

Meaning and Models  Key
Ideas 
 Adding negative numbers  Subtracting
negative numbers Multiplying negative numbers
 Dividing negative numbers 
Meaning
and Models quiz
answers
1.

Write each of the following as directed numbers: 

a)
150 metres below sea level, 150 metres 

b)
a fine of $75, $75 

c)
a temperature drop of 8 degrees, 8 degrees 

d)
1973 metres above sea level, +1973 metres 

e)
a lead of 25 metres, +25 metres 

f)
a drop of 30 centimetres, 30 centimetres 

g)
a loan of $1500, $1500 

h)
a profit of $300, +$300 


2. 
a)
If the temperature in the city today was 11 degrees and it dropped
by 5 degrees overnight, the minimum temperature was 11  5 = 6
degrees. 



b) If the temperature was only 8 degrees in The Dandenongs
during the day and dropped by 10 degrees overnight, the minimum
temperature reached was 8  10 = 2 degrees.




c)
The temperature at Mt Hotham last night was 3 degrees and has
risen to 7 degrees today. The temperature rose from 3 to 7, that
is the difference between 7 and (3) which is found by subtraction:
7  (3) = 10. So although the temperature is only 7 degrees now
is rose 10 degrees (from 3) overnight. 


3. 
a)
If Clara and Than actually climbed 100 metres and they started
off at 20 metres below sea level then they climbed to '20 +
100' metres above sea level, which is 80 metres above sea level.
b)
If Clara and Than climbed a further 450 metres, then they would
now be 80 + 450 metres above sea level, i.e. 530 metres above
sea level.

Key
Ideas quiz
answers
1. 
a)
6 > 1


b)
 9 > 12 

c)
0 > 3


d)
17 > 17 

e)
6 > 5 > 22


f)
41 < 8 and 2 < 8 so 41<2<8 


2. 
Order
the following sets of numbers from smallest to largest. 

a)
9, 7, 1, 1/3, 0, 0.5, 3, 7, 71


b)
15, 12, 9, 6, 3, 0, 0.15, 12 

c)
157, 31, 4, 1.3, 0.4, 0, 1/5, 4 

d)
419, 328, 325.36, 125, 2, 0, 12/15, 10, 12.5 


3. 
a)
45  79 = 34 

b)
53  (78) = 131 

c)
34 + 9 = 25 

d)
( 168)  94 = 262 

e)
67  ( 5) + 2 = 70 

f)
19 + (5)  17  3 = 44 


4. 
Put
the following numbers on a number line. 

0.22,
1.8, 0.17, 0.17, 1/17, 1/17, 1, 1 1/4, 1/4. 

The
numbers would be arranged in the following order on a number
line:
2,
1.8, 1, 0.17, 1/17, 0,
1/17, 0.17, 0.22, 1/4, 1, 1 1/4,
2



5. 
Which
is the greatest number? 

a)
(5), (4) or (1) Answer = 1 

b)
(10) ,(0) or (+0.1) Answer = +0.1 

c)
(0.1), (0.2) or (1/2) Answer = 0.1 
Adding negative numbers quiz
answers
1. 
a)
6 + (3) = 3 

b)
7 + 4 = 3 

c)
8 + (5) = 13 

d)
12 + (3) = 15



2. 
a)
14 + 6 = 8


b)
8 + 10 = 2


c)
22 + 13 = 35


d)
7 + (14) = 21


e)
15 + 5 + (8) + (7) + 10 = 15


f)
13 + 9 + (11)  3 = 10


g)
22 + (19) + 4 + (6) + 2 = 41


h)
10 + (11) + 1 + 2  3 = 21



3. 
The
water level was at the full mark after Winter. After Summer
it dropped by 5 metres and after Autumn it was raised by 1 metre.
So,
since Winter the water level has moved by, 5 + 1 metres (=
4 metres). This means it has dropped by 4 metres.
Therefore,
the current level of the reservoir is 4 metres below the full
mark.

Subtracting negative
numbers quiz
answers
1. 
a)
6  (+3) = 3


b)
7  4 = 11


c)
8  (5) = 3


d)
8 + 5 = 3



2. 
a)
4  16 = 20


b)
10  19 = 9


c)
22 13 = 35


d)
7  (14) = 7


e)
9  (5) + 15  7  (4) = 8


f)
12  (4) + (3)  9 + (11)  5 = 12


g)
6 + 8  (9) + 7 (10) = 28


h)
5  (17)  25 + (13) + 26 = 0



3. 
The
final balance is obtained by adding all the transactions.

1235.99

583.00

299.00


25.75


60.00

784.21

201.00


545.47




4. 
a)
From level B2, you need to travel 1 level up to get to B1.
b)
From level B2, you need to travel 2 levels up to get to ground
level.
c)
If I am shopping on level 5 of the shopping centre and I have
parked on level B3, I need to travel 8 levels down to get to
my car.
b
If I park on level B2, I need to travel 4 levels up to get to
level 2.



5. 
Write
each of the problems above as an addition or subtraction of
negative numbers. The first is done for you.
a)
(1)  (2) = 1 (the difference between B1 and B2)
or,
(2) + ? = 1, (2) + (1) = 1
b)
0  (2) = 2 (the difference between ground and B2)
or,
(2)
+ ? = 0, (2) + 2 = 0
c)
(3)  5 = 8 (the difference between B3 and level 5)
or,
5  ? = 3, 5  (8) = 3
d)
2  (2) = 4 (the difference between level and B2)
or,
(2) + ? = 2, (2) + 4 = 2

Multiplying negative
numbers quiz
answers
1. 
a)
3 x 2 = 6 

b)
4 x 5 = 20 

c)
7 x 1 = 7 

d)
3 x 6 = 18 


2. 
a)
2 x (4 x 5) 1 = 39 

b)
17 x 4 x 3 = 204 

c)
6 x (5) + 15 + (6) = 39 

d)
3  4 + (5 x 8) = 41 


3. 
Although
there is no adequate model to show that 4 x 5 = 20 we can
look at the patterns which emerge in the '4 times table' and
the '4 times table' or in the 'basic multiplication facts grid'.
We can also use the distributive law to show that this must
be the case.
See Multiplying Directed Numbers for more detail.



4. 
(a)
14 x (3  7) + (8 x 3) = (14 x 4) + (24) = 80
(b)
(4  (9)) x 2 + (6) = (4 + 9) x 2 + (6) = (5 x 2)  6 =
4



Dividing negative
numbers quiz
answers
1. 
a)
16 ÷ 4 = 4 

b)
40 ÷ 8 = 5 

c)
39 ÷ 13 = 3 

d)
12 ÷ 6 = 2 


2. 
a)
5(18 ÷ 9) = 10 

b)
5 + 4(12/3) = 11 

c)
(6 x 5) + (49 ÷
7) = 30 + (7) = 23 

d)
(128)/(4) + (144)/(3) = 32 + 48 = 16 


3. 
1st
quarter  $15 million loss
2nd quarter  $ 2 million profit
3rd quarter  $3 million loss
4th quarter  $4 million profit
To
find the average quarterly profit/loss we need to add these
amounts and then divide by the number of quarters.
15m
+ 2m + (3m) + 4m = 12 m
12
million / 4 =  4 million
So
the average quarterly loss was $ 4 million.





