Division

 Is a fast way to subtract. It only works when
you taking away the same number each time.
It is repeated subtraction.
 Division is the opposite of multiplication.

 40 − 5 − 5 − 5 − 5 − 5 − 5 − 5 −
5
 40 put into groups of 5 is 8
 40 ÷ 5 = 8
 Therefore, a 40 L tank can fill 8 five-litre bottles

40 sticks divided by 5 in
a group. We have 8
groups.

 A division expression can be viewed as
 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 ÷ 𝑑𝑖𝑣𝑖𝑠𝑜𝑟 = 𝑞𝑢𝑜𝑡𝑖𝑒𝑛𝑡
 40 ÷ 5 = 8
 40 =dividend, 5= divisor, 8=quotient
 If the dividend cannot be completely
divided by the divisor, it has a
remainder.

 Key words that equivalent to division
**Be careful of the phrase “out of” and not
to confused with “of”
3 out of 4 is 0.75 (division)
1/2 of 8 is 4 (multiplication)

Division is reverse of multiplication
e.g.
36 ÷ 3 is the same as 3 × ∎ = 36
In multiplication, 4 × 3 = 3 × 4
However, 10 ÷ 5 ≠ 5 ÷ 10
Think: 10 apples divided by 5 persons is not the
same as 5 apples divided by 10 persons.

 “6 eggs divided by 2 persons” is the same “12
eggs divided by 4 persons” or “6000 eggs
divided by 2000 persons”
 From the above example, you can see if I
double the number of eggs but also double the
number of persons, each person should still
have the same share.
 We learn a very important fact about division –
we can simplify the division for easier
manipulation.

270 ÷ 54
= 270 ÷ 2 ÷ 54 ÷ 2
= 135 ÷ 27
= 135 ÷ 3 ÷ 27 ÷ 3
= 45 ÷ 9
= 5
This may look clumsy in this example, but you
may find this method incredibly useful when you
need to deal with large numbers and algebraic
expressions

 𝒅𝒊𝒗𝒊𝒅𝒆𝒏𝒅 ÷ 𝒅𝒊𝒗𝒊𝒔𝒐𝒓 = 𝒒𝒖𝒐𝒕𝒊𝒆𝒏𝒕

𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 ÷ 𝑠𝑜𝑚𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 ÷ 𝑑𝑖𝑣𝑖𝑠𝑜𝑟 ÷ 𝑠𝑎𝑚𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 = 𝑞𝑢𝑜𝑡𝑖𝑒𝑛𝑡

𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 × 𝑠𝑜𝑚𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 ÷ 𝑑𝑖𝑣𝑖𝑠𝑜𝑟 × 𝑠𝑎𝑚𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 = 𝑞𝑢𝑜𝑡𝑖𝑒𝑛𝑡

 3 L of water poured into half-litre bottles.
How many half-litre bottles are needed?
 Ans:
6 bottles

 Mathematically, we formulate the above
question as:
 3 ÷
1
2
= 6
 Or we can rewrite our expression 3 ÷
1
2
as
 3 × 2 ÷
1
2
× 2 = 6 ÷ 1
= 6

 12 ÷
2
3
= 12 ×
3
2
÷
2
3
×
3
2
= 12 ×
3
2
72 ÷ 1
1
3
= 72 ÷
4
3
= 72 ×
3
4

 When a number divided by a fraction, the net
effect is equivalent to multiply the reciprocal of
the divisor!!
 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 ÷
𝑚
𝑛
= 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 ×
𝑛
𝑚

 To compare two ore more fractions size, which
one is bigger and which one is smaller, the
standard way is to convert the fractions into
fractions with same denominator.
 This method will always work. However, it
may not be not best or fastest way in some
cases.
 This presentation is to show the faster method.

 If two fractions with the same numerator, but
different denominator, e.g.
1
7
,
1
11
, the bigger of
the denominator, the smaller of number.
 Try this: arrange the fractions below in
ascending order*

2
153
,
2
41
,
2
197
,
1
3
,
2
9
,
4
204
 Ascending order means from the smallest to the
largest

 Can you sort the following numbers in
descending order? (without use of calculator)

2
3
,
7
8
,
5
6
,
127
128

 In primary school, quotient is always smaller
than dividend, e.g. 100 ÷ 4 = 25 , 25 < 100
 In secondary school, you may also notice that
quotient can be greater than the dividend, e.g.
4 ÷
1
2
= 8 , 8 > 4
 Does it make sense? Why?
 Think about the following question

 Ans: 4 ÷
1
2
= 8 8 people
 This is a perfect example of how quotient can
be greater than dividend.

 If divisor > 1, quotient < dividend
 𝑒. 𝑔. 12 ÷ 2 = 6 6 < 12
 If divisor =1, quotient = dividend
 𝑒. 𝑔. 45 ÷ 1 = 45 45 = 45
 If divisor < 1, quotient > dividend
 𝑒. 𝑔. 18 ÷
2
3
= 27 27 > 18
This can be
very useful
for checking
your answer
and see if the
answer makes
sense.

Performing division for decimals are
exactly the same as in normal division
except, you need to make sure the
decimal point of the dividend and
quotient are aligned.
e.g.
7.6 ÷ 2
= 3.8

 381.3 ÷ 3
= 12.3
 In this example, we used long division.
For the one who did know how to do
long division, don’t worry. As long as
you know how to perform division by
any method e.g. short division and
know where to put the decimal point,
your answer should be right.
 *Long division is very useful to deal
with division in algebraic expression. I
am highly recommend you learn some
basic operation.

 e.g 1.8072 ÷ 0.06
 Remember that if we multiply the dividend
and divisor by the same number, we still can
get the same quotient
 1.8072 × 100 ÷ 0.06 × 100
= 180.72 ÷ 6


 What we have just learned is that we can shift
the same decimal points of both dividend and
divisor. Here are a few more examples:

Division

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