2. Chapter 03 – Section 02 Solving Equation with Multiplication and Division

3. © William James Calhoun To simplify rational expressions, and identify values excluded from the domain of a rational expression. You can add and subtract to and from both sides of an equation to maintain balance. The same is true for multiplication and division. If you double or triple one side of the equation (multiply by 2 or 3) then you must also double or triple the other side to maintain balance. If you cut one side in half (divide by 2) then you must do the same to the other side. After asking how the letter and number are hooked up, we will be entering into the multiplication & division mode of solving.

4. © William James Calhoun Remember: WHATEVER YOU DO TO ONE SIDE OF AN EQUATION YOU MUST ALSO DO TO THE OTHER SIDE! Here are the official properties: For any numbers a, b, and c, if a = b, then ac = bc. 3.2.1 MULTIPLICATION PROPERTY OF EQUALITY For any numbers a, b, and c, if a = b, then =. 3.2.2 DIVISION PROPERTY OF EQUALITY

5. © William James Calhoun EXAMPLE 1α: Solve Rewrite the equation. What is the letter? g What is on the same side of the equation as g? 24 How are g and 24 combined? g is divided by 24 What is the opposite of division? multiplication What do we do to get g alone? multiply both sides by 24 On the left, the 24’s cancel away. On the right, you can multiply out with a calculator (or cancel and then multiply.) 1 2 g = 10 1 1

6. © William James Calhoun EXAMPLE 1β: Solve each equation. a. b. c.

7. © William James Calhoun In several of the problems so far, the problem became one fraction equal to another fraction. There is another way to solve these problems which we have already used: Cross-Multiplication Example: 3(12)=4a 36 = 4a Now, What is the letter? a What is on the same side? 4 How are they hooked up? multiplication The opposite of multiply is? divide Divide both sides by 4. Cancel. 44 9 = a

8. © William James Calhoun EXAMPLE 2α: Solve 12x = 180. 12x = 180 Write the equation. What is the letter? x What is on the same side? 12 Hooked up by? multiplication Undo with? divide Divide both sides by 12. x = 15 12

9. © William James Calhoun EXAMPLE 2β: Solve each equation. a. -5t = 60 b. 15 = 6n c. -3v = -129

10. © William James Calhoun EXAMPLE 3α: Solve. Rewrite the equation. Sometimes, rewriting the mixed number as an improper fraction helps, but… Your calculator can handle the dividing by 3 1 / 4. Do either method you wish. Cancel and simplify. 1 1 1 1

11. © William James Calhoun EXAMPLE 3β: Solve each equation. a. b. c.

12. © William James Calhoun PAGE 153 #15 – 33 odd