## Tuesday, July 3, 2012

### Solving Equations Using Multiplication and Division

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 $8 \times \1.50 = \12.00$. You solved this problem by multiplying. Here’s how to do the same thing algebraically, using $x$ to stand for the cost in dollars of the whole pizza. Example 4 Solve $\frac{1}{8} \cdot x = 1.5$. Our $x$ is being multiplied by one-eighth. To cancel that out and get $x$ by itself, we have to multiply by the reciprocal, 8. Don’t forget to multiply both sides of the equation. $8 \left ( \frac{1}{8} \cdot x \right ) &= 8(1.5)\\ x &= 12$ Example 5 Solve $\frac{9x}{5} = 5$. $\frac{9x}{5}$ is equivalent to $\frac{9}{5} \cdot x$, so to cancel out that $\frac{9}{5}$, we multiply by the reciprocal, $\frac{5}{9}$. $\frac{5}{9} \left ( \frac{9x}{5} \right ) &= \frac{5}{9}(5)\\ x &= \frac{25}{9}$ Example 6 Solve $0.25x = 5.25$. 0.25 is the decimal equivalent of one fourth, so to cancel out the 0.25 factor we would multiply by 4. $4(0.25x) &= 4(5.25)\\ x &= 21$ Solving by division is another way to isolate $x$. 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 $5x = 3.25$.
To cancel the 5, we divide both sides by 5.
$\frac{5x}{5} &= \frac{3.25}{5}\\ x &= 0.65$
Example 8
Solve $7x = \frac{5}{11}$.
Divide both sides by 7.
$x &= \frac{5}{11.7}\\ x &= \frac{5}{77}$
Example 9
Solve $1.375x = 1.2$.
Divide by 1.375
$x &= \frac{1.2}{1.375}\\ x &= 0.8 \overline{72}$
Notice the bar above the final two decimals; it means that those digits recur, or repeat. The full answer is 0.872727272727272...