Let's use some examples where we have order of operations and also there are negative numbers and signs involved:
Let's evaluate the following:
(-4) x 5 + (-6)
So order of operations tells us to first take care of the multiplications and after that, deal with the additions or subtractions.
So the multiplication goes first here:
(-4) times 5 = - 20
Recall that a positive number times a negative number gives alwasy a negative number. So negative times positive gives the negative sign to the multiplication, and then, once the sign is taken care of, you multiply the numbers (4 x 5 = 20)
Next, we do the indicated addition
-20 + (-6) = -20 - 6 = -26
weher again we use the property that the + times the - inside the parenthesis gives a minus. ad we finalize by doing -20 - 6 = -26 (combining of two negative numbers).
Another example:
(8 + (-5)) x (-8)
So we first work on solving what is inside the first parenthesis :
8 + (-5) this is 8 - 5 (as we did before, the plus outside the parenthesis where -5 is, results in a minus sign as it multiplies the "-" that is shown ahead of 5.
So, inside this parenthesis we get: 8 - 5 = 3
Now we are left to multiply 3 times (-8)
This is a product of a positive number (3) times a negative number (-8). Again, do the rule for product of the signs (positive times negative equals negative) , ad then the product of the numbers: 3 x 8 = 24
so the answer is - 24
Another example:
(-9) x ((-10)+ 10)
We need to start by solving the operation indicated inside the parenthesis:
(-10) + 10 This is the same as: - 10 + 10 = 0
Now, whenwe use this result in the full expression, we get:
(-9) x 0 = 0 SInce any number multiplied times zero is zero.