What if you had an algebraic equation involving multiplication or division like ? How could you solve it for the unknown variable *x*? After completing this Concept, you'll be able to solve equations like this one.

### Watch This

CK-12 Foundation: 0302S Solving Equations with Multiplication and Division (H264)

### Guidance

Suppose you are selling pizza for $1.50 a slice and you can get eight slices out of a single pizza. How much money do you get for a single pizza? It shouldn’t take you long to figure out that you get . You solved this problem by multiplying. Here’s how to do the same thing algebraically, using to stand for the cost in dollars of the whole pizza.

#### Example A

*Solve* .

Our is being multiplied by one-eighth. To cancel that out and get by itself, we have to multiply by the reciprocal, 8. Don’t forget to multiply **both sides** of the equation.

#### Example B

*Solve .*

0.25 is the decimal equivalent of one fourth, so to cancel out the 0.25 factor we would multiply by 4.

Solving by division is another way to isolate . Suppose you buy five identical candy bars, and you are charged $3.25. How much did each candy bar cost? You might just divide $3.25 by 5, but let’s see how this problem looks in algebra.

#### Example C

*Solve .*

To cancel the 5, we divide both sides by 5.

#### Example D

*Solve .*

Divide by 1.375

Notice the bar above the final two decimals; it means that those digits recur, or repeat. The full answer is 0.872727272727272....

To see more examples of one - and two-step equation solving, watch the Khan Academy video series starting at http://www.youtube.com/watch?v=bAerID24QJ0.

Watch this video for help with the Examples above.

CK-12 Foundation: Solving Equations with Multiplication and Division

### Guided Practice

*Solve:*

a) .

b) .

**Solutions:**

a) is equivalent to , so to cancel out that , we multiply by the reciprocal, .

b) Divide both sides by 7.

### Explore More

For 1-5, solve the following equations for .

For 6-10, solve the following equations for the unknown variable.

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 3.2.