5.2 The Integers; Order of Operations

Sets of Numbers The set of natural numbers or counting numbers is {1,2,3,4,5,6,…} The set of whole numbers is {0,1,2,3,4,5,…} The set of integers is {…,-4,-3,-2,-1,0,1,2,3,4,…}

Integers The positive integers are {1,2,3,4,5…}. Positive integers can be written with a + sign or no sign The negative integers are {…-4,-3,-2,-1}. Zero is neither positive nor negative. 0Negative integersPositive integers

Graph the following on a number line a.-3 b.4 c.0 d.-4 e.3 0

Comparing numbers To compare numbers using the number line, the lesser of 2 numbers is to the left on the number line For example: -3 is less than 1 (written –3 < 1) since –3 is to the left of 1 on the number line 0-31

Compare the numbers using 1.-4____3 2.-1____ ____-2 4.0____-3

Absolute value The absolute value of a number is its distance from 0 on the number line. Since distance is always positive the absolute value of a number is always positive. Example: |-3| = units

Example |-5| = |3| = |0| =

Adding Integers To add integers: If the signs are the same, add and keep the sign If the signs are different, subtract and keep the sign of the number with the bigger absolute value.

Example: Add (-15) (-6) 18 + (-18)Note: 18 and –18 are additive inverses

Subtraction The difference of two numbers a and b is a – b = a + (-b) Double Negative Rule: a – (- b) = a + b

Examples 17 – (-11) -18 – (-5) -18 – 5

Multiplication When multiplying two numbers: If the signs are the same the product is positive. If the signs are opposite the product is negative.

Examples 3(11) -5(-9) 7(-10) (-7)11 6(0)

Exponents base exponent

Examples

Dividing Integers When dividing two numbers: If the signs are the same the quotient is positive. If the signs are opposite the quotient is negative.

Order of Operations P arenthesis E xponents M ultiply D ivide A dd S ubtract Left to right

Examples

HW: p. /1-98 every other even