(4-16) (-8) =

Question

Use the distributive property to evaluate the equation.

I know how to do D.P. but this question confused me! Help me, please!

Answer 1

AS an alternative way (if you are allowed not to use the distributive property):

You could also use PEMDAS (= Please Excuse My Dear Aunt Sally; acronym for the order of operations: 1. P=Parentheses, 2. E=Exponents, 3. M=Multiplication, 4. D=Division, 5. A=Addition, 6. S=Subtraction)

 

Going by PEMDAS:

1. Parentheses first: Handle the expression inside first (4-16) =  -12; (-8) will remain by itself since there isn't any other expression in the parentheses

2.  Exponents = None present

3. Multiplication = -12 * (-8) <-- you may wonder why there still is a parenthesis: in mathematics it is not allowed to put two operational signs next to each other. Multiplication (indicated by *) and the negative sign are two operational signs and should be separated. Another hint: we can write parenthesis only without the multiplication sign. It is understood that multiplication is the required operation.

So now we have: -12 * (-8): the rule says that when you multiply 2 negatives you get a positive number therefore we know the answer will be positive and 12*8 is 96. Therefore your final answer will be 96.

My answer seem longer, but in the end the steps are come out to be same.

Hope this helps in the future.

Stephanie

Answer 2

Distributive property tells us that we can multiply each term (separated by a + or - sign) in the parentheses by each term in the next set of parentheses.

Thus, (4 - 16)(-8) means we are multiplying -8 by 4 AND -8 by -16

-8 x 4 = -32 and -8 x -16 = 128.

Together, we have -32 + 128, which gives us 96.

To check, we note that (4 - 16)(-8) = (-12)(-8) = 96, as above.