Let’s go back to the equation
.
The lowest common denominator of the fractions
and
is 8. So we’ll multiply the expression with those fractions by 8. Because we must
preserve the equality of the equation, we’ll multiply the expression on the other side by 8, too.
Now we’ve got
.
But wait—we just put parentheses back into the equation again. Now what? Simple, we go back
to our old friend the Distributive Property once again. Once we multiply each term inside the
parentheses by 8, both the parentheses and the fractions will disappear. Sweet.

In order to clear away the fractions from , we can multiply both sides of the equationby which of the following numbers?
3 6 9 18
A) 6
B) 3 and 6

C) 9D) 6 and 18
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Summary
Complex, multi-step equations often require multi-step solutions. Before we can begin to isolate
a variable, we might need to simplify the equation first. This may mean using the Distributive
Property to remove parentheses, or multiplying both sides of an equation by a common
denominator to get rid of fractions. Sometimes it requires both techniques.
common denominator
a number that is a multiple of all of the denominators in a
group of fractions
Distributive Property
states that the product of a number and a sum equals the
sum of the individual products of the number and the
addends: for all real numbers
a
,
b
, and
c
,
a
(
b
+
c
)
=
ab
+
ac
multi-step equation
an equation that requires more than one step to solve
variable
a symbol that represents an unknown value
Additive Inverse Property
states that every real number added to its additive inverse
(or opposite) will equal zero: For all real numbers a, a + (-
a) = 0; also called Inverse Property of Addition
coefficient
a number that multiplies a variable