Solving Equations

Using Multiplication and Division

After studying this lesson, you will be able to:

• Solve equations using multiplication and division.

Review of Steps for Solving Equations:

1. Remove parentheses by multiplying (this step is not always necessary)

2. Collect like terms on each side of the equal sign

3. Isolate the variable by undoing the operation

4. Check by substituting the solution into the original equation

Example 1

	This equation can be solved by cross multiplying.
56 = 7a	Use cross multiplication to create a new equation. (4 times 14 and 7 times a)
	To isolate the variable we have to "undo" the 7 times a. The opposite of multiplication is division, so we divide each side by 7
8 = a	56 divided by 7 is 8 and 7a divided by 7 is a

Example 2

	First, let's convert the mixed numbers to improper fractions
	Since we have multiplied by y, we need to "undo" by dividing Remember, dividing by a fraction is done by multiplying by the reciproc
	Multiply each side by
	and cancel out; cross cancel -81 and -27 and 20 and 5

Check:

substitute for 4 y 4 in the equation where we converted to improper fractions

Example 3

10p = -100	Since 10 is multiplied by p, we need to "undo" the operation by dividing by 10
	Both sides are divided by 10
p = -10

Check by substituting -10 in the original equation

10 (-10) = -100

-100 = -100