NP Chapter 3- Positives and Negatives- P. 70

[cnebons]

I am confused on page 70... under the topic "A Double Negative = A Positive"

The book says:
What is 7 - (12 - 9) ?

Many people... (yada yada yada) ... Therefore, this expression should be calculated as 7 - 12 + 9 = 4


but shouldn't this be calculated as 7 - (3) = 4 ?



I see that the two calculations come to the same answer... but where/how does the "-" become a "+" ???

[Abdulla]

Review the negative positive rules...

1-(2-3)= 1-2+3= -1+3=2

in your example: What is 7 - (12 - 9) ?

7-12+9 = -5+9= 4

when negative sign comes before parentheses - (12-9) it changes the number sign inside the parentheses (-12+9).

Cheers

[RonPurewal]

you can think of x - (y - z) as identical to x + (-1)(y - z). (in fact, that's exactly the way subtraction is defined in formal mathematics: you take the negative of the thing, and then add it.)

therefore, this is just another example of the DISTRIBUTIVE PROPERTY:
x - (y - z)
= x + (-1)(y - z)
= x + (-y + z)
= x - y + z

of course, you shouldn't have to go through all these steps every time. instead, just realize that you can "distribute subtraction" over sums/differences that are in parentheses, and then calculate accordingly.