Solving Equations Using Multiplication and Division

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 4**

*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 5**

*Solve*.

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

**Example 6**

*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 7**

*Solve .*

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

**Example 8**

*Solve*.

Divide both sides by 7.

**Example 9**

*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...

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