2.2 Addition of Real Numbers
PROPERTIES OF ADDITION
Commutative Property The order in which two numbers are added does not change the sum.
ex) 4 + 8 = 8 + 4 algebraically a + b = b + a
Associative Property
The way you group three numbers when adding does not change the sum.
ex) (5 + ­8) + ­23 = 5 + (­8 + ­23) algebraically (a + b) + c = a + (b + c)
Identity Property
The sum of a number and 0 is the number.
ex) 15 + 0 = 15 algebraically a + 0 = a
Property of zero (Inverse Property)
The sume of a number and its opposite is 0
ex) 42 + ­42 = 0 algebraically a + ­a = 0
Find the sum.
ex) 13 + 53 = ex) 24 + ­49 = ex) ­439 + 882
ex) 69 + ­43 + ­90
You cannot do all three numbers
at once. Take two at a time!!!!!
Positive and Negative Numbers used when looking at profit and loss.
If you had expenses of $250 during a fundraiser and took in $198. How much
money did you make? 1
Rules for addition ­ If both numbers positive ­ easy ­ Add like we learned in elementary.
If both numbers negative ­ Add the numbers together and the sum is NEGATIVE.
If one number is positive and one number negative ­ Here's the rule: You will subtract the two numbers. Which one goes on top?
(The one with the larger absolute value.) The answer takes on the sign of the number with the larger absolute value.
ex) ­89 + 53 ex) 72 + ­49
decimals and fractions work the same way as integers.
1.4 + ­2.6 + 3.1 Regroup first. Add positives, add negatives, add each answer.
­4 ⅜ + 5⅓
I expect you to be able to add integers without calculators. I expect you to be able to add positive and negative fractions with calculators.
I will allow calculators on problems such as the fraction above. 2
2.3 Subtraction of Real Numbers
Definition of Subtraction is to Add the Opposite. Algebraically a ­ b = a + ­b
ex) 3 ­ 5 = 3 + ­5
Once you have changed the subtraction sign, you have an addition problem
you will solve just like we did earlier. Find the difference. Write your problems vertically!!!
14 ­ 92 = 48 ­ (­48)
­54 ­ 45 = ­34 ­ (­60)
1/2 ­ 2/3 4/5 ­ 3/4
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Evaluating expressions when there is more than one subtraction sign.
Go through and change every subtraction sign to add the opposite. ex) 3 ­ (­4) ­2 + 8
ex)­8.5 ­ 3.9 + 16.2 ­ 11.8
Terms of an expression ­ The parts that are added in an expression
ex) What are the terms of 5x + 13?
What are the terms of 3y ­ 8?
What are the terms of ­9x ­ 3?
The above examples are not like terms and CANNOT be added together or
simplified any further. You can add numbers (constants): 7 + 3 ­ 6 + (­4)
You can add similar variables: x + 3 x + 8x ­ 4x
You CANNOT add constants and variables: 3x ­ 2 already simplified
­9x + 7 already simplified Evaluate the function y = ­5 ­x when x = ­2, ­1, 0, and 1
Write your results in a table (t­chart) and describe the pattern. 4
Examples page 81
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