# 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)
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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