Introduction to Real Numbers and Algebraic Expressions 1.4

SUBTRACTION of REAL NUMBERS 1.4
a. Subtract real numbers and simplify combinations of additions and subtractions.
b. Solve applied problems involving addition and subtraction of integers.

Objective a
Subtract real numbers and simplify combinations of additions and subtractions.

Subtraction a - b
The difference a - b is the number c for which a = b + c.

Example A

Subtract 4 - 9.

Solution
Think: 4 - 9 is the number that when added to 9 gives 4.
What number can we add to 9 to get 4?
The number must be negative.
The number is -5:
4 – 9 = –5.
That is, 4 - 9 = -5 because 9 + (-5) = 4.

Subtracting by Adding the Opposite
For any real numbers a and b,
a – b = a + (– b).
(To subtract, add the opposite, or additive inverse, of the number being subtracted.)

Example B



Example C



Example D



Objective b
Solve applied problems involving addition and subtraction of integers.

Example E

The Johnson’s were taking a vacation and one day they drove from mile marker 54 to mile marker 376. How far did they drive?

Solution
376 – 54 = 376 + (-54) Adding the opposite of 54.
= 322 miles