Add. See Examples 1 through 7.
EXAMPLE 1
Add: 3 + 2
Solution Recall that 3 and 2 are called addends. We start at 0 on a number line and draw an arrow representing the addend 3. This arrow is three units long and points to the right since 3 is positive. From the tip of this arrow, we draw another arrow, representing the addend 2. The number below the tip of this arrow is the sum, 5.
EXAMPLE 2
Add: − 1 + (− 2)
Solution Here, − 1 and − 2 are addends. We start at 0 on a number line and draw an arrow representing − 1. This arrow is one unit long and points to the left since − 1 is negative. From the tip of this arrow, we draw another arrow, representing − 2. The number below the tip of this arrow is the sum, − 3.
EXAMPLE 3
Add.
a. − 3 + (− 7)
b. − 1 + (− 20)
c. − 2 + (− 10)
Solution Notice that each time, we are adding numbers with the same sign.
a.
b.
c.
EXAMPLE 4
Add: − 4 + 6
Solution
EXAMPLE 5
Add.
a. 3 + (− 7)
b. − 2 + 10
c. 0.2 + (− 0.5)
Solution Notice that each time, we are adding numbers with different signs.
a.
b.
c.
EXAMPLE 6
Add.
a. − 8 + (− 11)
b. − 5 + 35
c. 0.6 + (− 1.1)
d.
e. 11.4 + (− 4.7)f.
Solution
EXAMPLE 7
Add.
a. 3 + (− 7) + (− 8)
b. [7 + (− 10)] + [− 2 + |− 4|]
Solution
a. Perform the additions from left to right.
b. Simplify inside brackets first.
− 18 + 49
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