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## Subtraction of Real Numbers

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**Subtraction of Real Numbers**Section 1.7 (50)**Objectives(50)**Subtract numbers Subtract numbers mentally Evaluate expressions containing more than two numbers**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**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**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”**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**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 – 250.69 567.23 - 250.69 316.54 Solution: The new balance is $316.54**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.**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.**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**Examples**-5 - ( +3) + 6 ( -5 ) + ( -3 ) + ( +6) ( -8 ) + ( +6 ) -2 6 + ( -2) - ( +4 ) ( +6 ) + ( -2 ) + ( -4 ) 4 + ( -4 ) 0**Example**-7 - ( -3 ) + ( -13 ) + ( -2 ) ( -7 ) + ( +3 ) + ( -13 ) + ( -2 ) ( -4 ) + ( -13 ) + ( -2 ) ( - 17 ) + ( -2 ) -19**Objectives(50)**Subtract numbers Subtract numbers mentally Evaluate expressions containing more than two numbers**Subtraction of Real Numbers**Section 1.7 (50)