Subtracting numbers Xavier High School

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					2-4 Subtraction of rational
        numbers
                                 Subtraction
Definition
   For all rational numbers a and b, the Difference a – b is the number c, such that   c+b=a
 a–b=c c+b=a
 5–3=2         2+3=5

The examples below show that adding the opposite of a rational number gives the same result as
     subtracting the rational number
8–3=5                           8 + (-3) = 5
4 – 7 = -3                      4 +(-7) = -3
-4.5 – 2 = -6.5                 -4.5 + (- 2) = -6.5

These examples suggest the following rule
  Subtracting numbers
       for all rational numbers a and b, a – b = a + (-b)
To subtract a rational number, add its additive inverse or opposite
                             Example
2 – 6 = 2 + (-6)
     =4



-86 – (-400) = -86 + 400
       = 314



-4.2 – (-3.6) = -4.2 + 3.6
       = -0.6




  1 3   1  3
       
  2 4   2  4
    5
 
    4
                        Try This
4–9          6 – (-4)        -4 – 17




-3 – (-12)                 3  1
                             
                           8  4
                            Subtraction
•   When addition and subtraction occur several times, we can use the rule for
    subtracting rational numbers to make them all addition



Example 7:

8 – (-4) – 2 – (-4) + 2        Original



8 + 4 -2 + 4 + 2            Rule for subtraction



= 16                         Solution
                                 Subtraction
-4 – (-2x) + x – (-5)                    Original



-4 + 2x + x + 5                         using rule for subtraction



= 3x + 1                                Soulution



Try this:

-6 – (-2) – (-4) – 12 + 3                     3 – ( -7.1) + 6.3 – (-5.2)

                            -8 – (-3x) + 2x – (-13)
                               Example
Mr. Casper had $75.50 in his checking account. He wrote a check for $95.00. By how
    much has he overdrawn his checking account? Let c = the amount in his checking
    account.

c = 75.50 – 95.00
 c = - 19.50             He has overdrawn his account by 19.50




Juan has saved $35 toward a new stereo system. The total cost of the system is $125.
   How much more money does Juan need?

				
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posted:4/20/2013
language:English
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