Signed Numbers

Numbers can be represented geometrically by points on a number line.

A positive number is a number > (greater than) 0

A negative number is a number < (less than) 0

Absolute Value: is the number of units of distance from zero to any point on the number

line, and is denoted by , read, absolute value of a

3 units of distance

3 units of distance

Addition of Numbers of Like Signs

(1) Add the absolute values of the numbers

(2) The sign of the answer is the common sign

Examples: Add

(a)

(b)

(c)

(d)

Addition of Numbers of Unlike Signs

(1) Subtract the smaller absolute value from the larger absolute value

(2) The sign of the answer is the sign of the number with the larger absolute value

Examples:

(a)

(b)

(c)

(d)

Problems

Add

(1) –15 + 6 (5)

(2) –20 + 32 (6)

(3) –16 + (-14) (7) 9 + (-5) + (-8) + 4 + 3

(4) –17 + (-9) (8) –12 + 15 + (-11) + (-4) + 2

Answers

(1) –9 (5)

(2) 12 (6)

(3) –30 (7) 3

(4) –26 (8) –10

Subtraction of Signed Numbers

12 – 8 = 4 and 12 + (-8) = 4

Thus 12 – 8 = 12 + (-8)

We then have a definition for subtraction: a – b = a + (-b), where a and b are any

numbers

To Subtract Two Signed Numbers

(1) Change the operation from subtraction to addition and change the sign of the

second number

(2) Follow the methods of adding signed numbers

Examples: Subtract

(a)

(b)

(c)

(d)

Problems

Subtract

(1) – 8 – (-12) (4)

(2) 6 – 14 (5) 12 – (-17)

(3) – 3 – 9 (6)

Answers

(1) 4 (4)

(2) –8 (5) 29

(3) –12 (6)

Multiplication of Signed Numbers

Using the definition of multiplication:

2(-4) = (-4) + (-4) = -8

4(-3) = (-3) + (-3) + (-3) + (-3) = -12

When we multiply a positive number and a negative number, we get a negative product:

2(-3) = -6

1(-3) = -3

0(-3) = 0

(-1)(-3) = 3

Pattern suggests that when we multiply a negative number with a negative number, we get a positive product.

To Multiply Two Signed Numbers of Like Sign

(1) Multiply their absolute values

(2) Product is positive

Examples:

(a)

(b)

(c)

To Multiply Two Signed Numbers of Unlike Signs

(1) Multiply their absolute values

(2) Product is negative

Examples:

(a)

(b)

Problems:

Multiply

(1) (-8)(-12) (4)

(2) (-5)(9) (5)

(3) (6)

Answers

(1) 96 (4)

(2) –45 (5) 60

(3) (6) -60

Division of Signed Numbers

because

because 5(-3) = -15

because (-4)(7) = 28

Thus: To Divide Two Numbers of Like Signs

(1) Divide the absolute values of the numbers

(2) Quotient is positive

Examples:

(a)

(b)

To Divide Two Numbers of Unlike Signs

(1) Divide the absolute values of the numbers

(2) Quotient is negative

Examples:

(a)

(b)

Problems

Divide

(1) (5)

(2) (6)

(3) (7)

(4)

Answers

(1) 5 (5)

(2) –5 (6) 2

(3) –7 (7) –0.012

(4)