Transcript Lesson #6 Addition, Subtraction, Multiplication and Division of

Lesson #6
Addition, Subtraction, Multiplication and
Division of Signed Numbers p.129-150
Absolute Value - the distance a number is from zero, regardless
of the direction.
|5| = 5
|-7| = 7
ADDITION OF SIGNED NUMBERS p. 129-138
Addition of Two Positive Numbers
Keep the sign and combine
Addition of Two Negative Numbers
Keep the sign and combine
Addition of a Positive and a Negative Number
Take the sign of the number farther from zero
(largest absolute valve), and take the difference between
the numbers absolute values.
SUBTRACTION OF SIGNED NUMBERS p. 138-142
To subtract one sign number from another,
add the opposite of the subtrahend to the minuend.
Examples:
(+9) - (+4) = to (+9) + (-4) =
(-8) - (-3) = to (-8) + (+3) =
(+7) - (-2) = to (+7) + (+2) =
(-6) - (+1) = to (-6) + (-1) =
(- x) - (- x) = - x + x = 0
(x) - (x - 5) = x + (- x) + 5 = 5
Uses of the Symbol (-)
To indicate that a number is negative:
-6 -> negative 6
To indicate the opposite of the number:
-(-5) -> opposite of negative 5
-x -> the opposite of x
To indicate subtraction:
9 - (-7) -> the difference between 9 and -7
MULTIPLICATION AND DIVISION
OF SIGNED NUMBERS p.142-153
Same Signs
if the signs are the same when you multiply or divide two
numbers, the answer is always positive.
Different Signs
- if the signs of two numbers are different when multiplying
or dividing them, the sign of the answer is always negative.
Properties of Signed Numbers
Closure
Commutative
Associative
Distributive
Multiplication Property of One
Multiplication Property of Zero
- Multiplication Property of Negative One
a * (-1) = -a
and
(-1) * a = -a
-
Dividing Zero by a Nonzero Number
0/a = 0
-Dividing by Zero is Undefined a/0 = undefined
-
a
Multiplicative Inverse
(a)(1/a) = 1