1. Subtraction of Real Numbers Section 1.7 (50)

2. Objectives (50) Subtract numbers Subtract numbers mentally Evaluate expressions containing more than two numbers

3. 1.7.1 Subtracting Numbers (50) If you know how to add numbers with different signs, you already know how to subtract. a - b ≡ a + ( -b ) In short, if you a subtracting a value from a number, you add the additive inverse. Examples: -2 - 8 = ( -2 ) + ( -8 ) = -10 -1 - ( -2) = ( -1) + ( +2) = +1

4. Chips The book gives a method using chips. Green chips are positive, red chips are negative. +5 would be ☺☺☺☺☺ -3 would be ☻☻☻ You would put your green chips to the left and compare the two values. If you added 3 + ( -5 ), you would write ☻☻☻☻☻☺☺☺ Cancel out one of each at a time until you have zero of one of them. Count how many left of the other one and that is your solution. ☻☻☻☻☻☺☺☺ The solution is -2

5. 9 - 2 “9 – 2” can be written as “9 minus 2”. But like most in math, things can be said or done multiple ways. It could also be written as “subtract 2 from 9”

6. Examples Subtract 10 from -5 ( -5 ) - ( +10 ) ( -5 ) + ( -10 ) = -15 Subtract -20 from -8 ( -8 ) – ( -20 ) ( -8 ) + ( +20 ) = +12 Subtract -2/3 from -5/3 ( -5/3 ) – ( -2/3 ) ( -5/3 ) + ( +2/3) = [ ( -5) + (+2) ]/3 = -3/3 = -1

7. Example Scott’s checkbook indicated a balance of $567.23 before he wrote a check of $250.69. Find the new balance. Given:original balance $567.23 Wrote a check for $250.69 Find:New balance How:Subtract check from original Solve:567.23 – 250.69567.23 -250.69 316.54 Solution:The new balance is $316.54

8. Example Yesterday the high temperature for Fargo, ND was -5ºF. The high is Dallas, TX was 64ºF. Find the difference in their temperatures. Given:High in Fargo -5 High in Dallas 64 Find:Temperature difference How:Subtract Fargo from Dallas Solve:64 – ( -5 ) = +64 + ( +5 ) = 69 Solution:Temperature difference is 69ºF.

9. 1.7.2 Subtract Numbers Mentally (55) Use mental addition and subtraction after you’ve done a hell of a lot of them writing them down. I will normally still write any problem either with more than three numbers or two numbers with more than three digits. This is particularly true on tests. I can see what you write, I can’t see what is in your mind.

10. 1.7.3 Evaluating Expressions Containing More Then Two Numbers (56) Will learn the Order of Operations (OOOs) shortly. One of the rules of OOOs is we have multiple additions or subtractions {with no parentheses}, the operations are done from LEFT to RIGHT. That means sometimes you do subtractions before additions. Example:5 - ( +3 ) + 2 2 + 2 4

11. Examples -5 - ( +3) + 6 ( -5 ) + ( -3 ) + ( +6) ( -8 ) + ( +6 ) -2 6 + ( -2) - ( +4 ) ( +6 ) + ( -2 ) + ( -4 ) 4 + ( -4 ) 0

12. Example -7 - ( -3 ) + ( -13 ) + ( -2 ) ( -7 ) + ( +3 ) + ( -13 ) + ( -2 ) ( -4 ) + ( -13 ) + ( -2 ) ( - 17 ) + ( -2 ) -19

13. Objectives (50) Subtract numbers Subtract numbers mentally Evaluate expressions containing more than two numbers

14. Subtraction of Real Numbers Section 1.7 (50)