Chapter 6. Section 1
Page 1
Section 6.1 – The Set of Fractions
Homework (page 226) problems 1-12
A Historical Perspective:
• To understand fractions we need to have a concept of discrete versus continuous
• As soon as we want to divide a single whole into parts we are faced with the inadequacy of whole
numbers
• 'Parts of a whole' is one way to explain fractions. But there are other ways. In cutting a cake, what
is passed to each person at a party is a single piece of cake, not a tenth of a cake. If we have another
piece, we think of two pieces, not two tenths. This is the way most ancient people treated fractions,
they avoided them by resorting to smaller units. So 3/4 was not regarded as 3 parts of a whole, but
as three of a new and smaller entity
• For example, we use ideas of part of a whole without using fractions every day. We split the unit up
into smaller 'units'. Can you think of two?
Definitions:
• The part to whole model of a fraction is represented by
a
b
, where a and b are whole numbers
(
0
b
≠
). Here we have a equal parts (or portions) of all parts (or the whole) b
• We can represent fractions visually with set, area or number line models
• Example, page 228 number 2. Illustrate 4/7
• Example, page 228 number 1a. (see figure)
5
8
• Example, page 228 number 1d. (see figure)
This is a bit misleading, because you don't want to assume that the 'whole' is 12
Doing so you would arrive at the solution
9
12
(which is wrong)
In reality, when you use a ruler, you measure parts of the whole out of one unit
So you would therefore have
119
22
444
+==
• In the fraction
a
b
, a is called the numerator and b is called the denominator
