1. 7.1 - Introduction To Signed Numbers

2. 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.
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 1 2 3 … | -3 -2 -1 1 2 3 …

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.

4. 7.2 - Adding Signed Numbers

5. 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.

6. 7.3 - Subtracting Signed Numbers

7. 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 = (-3) = -5
Example: 5 – (-1) = = 3
↑ Minus a negative turns into a plus.

8. 7.4 – Multiplying Signed Numbers

9. 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.

10. 7.5 – Dividing Signed Numbers

11. 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.

12. Properties of Real Numbers

13. 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.

14. 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.

15. 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: /a is called the multiplicative inverse or reciprocal of a.
Distributive Property
a·(b + c) = a·b + a·c