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

Chapter 03 – Section 02

Solving Equation with Multiplication and Division

© 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.


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

ca

cb


g 524 24

24 12

EXAMPLE 1α: Solve

EX1β

.125

24g

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

g 5

24 12


EXAMPLE 1β: Solve each equation.

a. b. c.3 a

4 12

2 b

7 14

3 c

5 30


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 a

4 12

3(12) = 4a

36 = 4a

Now,What is the letter?

aWhat is on the same side?

4How are they hooked up?

multiplication

The opposite of multiply is?

divide

Divide both sides by 4.

Cancel.

4 4

9 = a


EXAMPLE 2α: Solve 12x = 180.

EX3β

12x = 180Write 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 12


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


EXAMPLE 3α: Solve.

EX2β

1 13 p 2

4 2

Rewrite the equation.

Sometimes, rewriting the mixed number as an improper fraction helps, but…

Your calculator can handle the dividing by 31/4.

Do either method you wish.

Cancel and simplify.

13 5p

4 2

1 13 p 2

4 2

10p

13

1 13 p 2

4 2

13

41

34

134

134

1

1

1

1


EXAMPLE 3β: Solve each equation.

a. b. c.1 1

3 t 52 4

3 11 m 4

4 2

2 15 y 4

5 20


PAGE 153#15 – 33 odd

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

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