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. |
| 12r = 120 |
Use cross multiplication to create a new
equation. (5 times r and 12 times 24) |
 |
To isolate the variable we have to undo
the 12 times r. The opposite of multiplication is
division, so we divide each side by 12.we use the
fraction bar symbol for division. |
| r = 10 |
12r divided by 12 is r and 120 divided by
12 is 10 |
Check:
substitute 10 for r in the equation we created by cross
multiplying
12 (10) = 120
120 = 120 (always be sure the 2 sides are equal)
Example 2
 |
First, lets convert the
mixed numbers to improper fractions |
 |
Since we have  multiplied by m, we need to undo by dividing
Remember, dividing by a fraction is done by multiplying
by the reciprocal |
 |
Multiply each side by  |
 |
 cancel out; cross cancel 28 and 7 and 9 and
3 to get  |
Check:
Substitute for m in the equation where we converted
to improper fractions
Example 3
| -6x = 11 |
Since is multiplied by x, we need to undo
the operation by dividing by - 6 |
 |
Both sides are divided by -6 |
 |
In Algebra, we usually leave answers as improper
fractions (reduced) |
Check by substituting 
in the original equation
 (the s cancel)
11 = 11
|
