You can help keep this site free, by visiting our sponsor, Algebrator - an incredible software program that provides step - by - step solution to not only equations but to any other algebra problem as well!
home
solving equations with fractions
methods for solving quadratic equations
solving equations
solving equations
linear equations
solving equations
solving equations with variables on each side
solving equations
linear equations
solving linear equations
steps for solving linear equations
solving equations with variables on each side
solving quadratic equations
solving equations
solving equations
steps for solving linear equations
quadratic equations
writing linear equations
solving equations
solving rational equations
solving equations
solving equations
solving systems of equations using elimination
solving linear equations
solving equations
solving quadratic equations
methods for solving quadratic equations
solving equations
solving equations
equation solving resources
Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


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