Transcript Introduction To Signed Numbers

7.1 - Introduction To Signed
Numbers
Definitions
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A positive number is a number greater than (>) 0.
A negative number is a number less than (<) 0.
A signed number is a number with a sign that is
either positive or negative.
A number line is a horizontal line that represents
all numbers.
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-3
-2
-1
0
1
2
3
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Definitions
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The integers are negative, positive whole numbers and
0. That is, the numbers … -4, -3, -2, -1, 0, 1, 2, 3, 4, …,
continuing indefinitely in both directions.
Two numbers that are the same distance from 0 on the
number lines but on opposite sides of 0 are called
opposites.
A number to the left of another number on a number
line is less than (<) first number.
The absolute value of a number, denoted | the number |,
is the distance the number is from 0.
7.2 - Adding Signed Numbers
To Add Two Signed Numbers
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If they have the same signs, add the absolute
values of each number and keep the sign.
If they have different signs, subtract the
smaller absolute value from the larger absolute
value and take the sign of the number with the
larger absolute value.
7.3 - Subtracting Signed
Numbers
To Subtract Two Signed Numbers
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Change the operation of subtraction to addition
and change the number being subtracted to its
opposite.
Follow the rules for adding signed numbers.
Example: -2 – 3 = - 2 + (-3) = -5
Example: 5 – (-1) = 2 + 1 = 3
↑ Minus a negative turns into a plus.
7.4 – Multiplying Signed
Numbers
To Multiply Two Signed Numbers
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Multiply the absolute values of each number.
If the two numbers have the same sign, the
product is positive. If the two numbers have
opposite signs, the product is negative.
Note: If you are multiplying several signed
numbers and there are an even number of
negative signs, the product will be positive. If
there are an odd number of negative signs, the
product will be negative.
7.5 – Dividing Signed
Numbers
To Multiply Two Signed Numbers
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Divide the absolute values of each number.
If the two numbers have the same sign, the
quotient is positive. If the two numbers have
opposite signs, the quotient is negative.
Note: If you are dividing several signed
numbers and there are an even number of
negative signs, the quotient will be positive. If
there are an odd number of negative signs, the
quotient will be negative.
Properties of Real Numbers
Properties of Real Numbers
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Real numbers are all the numbers you can
think of and with which we’ve been using.
They include:
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Whole Number: {0, 1, 2, 3,…}.
Integers: {…, -3, -2, -1, 0, 1, 2, 3, …}.
Also include fractions and decimals.
Properties of Real Numbers
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Associative Property
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Addition: a + (b + c) = (a + b) + c
Multiplication: a·(b·c) = (a·b)·c
The associative property does not work for subtraction or
division.
Commutative Property
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Addition: a + b = b + a
Multiplication: a·b = b·a
The commutative property does not work for subtraction
or division.
Properties of Real Numbers
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Identity Property
 Addition: a + 0 = a. Zero is the identity element of addition.
 Multiplication: a · 1 = a. One is the identity element of
multiplication.
Inverse Property
 Addition: a + (-a) = 0. -a is the additive inverse of a.
1
 Multiplication: a 
 1 . 1/a is called the multiplicative
a
inverse or reciprocal of a.
Distributive Property
 a·(b + c) = a·b + a·c