Positive and negative numbers

Positive and negative numbers can represent or describe
many different situations which demonstrate the
concept of opposites:
bullet

Numbers on a number line.


bullet Temperatures on a thermometer: Temperatures above zero degrees are positive (+10) and temperatures below zero degrees are negative (-10).

bullet Sports scores: If your favorite football team gained 4 yards during the big game, it could be represented by +4. Should your team lose 4 yards, it could be represented by –4.

bullet Weight gain and loss: Sam gained 8 pounds while on a Caribbean cruise (+8), but lost the 8 pounds after he returned home (-8).

bullet Geography: A location in Death Valley has an elevation of -282 feet (which is below sea level), while a location near Coffin Peak has an elevation of +282 feet (which is above seal level).

bullet Altitude: An airplane leaves the airport and climbs to an altitude (height) of 2500 feet (+2500). To land, the plane must lose 2500 feet of altitude (-2500).

bullet Profit and loss: A candy store lost $28,400 (-28,400) the first year of business but recovered the amount (+28,400) the second year.

bullet Recorded time: When referring to historical times, 2000 years BC (-2000) can be compared to 2000 years AD (+2000).

bullet Elevator movement: The elevator went up 15 floors
(+15), and then went down 15 floors (-15).

Adding Signed Numbers


Rules:
When you add two numbers with the same signs,
1. add the absolute values, and
2. write the sum (the answer) with the sign of the
numbers.
When you add two numbers with different signs,
1. subtract the absolute values , and
2. write the difference (the answer) with the sign of
the number having the larger absolute value.

Examples: Add :

1. -9 + (-7) = -16
2. –20 + 15 = -5
3. (-23) + (-7) = -30
4. (+3) + (+5) = 8
5. 6 + (-2) = 4
6. (-21) + 21 = 0
7. –3 + 8 = 5
8. -9 + 6 = -3
9. Add -9 and -5. Answer: -14
10. Add (-7), (+3), and (-12). Answer: -16


Subtracting Signed Numbers

Rule: You can subtract a number by adding its opposite.

Examples: Subtract :

1. 9 – (- 3) = 5. -10 - (-15) =
9 + (+3) = 12 -10 + (+15) = 5


2. -7 – (-5) = 6. -25 - (+25) =
-7 + (+5) = -2 -25 + (-25) = -50


3. 21 – (-19) = 7. 3 - (+5) =
21 + (+19) = 40 3 + (-5) = -2


4. - 5 - 4 = 8. 9 - 3 =
- 5 + (-4) = -9 9 + (-3) = 6


9. Subtract (-5) from (10).
10 - (-5) = 10 + (+5) = 15


10. Subtract 4 from (-14).
-14 - 4 = -14 + (-4) = -18

Multiplying and Dividing Signed Numbers


Rules:

Multiplying ...

* The product of two numbers with the same signs is positive.
* The product of two numbers with different signs is negative.

Dividing ...

* The quotient of two numbers with the same sign is positive.
* The quotient of two numbers with different signs is negative.

Examples:
Perform the indicated operations:


1. (+3) (–5) = -15 5. – 12 (-3) = 4


2. (–8) (7) = -56 6. –27 3 = -9


3. (–6) (-5) = 30 7. –6 (-8) = 0.75


4. (+4) (+3) = 12 8. –18 / 2 = -9


9. Multiply (-5) by (-3).
(-5) x (-3) = +15


10. Divide (-24) by (+6).
(-24) / (+6) = -4


Using Your Calculator with Signed Numbers

f your scientific calculator has the
"change sign" key PlusMin.gif ,
you can use it to find the opposite of a number.

On most scientific calculators, this key is pressed
AFTER the number is entered.

On most graphing calculators, this key is pressed
BEFORE the number is entered.