Problem

Find the sum. See ExampleEXAMPLE Adding Numbers on a Number LineUse a number line to find...

Find the sum. See Example

EXAMPLE Adding Numbers on a Number Line
Use a number line to find each sum.
(a) 2 + 3
Step 1 Start at 0 and draw an arrow 2 units to the right. See FIGURE.
Step 2 From the right end of that arrow, draw another arrow 3 units to the right.
The number below the end of this second arrow is 5, so 2 + 3 = 5.
FIGURE
(b) −2 + (−4)
(We put parentheses around −4 due to the + and − next to each other.)
Step 1 Start at 0 and draw an arrow 2 units to the left. See FIGURE.
Step 2 From the left end of the first arrow, draw a second arrow 4 units to the left to represent the addition of a negative number.
The number below the end of this second arrow is −6, so −2 + (−4) = −6.
FIGURE
EXAMPLE Adding Two Negative Numbers
Find each sum.
(a) −2 + (−9) = −(| −2| + |−9|) = −(2 + 9) = −11
(b) −8 + (−12) = −20
(c) −15 + (−3) = −18
EXAMPLE 3 Adding Numbers with Different Signs
Use a number line to find the sum −2 + 5.
Step 1 Start at 0 and draw an arrow 2 units to the left. See FIGURE.
Step 2 From the left end of this arrow, draw a second arrow 5 units to the right.
The number below the end of the second arrow is 3, so −2 + 5 = 3.
FIGURE
EXAMPLE Adding Numbers with Different Signs
Find the sum −12 + 5.
Find the absolute value of each number.
|−12| = 12 and |5| = 5
Then find the difference between these absolute values: 12 − 5 = 7. The sum will be negative, since |−12| > |5|.
−12 + 5 = −7
EXAMPLE Adding Mentally
Check each answer by adding mentally. If necessary, use a number line.
(a) 7 + (−4) = 3
(b) −8 + 12 = 4
(c)
(d)
(e) −4.6 + 8.1 = 3.5
(f) −16 + 16 = 0
(g) 42 + (−42) = 0
Notice in parts (f) and (g) that when additive inverses are added, the sum is 0.
EXAMPLE Using the Definition of Subtraction
Subtract.
(a)
(b)
(c)
(d)
(e)
EXAMPLE Adding and Subtracting with Grouping Symbols
Perform each indicated operation.
(a)
(b)
(c)
(d)