Download Pa g e1 2.2 Add Real Numbers Goal • Add positive and negative

2.2 Add Real Numbers
Goal • Add positive and negative numbers.
Adding Integers Using a Number Line
Graph the first number. If you are adding a positive number, move the absolute value of the second number to
the right. If you are adding a negative number, move the absolute value of the second number to the left. We
will do the first four together:
1) 3 + 5 =
2) -4 + -9 =
3) 2 + -12 =
4) -7 + 12 =
Now work with your group to finish the rest of these problems.
5) -9 + 20 =
6) -9 + -6 =
7) 3 + -17 =
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9) 3 + 12 =
1
8) 9 + -9 =
10) -11 + 12 =
13) Discuss what you found with your group. Try to summarize the rules for adding two integers by filling in
the following sentences:
A) When you add two positive numbers, ____________________ the absolute values of the numbers; the
answer will always be _______________________.
Show an example:
B) When you add two negative numbers, ____________________ the absolute values of the numbers; the
answer will always be _______________________.
Show an example:
c) When you add a positive number and a negative number, and the positive number is larger,
____________________ the absolute value of the smaller number from the absolute value of the larger
number; use the sign of the _____________________ absolute value.
Show an example:
D) When you add a positive number and a negative number, and the negative number is larger,
____________________ the absolute value of the smaller number from the absolute value of the larger
number; use the sign of the _____________________ absolute value.
Show an example:
6) 18 + -20 =
2) 99 + -10 =
7) -25 + 50 =
3) -17 + -17 =
8) -10 + -33 =
4) -27 + 27 =
9) 24 + 36 + -75 =
5) -30 + -20 =
10) -12 + -12 + 13 =
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1) -9 + 20 =
2
Now you try it! Now try these without a number line:
PROPERTIES OF ADDITION
Commutative Property of Addition The order in which you add two numbers does not change the sum.
a + b = ___ + ___
Example: −1 + 3 =___+_____
Associative Property of Addition The way you group three numbers in a sum does not change the sum.
(a + b) + c = ___ + (___ + ___)
Example: (1 + 2) + 3 =___ + (___+___)
Identity Property of Addition The sum of a number and 0 is the number. (You don’t change the identity of
the number!)
a + 0 = ___ + ___ = ___
Example: 4 + 0 = ___
Additive Identity is _____ because:
Inverse Property The sum of a number and its opposite is 0.
a + (−a) = ____ + ___ = ___
Example: −9 + ___ = 0
Additive Inverse is _____________________________________________________________ because:
Now you try it!
Identify the property demonstrated below:
1) -19 + 19 = 0
2) -19 + 19 = 19 + -19
3) -19 + 0 = -19
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3
4) -19 + (19 + 0) = (-19 + 19) + 0