how do I think correctly when the questions are 5 + (-2) * (-3), and -8 + 3 * (-4)

Question

at the first question I changed the place of the numbers, making the question (-2) * (-3) +5. After that I tried to solve it with this method : (-2) * (-3)=6, 6+5=11
but at the second question I also changed the place of the numbers making the question -8 * (-4) +3. and I tried to solve it with this method : -8 * (-4)= 4*8=32 +3 =35

I did the very same thing at both questions, and the second question is wrong. How do I think correctly to make the right awnser?

 

Answer 1

Ah! Order of operations! There is a certain order in which math problems with different functions occur. Here is a mnemonic (memory aid) for you:

Parachute Expert, My Dear Aunt Sally. The first letters in this sentence:

P

E

M

D

A 

S

give you the order in which operations need to occur. 

P = parenthesis: any math function (+,-,*,divide) in parenthesis is performed FIRST

E = after parenthesis, exponents are computed

M = multiplication comes next

D = division next

A = adding after multiplication and division and finally,

S = subtraction. 

So, in your first problem: 5 +(-2) * (-3) =, note that multiplication must occur BEFORE addition, so we multiply (-2) * (-3) = 6 (remember, a negative times a negative results in a positive number). After the multiplication, we can then add the 5 to the 6, resulting in the answer: 11. This is essentially what you did, but for the wrong reason. 

 

Here's your second problem: (-8) + 3 * (-4). Multiplication must occur BEFORE addition, so we multiply 3 * (-4) = -12. After the multiplication, we can then add the -12 to the (-8), resulting in the answer: -20.

Note that we do NOT perform operations left to right, as you may think, but PEMDAS.

 

Hope this helps!

Karen