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MATHEMATICAL REFLECTIONS
INVESTIGATION 2
In this investigation, you applied your ideas about integers to develop
algorithms for calculating any sums and differences.
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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.