7.1 - Introduction To Signed Numbers

Definitions

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.

|

-3

|

-2

|

-1

|

0

|

1

|

2

|

3… …

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.

|

-3

|

-2

|

-1

|

0

|

1

|

2

|

3… …

Definitions 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 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 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 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 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 Real numbers are all the numbers you can

think of and with which we’ve been using. They include: Whole Number: {0, 1, 2, 3,…}. Integers: {…, -3, -2, -1, 0, 1, 2, 3, …}. Also include fractions and decimals.

Properties of Real Numbers Associative Property

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

Addition: a + b = b + a Multiplication: a·b = b·a The commutative property does not work for subtraction

or division.

Properties of Real Numbers 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. Multiplication: . 1/a is called the multiplicative

inverse or reciprocal of a. Distributive Property

a·(b + c) = a·b + a·c

11 aa