Solving Equations with 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.
1. 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.
2. 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.
3. Solve .
To cancel the 5, we divide both sides by 5.
4. 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....
is equivalent to , so to cancel out that , we multiply by the reciprocal, .
Divide both sides by 7.
For 1-5, solve the following equations for .
For 6-10, solve the following equations for the unknown variable.
To view the Review answers, open this PDF file and look for section 3.2.