Name of Lecturer: Mr. J.Agius
Course: FCES
LESSON 13
Fractions
13.1 Reciprocals
If the product of two numbers is 1, then each number is called the reciprocal of the
other.
We know that
so
To find the reciprocal of
we require the number which, when multiplied by , gives 1.
Now
is the reciprocal of 3 and 3 is the reciprocal of .
So
is the reciprocal of
In all cases the reciprocal of a fraction is obtained by turning the fraction upside down.
,…
Any number can be written as a fraction. E.g.
,
So
is
or
13
is
or
25
the reciprocal of
The reciprocal of
2.5
The reciprocal of a number is 1 divided by that number,
Example 13a
Find the reciprocal of
a) 25
b)
2
5
Answer
a)
The reciprocal of 25 
1
25
b)
The reciprocal of
2 5

5 2
Exercise 13a
Find the reciprocal of
a)
5
b)
Learning Outcome 1 – Numerical Calculations
3.5
c)
Page 81
Name of Lecturer: Mr. J.Agius
Course: FCES
13.2 Division By a Fraction
Consider
This can be interpreted as
Now
is the reciprocal of , i.e. .
Therefore
i.e., to divide by a fraction we multiply by its reciprocal.
Example 13b
Find
(Before multiplying or dividing, mixed numbers must be changed into improper
fractions.)
Exercise 13b
Find
a)
b)
c)
d)
Learning Outcome 1 – Numerical Calculations
Page 82
Name of Lecturer: Mr. J.Agius
Course: FCES
13.3 Mixed Multiplication and Division
Suppose we want to find the value of an expression like
. Two things need
to be done:
Step one – If there are any mixed numbers, change them into improper fractions.
Step two – Turn the fraction after the  sign upside down and change  into .
Then
(Step 1)
(Step 2)
Exercise 13c
Find
a)
b)
c)
d)
Learning Outcome 1 – Numerical Calculations
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Name of Lecturer: Mr. J.Agius
Course: FCES
Mixed Exrecises
1)
Work out
a)
b)
c)
d)
e)
f)
g)
h)
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
2)
3)
Work out
A grocer buys pieces of cheese weighing 5kg.
a)
How many kg pieces can he get from this?
b)
4)
How many kg pieces can he get from this?
A box is
inches long, 5 inches wide and
inches high.
Toy bricks are cubes with edges
inches long.
How many toy bricks can fit into the box?
5)
Jermaine’s car does 35 miles per gallon and he has 6 gallons of petrol in the tank.
How many times can he go to Fiona’s house and back if Fiona lives
miles away
from Jermaine.
6)
A bookshelf is
a)
inches long. How many books can fit on the shelf if each book is
inch thick?
b)
inches thick?
c)
inches thick?
Learning Outcome 1 – Numerical Calculations
Page 84