Ch 4 – Multiplication and Division Equations
4.1 – Multiplying Rational Numbers
Multiplying Two Rational
Numbers
Words
Numbers
Different Signs
Same Sign
Example: Find each product.
2.3(-4)
-5(-1.3)
-3.5(-0.8)
-2.4(7.5)
-3.2(5)
8(-3.2)
-4.7(-0.4)
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 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 3
 
7 5
35
 
47
 3
8    
 7
4
  3 
5
1 1
3   
3 7
1 3
  1 
2 8
Multiplicative Property of -1:
Example: Simplify.
5b(-2.2y)
2x(-4.5y)
5 2 
g  h
7 3 
2 3 
m n
5 5 
Closure Property of Rational Numbers:
4.2 – Counting Outcomes
Tree Diagram:
Outcomes:
Sample Space:
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.
Event:
Fundamental Counting Principle:
Example: How many different kinds of photo processing are possible?
Example: How many different kinds of school sweatshirts are possible?
4.3 – Dividing Rational Numbers
Dividing Rational Numbers
Different Signs
Same Sign
Multiplicative Inverse or Reciprocal:
Multiplicative Inverse Property:
Words
Numbers
Example: Find each quotient.
8  (2.5)
3.9  3
9.3  (0.3)
8.4  (1.2)
16  (2.5)
Dividing Fractions:
Example: Find each quotient.
12 
2
5
3 1
2 
7 2
5  2
 1 
6  5
Example: How much of each ingredient is needed to make one dozen
cookies?
3
Example: Evaluate if x  .
5
6
x

x
2
4.4 – Solving Multiplication and Division Equations
Division Property of Equality:
Example: Solve each equation. Check your solution.
4
7x
5b = 30
-5.5z = -22
-24 = 3g
4t = 28
-0.1m = -7
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 certificates?
Multiplication Property of Equality:
Examples: Solve each equation. Check your solution.
w
6
7
9 
1
m
2
2
 x  8
5
Example: The manager of a movie theater estimates that 5
t
8
4
of the people who attend a matinee are
7
children. How many people attended the 1:00 PM matinee today if 250 children’s tickets were sold?
4.5 – Solving Multi-Step Equations
Procedure:
Goal:
Examples: Solve each equation. Check your solution.
x
4  2
6
3m 12  27
6.2 
3 n
15
Consecutive Integers:
Example:
11  9v  119
a
 5.2  3
8
b4
6
7
Find three consecutive integers whose sum is 27.
Find four consecutive odd integers whose sum is -8.
Find three consecutive even integers whose sum is -18.
4.6 – Variables on Both Sides
Goal:
Example: Solve each equation. Check your solution.
y 8  9y
2
1
x  6 x
5
5
a  9  4a
2
1
n  n2
3
3
5k  2.4  3k 1
Example: In the 1996 Olympics, the winning times for the 100-meter freestyle were 48.7 seconds for men
and 54.5 seconds for women. Suppose the men’s time 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:
Identity:
Example: Solve each equation.
2t + 4 – t = 4 + t
16h + 7 = 16 + 16h
4.7 – Grouping Symbols
Examples: Solve and check.
8 = 4(3x + 5)
5(h + 6) – 6 = 3(5h – 2)
5(2x – 1) = -25
7 = 3(x + 1) – 2
4(t + 5) + 6(2t – 3) = 12
Example: The area of the trapezoid is 64 square millimeters. Find the value of x.