Wetzel

Math 155

5.2 – The Integers; Order of Operations

Natural Numbers = {1, 2, 3, 4,…}

Whole Numbers = {0, 1, 2, 3, 4,…}

Integers = {…-3, -2, -1, 0, 1, 2, 3,…}

Number Line –

Inequality Signs -         QUOTE     less than                            QUOTE     greater than

                                     QUOTE     less than or equal to            QUOTE    greater than or equal to

            Ex.:

1.)     Graph   QUOTE                                2.)  Graph   QUOTE  

Absolute Value -        

            Def. –

            Ex.:

3.)       QUOTE   =                                           4.)   QUOTE   =

Adding Integers –

            Steps:

·         If the integers have the same sign, add the numbers keeping their sign.

·         If the integers have different signs, subtract the smaller number from the larger number keeping the sign of the larger number.

Ex.:

            5.)  7 + 9 =                    6.)  -1 + (-4) =               7.)  5 + (-3) =                8.)  -12 + 7 =

Subtracting Integers –

            Additive Inverse Property:                     a – b  =  a + (-b)

                                                            for all integers a and b

            Steps:

1.)  Rewrite the expression changing the subtraction to addition

2.)  Follow the steps for adding integers.

            Ex.:

            9.)  4 – 9 =                    10.)  -3 + 19 =               11.)  9 – 2 =             12.)  6 – 9 – 16 =

Multiplying Integers –

            Steps:

·         If multiplying two integers with the SAME sign, the product of the numbers will be positive.

·         If multiplying two integers with DIFFERENT signs, the product of the numbers will be negative.

**The product of any number and zero is zero.

***Multiplying a number of one does not change that number.

Ex.:

13.)  5 · 7 =                   14.)  -4 · 9 =                  15.)  (-3)(-2) =              16.)  (0)(8) =

17.)  2 · 1 =                   18.)  5(12)(2) =                         19.)  -6(3)(-4) =            

Exponential Notation –

Ex.:

20.)                         21.)                          22.)                23.)  

Dividing Integers –

            Steps:

·         If dividing two integers with the SAME sign, the quotient of the numbers will be positive.

·         If dividing two integers with DIFFERENT signs, the quotient of the numbers will be negative.

                                                              does not exist

            Ex.:

            24.)  =                      25.)                       26.) 

Order of Operations –

                                    P  E  M  D  A  S

HW:  p.247 #5 – 97 every other odd (5, 9, 13, 17, …)