Use the distributive property to remove the parentheses
in the following expression. Then simplify your result
if possible.
10(8 + 4)
The PEMDAS rule says we have to do all operations inside
parentheses before we can multiply.
However, the DISTRIBUTIVE PROPERTY allows us to VIOLATE
the PEMDAS rule to a certain extent!!!
It allows us to multiply first WITHOUT doing the operations
of addition or subtraction inside the parentheses first.
However, when we use the DISTRIBUTIVE PROPERTY we must
multiply by every term inside the parenthesesw.
To demonstrate the DISTRIBUTIVE PROPERTY in your example
we do not have to add the 8 and the 4 in the parentheses
first.
Instead we can multiply the 10 by BOTH the 8 and the 4.
10(8 + 4) =
10(8) + 10(4) =
80 + 40 =
120
That's the answer. You can check it by using PEMDAS, where
we must do the addition inside the parentheses first:
10(8 + 4)
10(12)
120
We get the same answer using PEMDAS that we get when we use
the DISTRIUTIVE PROPERTY.
Now you may wonder why we need to learn the DISTRIBUTIVE
PROPERTY since we can just use PEMDAS, and PEMDAS is
easier.
The answer is that in algebra where we have
unknowns like x sometimes we CANNOT add what is inside
the parentheses, as in the expression 10(8 + x).
We CANNOT add the 8 and the x because x is unknown.
However we can use the DISTRIBUTIVE PROPERTY and get
rid of the parentheses:
10(8 + x) =
10(8) + 10(x) =
80 + 10x
And so the DISTRIBUTIVE PROPERTY allows us to at least
eliminate the parentheses even when we can't add the
terms inside them.
Edwin
