Math 6 Honors Periods 6 & 7 (Tuesday & Wednesday)

Negative Numbers 11-1

On a horizontal number line we use negative numbers for the coordinates of points to the left of zero. We denote the number called ‘negative four’ by the symbol -4. The graphs of 4 and -4 are the same distance from 0—but in opposite directions. Thus they are opposites. -4 is the opposite of 4.

The opposite of 0 is 0

Absolute Value is a distance concept. Absolute value is the distance of a number from 0 on a number line. The absolute value of -4 is 4. l-4l = 4

The absolute value of 5 is 5. l5l= 5

Counting numbers: 1, 2, 3, 4, ….

Whole numbers 0, 1, 2, 3, 4….

Integers are whole numbers and their opposites.

…-4, -3, -2, -1, 0, 1, 2, 3, 4….

The opposite of 0 is 0.

The integer 0 is neither positive nor negative.

The farther we go to the right on a number line--- the bigger the number. We can compare two integers by looking at their position on a number line.

if x <0>

Adding Integers 11-2

Rules: The sum of two positive integers is a positive integer.

The sum of two negative integers is a negative integer.

So- if the two numbers have the same sign, use their sign and just add the numbers.

-15 + -13 = - 28 -10 + -4 = -14

Rules: The sum of a positive integer and a negative integer is :

POSITIVE… IF the positive number has a greater absolute value

NEGATIVE… IF the negative number has a greater absolute value

ZERO… IF both numbers have the same absolute value

30 + -16 … ask yourself the all important question… “WHO WINS? in this case the positive and then ask “BY HOW MUCH?” take the difference so 30 + -16 = 14

14 + - 52… “WHO WINS?” the negative… “BY HOW MUCH?”

38 so 14 + -52 = -38

(-2 + 3) + - 6 you can work this 2 ways

(-2 + 3) + - 6 = 1 + -6 = -5 or

using all the properties that work for whole numbers

Commutative and Associative properties of addition

can change expression to (-2 + -6) + 3 or -8 + 3 = -5 you still arrive at the same solution.