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Name of Lecturer: Mr. J.Agius
Course: HVAC1
Lesson 8
Chapter 2. Fractions

Multiplying Fractions

When multiplying together two or more fractions, first multiply all the numerators
together and all the denominators together. (There is no need to find a common
denominator).

Mixed numbers cannot be multiplied together unless one changes them into improper
fractions first.

It would be easier if one cancel factors that are common to the numerator and
denominator before multiplication since one can multiply smaller numbers easier.

The answer shall be expressed to its lowest term and as a mixed number where possible.
Example 1
Simplify
Step 1: Change any mixed number into an improper fraction. i.e.
Step 2: The whole number 5 is treated as .
So
Step 3: Cancel factors that are common to the numerator and denominator before multiplication.
So
2 Fractions
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Name of Lecturer: Mr. J.Agius

Course: HVAC1
Fractions of Quantities
Sometimes in calculations with fractions the word ‘of’ appears. It should always be taken as
meaning multiply. Thus, to find of the number of tiles on this floor, one need to find how
many tiles are there on the floor and then multiply the
answer by .
There are 12 × 12 tiles = 144 tiles on this floor.
12 tiles
So
tiles.
12 tiles
Example 2
Find three fifths of 95 metres.
Three fifths of 95 means
So

3
of 95 metres is 57 metres.
5
Reciprocals
If the product of two numbers is 1, then each number is called the reciprocal of the other.
For example;
1
 3  1 so
3
So, to find the reciprocal of
Now
4 3
 1
3 4
1
1
is the reciprocal of 3 and 3 is the reciprocal of .
3
3
3
3
one needs the number which, when multiplied by , gives 1.
4
4
So
4
3
is the reciprocal of
3
4
In all cases the reciprocal of a fraction is obtained by turning the fraction upside down.
Remember that any number can be written as a fraction. i.e.
So the reciprocal of
2 Fractions
is
.
or 1  3.
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Name of Lecturer: Mr. J.Agius
Course: HVAC1
Example 3
Find the reciprocal of;
a) The reciprocal of 14 (
a) 14
) is
b) 3.5
.
b) In order to find the reciprocal of 3.5 one needs to change this number into an improper
fraction. i.e. 3.5

=
. So the reciprocal of
is
.
Dividing Fractions

When dividing together two fractions, first find the reciprocal of the divisor (the number
after the division sign).

Before starting to work, change all the mixed numbers into improper fractions.

Now change the division sign into multiplication and work as usual.

Remember that the answer shall be expressed to its lowest term and as a mixed number
where possible.
Example 4
Work out
.
Before multiplying or dividing, mixed numbers must be changed into improper fractions.
So
2 Fractions
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Name of Lecturer: Mr. J.Agius
Course: HVAC1
Multiplying Fractions
Q1
Multiply the following quantities:
a)
b)
c)
d)
e)
f)
Q2
Multiply the following quantities:
a)
b)
c)
d)
e)
f)
Q3
Four pieces of wood each
inches long are needed to build a cabinet. To get all four pieces
from one board, how long must that board be?
Q4
In making a chair,
feet of oak are used, including waste. How many feet of oak are needed
to complete an order of 64 chairs?
Q5
Beams are placed
m apart on a roof. If there are 6 beams from end to end, find the length of
the floor? (First check how many spaces there are).
Q6
This picture represents a square thread of a bolt. If each thread has
mm pitch, find the total
length of 12 threads.
Thread
pitch
2 Fractions
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Name of Lecturer: Mr. J.Agius
Course: HVAC1
Dividing Fractions
Q1
Divide the following quantities:
a)
b)
c)
d)
e)
f)
g)
h)
i)
Q2
An ironmonger buys 50 kg cement. How many
Q3
Determine the number of pieces of
Q4
Find how many threads
Q5
A bookshelf is
a)
kg bags can he get from this?
inch plywood in a stack 45 inches high.
mm pitch there are in a bolt of
inches long.
inches long. How many books can fit on the shelf if each book is
b)
inch thick?
inch thick?
c)
inch thick?
Q6
What is the height of each riser in a stair with 14 risers and a total rise of
Q7
How many treads are needed for a set of stairs with a total run of
tread is
inches?
inches when each
inches wide?
Height
of riser
Total rise
(floor to top
of top tread)
Run or
width of
one thread
Total run of
stairs
2 Fractions
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