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Name__________________________________ HR#__________ MATHEMATICAL REFLECTIONS INVESTIGATION 2 In this investigation, you applied your ideas about integers to develop algorithms for calculating any sums and differences. _____________________________________________________________ Answer each question below in complete sentences and give examples to support each of your responses. 1. a. How can you decide if the sum of two numbers is positive, negative, or zero without actually calculating the sum? *If both numbers are positive then the sum will be positive. *If both numbers are negative then the sum will be negative. *If one number is positive and one is negative then the sign of the sum is the sign of the greater absolute value. b. How can you decide if the difference of two numbers is positive, negative, or zero without actually calculating the difference? *If the beginning number is greater than the number you subtract, the difference is positive. * If the beginning number is smaller than the number you subtract, the difference is negative. *The difference is zero if both numbers are equal. 2. a. What procedure (s) will find the sum a + b of two numbers where a and b represent any integer? *If both numbers are positive or negative, add the numbers and keep the sign. *If one number is positive and one number is negative, find the difference between the absolute values. Keep the sign of the number with the greater absolute value. b. What procedure(s) will find the difference a – b of two numbers where a and b represent any integer? *When both numbers are positive: If the first number is greater than the second, just subtract. If the first number is less than the second, subtract the absolute values and the answer will be negative. *When both numbers are negative or one is positive and one is negative: Change subtraction to addition and change the sign of the second value. Add to find the answer. 3. How can any difference a – b of two numbers be restated as an equivalent addition statement? *a-b = a + -b For any difference you can add the opposite.