Add Real Numbers Section 2.2 P. 74 -79
Add Real Numbers
Section 2.2
P. 74 -79
Properties of Addition
• Commutative Property: - the order in which two numbers are added does NOT change the sum. 4 + -8 = -8 + 4
• Associative Property: The way you group three numbers when adding does NOT change the sum.
(-5 + 8) + 9 = -5 + ( 8 + 9 )
Properties of Addition
• Identity Property: The sum of a number and zero is always the number. -9 + 0 = -9 x + 0 = x
• Inverse Property:
The sum of a number and its opposite is 0. a + (- a ) = 0 -4 + 4 = 0
EXAMPLE 1 Add two integers using a number line
Use a number line to find the sum.
a. – 3 + 6
ANSWER
The final position is 3. So, – 3 + 6 = 3.
EXAMPLE 1
b. – 4 + (– 5)
ANSWER
The final position is – 9. So, – 4 + (– 5) = – 9.
Add two integers using a number line
GUIDED PRACTICE for Example 1
Use a number line to find the sum.
1. 7 +(– 2)
ANSWER
The final position is 3. So, 7 +(– 2) = 5.
Move Units to the left.– 2
End at 5 Start at 7
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
GUIDED PRACTICE for Example 1
Use a number line to find the sum.
3. – 8 + (4)
ANSWER
The final position is – 4. So, – 8 +4 = – 4.
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Start at - 8 End at - 4
Move Units to the right.4
GUIDED PRACTICE for Example 1
Use a number line to find the sum.
3. –1 + (– 4)
ANSWER
The final position is – 5. So, – 1 + (– 4) = – 5.
– 7 – 6 – 5 – 4 – 3 – 2 – 1 0
Start at – 1End at – 5
Move Units to the left.– 4
EXAMPLE 2 Add real numbers
Find the sum.
Rule of same signs
Take absolute values.= – (5.3 + 4.9)
= – 10.2 Add.
a. – 5.3 + (– 4.9)
Rule of different signs
Take absolute values. = 19.3 – 12.2
= 7.1 Subtract.
b. 19.3 + (–12.2)
EXAMPLE 3
Identify properties of addition
Statement Property illustrated
a. (x + 9) + 2 = x + (9 + 2) Associative property of addition
b. 8.3 + (– 8.3) = 0 Inverse property of addition
c. – y + 0.7 = 0.7 + (– y) Commutative property of addition
3 11 5
4 2
36 12
8
GUIDED PRACTICE for Examples 2, 3 and 4
Find the sum.
Take absolute values.= – 13.1 + 8.7
= – 4.4
7. – 13.1 + 8.7 Rule of different signs
Identify the property being illustrated.8. 7 + (– 7) = 0 Inverse property of addition
9. – 12 + 0 = – 12 Identity property of addition
10. 4 + 8 = 8 + 4 Commutative property of addition
Subtract.
• Assignment: P. 77 (#1-31)
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