
An Introduction to fractions

3. Outline
What is a fraction?
Whole Numbers
Addition and Subtraction
Halves, Quarters and Eighths
Multiplication
Division
Whole Numbers - Integers
Whole numbers are numbers that have no decimal points.
These numbers can also be called integers. The integers are
the set of all whole numbers (both positive and negative. i.e.
An Introduction to fractions

4. Outline
What is a fraction?
Whole Numbers
Addition and Subtraction
Halves, Quarters and Eighths
Multiplication
Division
Whole Numbers - Integers
Whole numbers are numbers that have no decimal points.
These numbers can also be called integers. The integers are
the set of all whole numbers (both positive and negative. i.e.
..., −3, −2, −1, 0, 1, 2, 3, ...
An Introduction to fractions

5. Outline
What is a fraction?
Whole Numbers
Addition and Subtraction
Halves, Quarters and Eighths
Multiplication
Division
Whole Numbers - Integers
Whole numbers are numbers that have no decimal points.
These numbers can also be called integers. The integers are
the set of all whole numbers (both positive and negative. i.e.
..., −3, −2, −1, 0, 1, 2, 3, ...
At this stage we will deal only with the positive integers which
are sometimes called the Naturals. i.e.
An Introduction to fractions

6. Outline
What is a fraction?
Whole Numbers
Addition and Subtraction
Halves, Quarters and Eighths
Multiplication
Division
Whole Numbers - Integers
Whole numbers are numbers that have no decimal points.
These numbers can also be called integers. The integers are
the set of all whole numbers (both positive and negative. i.e.
..., −3, −2, −1, 0, 1, 2, 3, ...
At this stage we will deal only with the positive integers which
are sometimes called the Naturals. i.e.
0, 1, 2, 3, ...
An Introduction to fractions

7. Outline
What is a fraction?
Whole Numbers
Addition and Subtraction
Halves, Quarters and Eighths
Multiplication
Division
Representing whole numbers and fractions
We will represent whole numbers by circles, and fractions by parts
of those circles. i.e.
Figure: Represents the number ’3’
and
Figure: Represents the number ’2 1 ’
2
An Introduction to fractions

8. Outline
What is a fraction?
Whole Numbers
Addition and Subtraction
Halves, Quarters and Eighths
Multiplication
Division
Halves, Quaters and Eighths
We can represent two different fractions by two different circles.
Two fractions are equal if the shaded area in each circle is the
same. i.e.
3 6
Figure: 4 and 8
While the two fractions contain different numbers, they must
actually be equal.
An Introduction to fractions

9. Outline
What is a fraction?
Addition and Subtraction
Multiplication
Division
Common Denominators
Before we can add or subtract any fractions, we must always
ensure that both fractions have common denominators. (The
denominator is the number on the bottom of a fraction)
Example
1/2 + 1/8
In this example we must make sure that the number on the
bottom of both fractions is the same. The easiest way to do this is
to change the 1/2 into 4/8. Recall that these two fractions are in
fact equal.
= 4/8 + 1/8
Now we simply add the numerators (top number) of both fractions.
= 5/8
Try a few examples yourself.
An Introduction to fractions

10. Outline
What is a fraction?
Addition and Subtraction
Multiplication
Division
Questions
Try these questions yourself:
1/4 + 3/8 =
1/2 + 3/8 =
1/4 + 1/8 =
3/4 + 5/8 =
2/3 + 3/4 =
An Introduction to fractions

11. Outline
What is a fraction?
Addition and Subtraction
Multiplication
Division
Multiplication of fractions
Multiplying fractions is much easier than adding or subtracting. All
you need to do to multiply two fractions is multiply the numerators,
and the denominators. i.e. Just multiply straight across.
Example
2 3
5 × 4 =
2×3
5×4 =
6
20 =
3
10
We must be careful to always reduce a fraction to it’s lowest
possible form.
An Introduction to fractions

12. Outline
What is a fraction?
Addition and Subtraction
Multiplication
Division
Questions
3 2
8 × 5 =
2 6
9 × 7 =
5 8
3 × 7 =
An Introduction to fractions

13. Outline
What is a fraction?
Addition and Subtraction
Multiplication
Division
Division
Dividing fractions is very similar to multiplication, however we
must do one small step to begin with. We start by saying that all
whole numbers can be written as a fraction. i.e. 3 can be written
as 3 . Now if we divide a number by say three, it is the same as
1
taking one third of the original number.
Example
12 ÷ 3 = 4
1
and 12 × 1 = 4
3
From this example it seems that dividing by any fraction is the
same as multiplying by the inverse (upside down) fraction. This is
in fact the case. If you ever need to divide a fraction, simply
change the divide to a multiply andAn Introductionsecond fraction upside
turn the to fractions

14. Outline
What is a fraction?
Addition and Subtraction
Multiplication
Division
Questions
4
5 ÷27
7
3 ÷45
12
5 ÷ 17
4
An Introduction to fractions