Multiplication and Division Equations

Ch 4

Multiplication and Division Equations

4.1

Multiplying Rational Numbers

Multiplying Rational Numbers

Example

• Find each product. 2.3(-4)

-3.5(-0.8)

-3.2(5)

-4.7(-0.4)

Example

Find each product. -5(-1.3)

-2.4(7.5)

8(-3.2)

Example

A skydiver jumps from 12,000 feet. Solve the equation h = 12,000 + (0.5)(-32.1)(576) to find his height after he free falls for 24 seconds.

Example

Same skydiver. Solve the equation h = 12,000 + (0.5)(-32.1)(144) to find his height after 12 seconds.

Multiplying Fractions

Example

Find each product.2 37 5

387

Example

Find each product.

1 133 7

3 54 7

Example

Find each product.

4 35

1 312 8

Multiplicative Property of -1

Example

Simplify

5 ( 2.2 )b y

2 ( 4.5 )x y

Example

Simplify

5 27 3

g h

2 35 5

m n

Closure Property

Assignments

#1 – due today P144: 2, 4 – 16

#2 – due next time P144: 18 – 44 even, 49 – 51, 53 – 58 Do multiplication in fraction packet

**You MUST write out each problem and show work on each! Calculators on for checking!!

4.2

Counting Outcomes

Tree Diagram• A diagram used to show the total number of

possible outcomes of an event

Counting Outcomes

• Outcomes – One possible result of a probability event

Ex – there are 16 outcomes for rock characteristics

• Sample Space – The list of all possible outcomes

Example

• Brooke is shopping for a new computer system. She has a list of 2 different CPUs, 3 different monitors, and 3 different printers. How many different ways can she choose one CPU, one monitor, and one printer from her list.

Example

• The Ice Cream Parlor offers the choices from the menu. Draw a tree diagram to find the number of different sundaes that can be made.

Events

• Event – A subset of possible outcomes

Ex – selecting a flavor of ice cream

Ex – selecting a topping

Counting

How many outcomes for sundaes was there?

How many choices for ice cream?

How many choices for toppings?

How many choices for whipped cream?

Is there any relation between those numbers?

Fundamental Counting Principle

Example

• How many different kinds of photo processing are possible?

Example

• How many different kinds of school sweatshirts are possible?

Assignments

• #1 – due today P148: 4 - 14

• #2 – due next time P148: 15 – 18, 20 – 23, 25 – 27, 29

P698 (4-1): 2 – 28 even

4.3

Dividing Rational Numbers

Dividing Rational Numbers

Example

• Find each quotient.• 8 ÷ (-2.5)

• -9.3 ÷ (-0.3)

• 16 ÷ (-2.5)

• -3.9 ÷ 3

• -8.4 ÷ (-1.2)

Multiplicative Inverse

• Multiplicative Inverse or Reciprocal –• Two numbers whose product is 1

3 4 14 3

15 15

Multiplicative Inverse Property

Dividing Fraction

Example

• Find each quotient.

2125

3 127 2

5 216 5

Example

• How much of each ingredient is needed to make one dozen cookies?

Example

• Evaluate if . 35

x

6x

2x

Example

• Evaluate if . 35

x

47x

Assignments

• #1 – due today• P156: 4 - 17

• #2 – due next time• P157: 18 – 34 even, 36 – 41, 51, 54, 56 – 63

• Finish division in fraction packet

Daily Agenda – Jan. 14

• 5-Minute Check

• Grade Assignment

• Quiz A

• 4.4 notes / assignment

4.4

Solving Multiplication and Division Equations

Division Property of Equality

Example

• Solve each equation. Check your solution.

5 30b

Example


24 3g

Example


5.5 22z

Example


4 28t

Example


0.1 7m

Example

• Brian received a $25 gift certificate from his grandparents for his birthday. How many $2.35 packages of trading cards can he buy with the gift certificate?

Multiplication Property of Equality

Example


67w

Example


192

m

Example


2 85

x

Example


84t

Example

• The manager of a movie theater estimates that 5/7

of the people who attend a matinee are children. How many people attended the 1:00 PM matinee today if 250 children’s tickets were sold?

Assignments

• #1 – due today P163: 1, 2, 4 - 10

• #2 – due next time P163: 12 – 32 even, 33 – 36, 38, 41 – 47, 49

4.5

Solving Multi-Step Equations

Procedure

• Work backwards Undo each operation

• Goal: Get the variable by itself

Example


4 26x

Example


3 12 27m

Example


36.215

n

Example


11 9 119v

Example


5.2 38a

Example


4 67

b

Consecutive Integers

• Integers in counting order 4, 5, 6, 7, 8…

• Consecutive even integers 2, 4, 6, 8…

• Consecutive odd integers 5, 7, 9, 11…

Example

• Find three consecutive integers whose sum is 27.

Example

• Find four consecutive odd integers whose sum is -8.

Example

• Find three consecutive even integers whose sum is -18.

Assignments

• #1 – due today P168: 4 - 12

• #2 – due next time P168: 4 – 32 even, 38, 44, 48

Daily Agenda – Jan. 26

• Turn worksheets into Inbox

• 4.6 notes / assignment

4.6

Variables on Both Sides

Goal

• Get the variables on the same side, then solve

Example


8 9y y

Example


9 4a a

Example


2 165 5

x x

Example


2 1 23 3

n n

Example


Example

• In the 1996 Olympics, the winning times for the 100-meter freestyle were about 48.7 seconds for men and 54.5 seconds for women. Suppose the men’s times decrease 0.2 seconds per year and the women’s times decrease 0.3 seconds per year. Solve 48.7 – 0.2x = 54.5 – 0.3x to find when men and women would have the same winning times.

Solutions

• No solution – No value for the variable will make the equation

true Ex: 0 = 7

• Identity – Every value of the variable will make a true

equation Ex: x = x or 5 = 5

Example

• Solve each equation.

2 4 4t t t

Example

• Solve each equation.

16 7 16 16h h

Assignments

• #1 – due today P173: 4 – 15

• #2 – due next time P173: 16 – 32 even, 38 – 45

4-7

Grouping Symbols

Example

• Solve and check.

8 = 4(3x + 5)

Example


5(2x – 1) = -25

Example


5(h + 6) – 6 = 3(5h – 2)

Example


7 = 3(x + 1) - 2

Example


4(t + 5) + 6(2t – 3) = 12

Example

• The area of the trapezoid below is 64 square millimeters. Find the value of x.

Assignments

• #1 – due today P178: 4 – 10

• #2 – due next time P178: 12 – 30 even, 32, 35 – 38

Review

• P180: 1 – 57

Multiplication and Division Equations

Documents

Transcript of Multiplication and Division Equations