FOUR BASIC ARITHMETIC OPERATIONSReview of Introductory MathematicsStarting at zero, we first move two places to the right on the number line to represent the number2. We then move an additional 3 places to the right to represent the addition of the number 3.The result corresponds to the position 5 on the number line. Using this very basic approach wecan see that 2 + 3 = 5. Two rules govern the addition of whole numbers.The commutativelaw for addition states that two numbers may be added in either orderand the result is the same sum. In equation form we have:a + b = b + a(1-1)For example, 5 + 3 = 8 OR 3 + 5 = 8. Numbers can be added in any order andachieve the same sum.The associativelaw for addition states that addends may be associated or combined in anyorder and will result in the same sum. In equation form we have:(a + b) + c = a + (b + c) (1-2)For example, the numbers 3, 5, and 7 can be grouped in any order and added toachieve the same sum:(3 + 5) + 7 = 15 OR 3 + (5 + 7) = 15The sum of both operations is 15, but it is not reached the same way. The firstequation, (3 + 5) + 7 = 15, is actually done in the order (3 + 5) = 8. The 8 isreplaced in the formula, which is now 8 + 7 = 15.The second equation is done in the order (5 + 7) = 12, then 3 + 12 = 15.Addition can be done in any order, and the sum will be the same.MA-01 Page 8 Rev. 0

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