STRAND: Number
TOPIC:
Positive & negative numbers
The meaning of
negative numbers
LITERACY TASK • Find the meanings of these key terms:
1. positive: ..............................................................................................................................................................................
2. negative:.............................................................................................................................................................................
3. integer: ...............................................................................................................................................................................
4. overdraft: ...........................................................................................................................................................................
5. credit: .................................................................................................................................................................................
6. overdrawn: ........................................................................................................................................................................
7. elevation:............................................................................................................................................................................
8. mean:..................................................................................................................................................................................
9. deviation: ...........................................................................................................................................................................
When we talk about positive numbers it is easy to visualise what they mean. For example, if we consider the number 5, it is
easy to visualise 5 objects. Negative numbers are more difficult to understand unless they are placed in context.
Negative numbers in finance:
Chris has a bank account with an overdraft facility ie. he can spend more money than he currently holds in the bank. When his
bank account is in credit, the balance is shown as an amount of money with a CR tag (for credit). When Chris’ account is
overdrawn, the balance is shown as an amount of money followed by DR (for debit or overdrawn).
A sample of Chris’ bank statement is shown below:
Date
Transaction
1 Jan
4 Jan
7 Jan
12 Jan
15 Jan
Withdrawal $500.00
Deposit $100.00
Withdrawal $300.00
Deposit $1000.00
Balance
$200.00CR
$300.00DR
$200.00DR
1. Complete the balance column of Chris’ statement.
2. Explain how positive and negative numbers relate to the bank balance in this situation.
3. Kylie has a balance in her account of $200.00DR. What is her balance after she makes the following five transactions:
withdrawal $400.00, deposit $250.00, withdrawal $392.00, withdrawal $712.00 and deposit $1000.00?
4. Kylie wants to close her bank account. What amount must she pay or receive upon closing the account to make the final
balance $0.
5. Other banks issue statements with balances reading $500.00+ or $500.00–. What do these balances mean?
 John Wiley & Sons Australia, Ltd 2001
STRAND: Number
TOPIC:
Positive & negative numbers
INVESTIGATION: The meaning of
negative numbers
Negative numbers in geography:
One of the most significant geographical features in North America is Death Valley in California. A cross-section of the valley
is shown below:
Telescope Peak
elevation: 3368 m
3500
Furnace Creek
elevation: –54 m
record high temperature
in North America (in the
shade): 134°F (July, 1913)
3000
Park Headquarters
elevation: –58 m
2500
2000
Lowest point in the
Western Hemisphere
elevation: –86 m
1500
Coffin Peak
elevation: 1677 m
1000
500
0
–500
DEATH VALLEY
6. Find the difference between the elevation of the highest peak and the lowest point in the valley.
7. Find the difference between the elevation at Furnace Creek and Park Headquarters.
8. Explain the meaning of a negative elevation in this context.
9. Julie hikes from the top of Telescope Peak to the lowest point in the valley and then to the top of Coffin Peak.
(a) What is the change in elevation between the start of Julie’s hike and the finish?
(b) What is the total change in elevation that Julie passes through? (Consider the elevation that Julie goes down and then
goes back up).
Negative numbers in temperature:
There are two units of temperature used around the world. In Australia, we use degrees Celsius (°C) while other places still use
degrees Fahrenheit (°F). Degrees Fahrenheit was used in Australia until 1972.
To convert from °C to °F the formula: F = 9--- C + 32 is used.
5
10. Water will freeze at 0°C. Use the formula to find what temperature water will freeze at in °F.
11. Water will boil at 100°C. Use the formula to find what temperature water will boil at in °F.
To convert from °F to °C the formula: C = 5--- (F – 32) is used.
9
12. Leong is holidaying in Malaysia where the temperature is given as 100°F. What is this in °C?
13. Jasmine is going skiing in Canada where the temperature is given as 5°F. Convert this temperature to °C.
14. Explain what is meant by a negative temperature in °C. Is this any different to the meaning of a negative temperature in °F?
15. Ethylene glycol is used as antifreeze in car radiators to prevent the water freezing at 0°C. When antifreeze is added to
radiator water, it will not freeze until it reaches –15°C. Convert this temperature to °F.
RESEARCH TASK ONE
Ocean water will not freeze at °C.
1. Why not?
2. At what temperature will ocean water freeze?
 John Wiley & Sons Australia, Ltd 2001
STRAND: Number
TOPIC:
Positive & negative numbers
INVESTIGATION: The meaning of
negative numbers
Negative numbers in statistics:
The table below shows the scores of 25 students on their maths exam.
Student
Mark
Student
Mark
Student
Mark
Anthea
42
Bradley
65
Cory
98
David
63
Ethan
36
Farood
77
Gai
48
Harry
74
Ian
80
Jerri
62
Kai
99
Leonie
24
Mary
65
Neville
62
Orville
72
Peter
69
Quentin
63
Raul
48
Susan
74
Tracey
67
Ursula
55
Valli
83
Wendy
71
Yvette
92
Zed
35
16. Find the mean mark.
17. The deviation of each student’s mark is found by subtracting the mean from each score. Now complete the table below:
Student
Deviation
Student
Deviation
Student
Anthea
Bradley
Cory
David
Ethan
Farood
Gai
Harry
Ian
Jerri
Kai
Leonie
Mary
Neville
Orville
Peter
Quentin
Raul
Susan
Tracey
Ursula
Valli
Wendy
Yvette
Deviation
Zed
18. Explain the meaning of a negative deviation.
 John Wiley & Sons Australia, Ltd 2001