Question

1. If a and b are any two real numbers, explain how you calculate the difference a – b. Please answer all parts to the problem.
a. How are addition and subtraction related?
b. How you can determine the sign of your solution?
c. How you can use a number line to help with the calculation? Include an example using a value for both a and b.

Answer 1

Rules:


Rule 1)

if both a & b are positive, and a > b, then you just subtract like normal

if both a & b are positive, and a < b, then you just subtract (larger - smaller) and you make the result negative

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Rule 2)

if a is positive and b is negative, then a-b will turn into an addition problem

example:
let a = 2, b = -3

a-b = 2 - (-3) = 2+3 = 5

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Rule 3)

if a is negative and b is positive, then you add up the terms without the negative sign and then make the result negative

example:
let a = -7 and b = 10

a-b = -7 - 10 = -17

notice how i did 7+10 = 17 and made the result negative

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Rule 4)

if a & b are both negative then you'll refer to rule 1

example

a = -2, b = -5

a - b = -2 - (-5) = -2 + 5 = 5 - 2 = 3