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Name of Lecturer: Mr. J.Agius
Course: HVAC1
Lesson 5
Chapter 2. Fractions

Equivalent Fractions
A fraction is a part of a whole. If one divides a piece of plywood into 2 equal parts, each part
can be written as of the original size. Furthermore, if one divides the same piece of plywood
into four parts and takes two, one can see that is equivalent to .
One can say that , , , etc all mean the same thing.
These are called equivalent fractions. They can all be written as .
is the simplest form because it has the smallest numbers.
To find equivalent fractions, multiply (or divide) the top and bottom by the same number.
×4
÷3
=
=
×4
÷3
The top number of a fraction
is called the numerator.
To
note:
9

The bottom number of a fraction is
called the denominator.
Reducing a Fraction to its Lowest Terms
Fractions like , , , and are said to be in their lowest terms because it is impossible to find a
number which will divide exactly into both the numerator and denominator. There exists other
fractions like , , , which are not in their lowest terms because they can be reduced
further by dividing both numerator and denominator by a number which divides exactly into
both of them. So
2 Fractions
Page 1
Name of Lecturer: Mr. J.Agius
Course: HVAC1
÷2
÷4
=
=
÷2
÷4
÷ 30
÷ 11
=
=
÷ 30
÷11
Sometimes one can divide the numerator and the denominator several times before one reaches
the lowest terms.
Example 1
Reduce
to its lowest terms.
÷5
÷3
=
÷5

÷3
=
÷3
9
=
9
÷3
Types of Fractions
If the numerator of a fraction is less than its denominator the fraction is called a proper
fraction. , , , and are all proper fractions. Note that a proper fraction has a value which is
less than 1.
If the numerator of a fraction is greater than its denominator then the fraction is called an
improper fraction. , , , and
are all improper fractions. Note that an improper fraction
has a value which is greater than 1.
Every improper fraction can be expressed as a whole number and a proper fraction together.
These are called mixed numbers. , ,
, and
are all mixed numbers.
Consider these two sheets of plywood.
One can say that there is 1 whole sheet and 4 parts out of seven from another sheet. The total
number of sheets can be expressed as
sheets. But if one divides the first sheet into 7 equal
parts, the total becomes
2 Fractions
sheets, which is an improper fraction. So
and
are equal.
Page 2
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Example 2
How many pieces of plywood are there if there are
be divided into 9 pieces.
sheets of plywood and each sheet has to
Each sheet has to be divided into 9 pieces means that;
9
+
9
+
5
= 23
ANSWER: There are 23 pieces of plywood.
Example 3
Express the mixed number
as an improper fraction.
represents 2 whole parts plus of another part.
One can use the same method as done in Example 2 and say that there are 23 parts.
So in this case
can be written as
.
To convert from mixed numbers to improper fractions faster, multiply the denominator with the
whole number and add the answer with the numerator to find the numerator of the answer. Put
this answer onto the same denominator.
i.e.
Example 4
Express
as a mixed number.
First divide 13 by 4 to find how many times, 4 goes into 13 and see, what is the remainder left.
3 r1
4 13
So
can be written as
.
3 represents the number of times 4 goes into 13 and 1 represents the remainder left.
2 Fractions
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Name of Lecturer: Mr. J.Agius
Course: HVAC1
Manipulating Fractions
Q1
Express each of the following fractions as eighths. (Denominator equal to 8)
a)
b)
c)
d)
e)
f)
g)
h)
Q2
Express each of the following fractions as fifteenths. (Denominator equal to 15)
a)
b)
c)
d)
e)
f)
g)
h)
Q3
Find the missing number in each of these.
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
Q4
Write these fractions in their simplest form.
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
m)
n)
o)
p)
Q5
Change these mixed numbers into improper fractions.
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
Q6
Change these improper fractions into mixed numbers.
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
2 Fractions
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