Fundamentals of Mathematics, 2008a

599
Exercise 10.5.58
(Section 10.4) Find the value of | −12 |.
10.6 Subtraction of Signed Numbers 6
10.6.1 Section Overview
• Denition of Subtraction
• The Process of Subtraction
• Calculators
10.6.2 Denition of Subtraction
We know from experience with arithmetic that the subtraction 5 − 2 produces 3, that is 5 − 2 = 3. We can
suggest a rule for subtracting signed numbers by illustrating this process on the number line.
Begin at 0, the origin.
Since 5 is positive, move 5 units to the right.
Then, move 2 units to the left to get to 6. (This reminds us of addition with a negative number.)
From this illustration we can see that 5 − 2 is the same as 5 + (−2). This leads us directly to the denition
of subtraction.
Denition of Subtraction
If a and b are real numbers, a − b is the same as a + (−b), where −b is the opposite of b.
10.6.3 The Process of Subtraction
From this denition, we suggest the following rule for subtracting signed numbers.
Subtraction of Signed Numbers
To perform the subtraction a − b, add the opposite of b to a, that is, change the sign of b and add.
10.6.3.1 Sample Set A
Perform the indicated subtractions.
Example 10.26
5 − 3 = 5 + (−3) = 2
Example 10.27
4 − 9 = 4 + (−9) = −5
Example 10.28
−4 − 6 = −4 + (−6) = −10
Example 10.29
−3 − (−12) = −3 + 12 = 9
6 This content is available online at .
Available for free at Connexions