Question about positive and negative signs to left of a number

[The_Bad_Guy]

Hi everyone. So I have a pre-algebra book and it says "The sign in front of a term belongs to that term" (a term is a single number or variable or number and variable multiplied together; 5, X, 7y, etc). Anyways when I was doing a few math problems and it was time to use PEMDAS, when I applied the sign to the left of a number, I would get the wrong answer. Here are a few examples:

-6-8÷(-4)
Negative 8 divided by negative 4 equals 2. So you have -6(2)? The final answer is -4 but how is that. Here are some more problems.

6-2·(-2)+2^3

(5-6)^3-4·(-2)

^ means exponent in case someone wasnt sure what that symbol meant.
Any help would be greatly appreciated.

 

[mmm4444bot]

-6 - 8÷(-4)

The red character is a subtraction operator, not a negative sign. Divide 8 by -4 first, to get -2, then subtract.

The result is -6 - (-2) which is the same as -6 + 2.

When people say the eight is negative, they're thinking in terms of addition, not subtraction. In other words, each of the following expressions are equivalent because subtraction means "adding the opposite".

-6 - 8÷(-4)

-6 + (-8)÷(-4)

So, you may switch back and forth between addition and subtraction, if you change the sign of the second term.

6 - 2·(-2) + 2^3

(5-6)^3 - 4·(-2)

Again, think of those red characters as subtraction operators.

Or, switch to addition:

6 + (-2)·(-2) + 2^3

(5-6)^3 + (-4)·(-2)

:cool:

 

[The_Bad_Guy]

The red character is a subtraction operator, not a negative sign. Divide 8 by -4 first, to get -2, then subtract.

The result is -6 - (-2) which is the same as -6 + 2.

When people say the eight is negative, they're thinking in terms of addition, not subtraction. In other words, each of the following expressions are equivalent because subtraction means "adding the opposite".

-6 - 8÷(-4)

-6 + (-8)÷(-4)

So, you may switch back and forth between addition and subtraction, if you change the sign of the second term.


Again, think of those red characters as subtraction operators.

Or, switch to addition:

6 + (-2)·(-2) + 2^3

(5-6)^3 + (-4)·(-2)

:cool:

Awesome! Thank you so much! This cleared it up for me. I have one more question if that's ok that's semi related.
When combining like terms, is that the only instance where the sign in front of a term belongs to that term?
Like for example:
4q-5-6q+2 which would equal -2q-3

Thanks again!

 

[JeffM]

Awesome! Thank you so much! This cleared it up for me. I have one more question if that's ok that's semi related.
When combining like terms, is that the only instance where the sign in front of a term belongs to that term?
Like for example:
4q-5-6q+2 which would equal -2q-3

Thanks again!

It is definitely a pain for beginning students that the same symbol is used to indicate three different things: (1) the operation of subtraction, (2) an indicator that a variable is an additive inverse, and (3) that a number is not positive.

Try this as a rule of thumb. Interpret this ambiguous symbol as an operator if you can.

So \(\displaystyle 4q - 5 - 6q + 2 = (4q - 6q) + (2 - 5) = -\ 2q - 3.\)

 

[The_Bad_Guy]

It is definitely a pain for beginning students that the same symbol is used to indicate three different things: (1) the operation of subtraction, (2) an indicator that a variable is an additive inverse, and (3) that a number is not positive.

Try this as a rule of thumb. Interpret this ambiguous symbol as an operator if you can.

So \(\displaystyle 4q - 5 - 6q + 2 = (4q - 6q) + (2 - 5) = -\ 2q - 3.\)

Ah ok that makes sense. Yeah it can be a little confusing sometimes starting out with - signs but I'm getting it. Thank you for all your help, its helped me out big time!