Transcript Powerpoint of Notes

PRE-ALGEBRA
Lesson 1-9 Warm-Up
PRE-ALGEBRA
Multiplying and Dividing
Integers (1-9)
What is the “Identity
Property of
Multiplication”?
Identity Property of Multiplication: A number times 1 is equal to the
original number [In other words, the number keeps its identity (doesn’t
change) when it is multiplied by one.]
Examples:
1 x (-5) = -5
nx1=n
What is the “Zero
Property of
Multiplication”?
Zero Property of Multiplication: A number times zero is equal to zero.
Examples:
0 x (-17) = 0
nx0=0
What is the Multiplication Multiplication Property of -1: A number times -1 is equal to the
Property of -1?
opposite of the original number [In other words, the original number
becomes negative if it was positive or positive if it was negative.]
Examples:
-1 x (-5) = 5
n x -1 = -n
PRE-ALGEBRA
Multiplying and Diving
Integers (1-9)
How can you use a
number line to multiply
integers?
Multiplication is repeated addition, so to multiply integers, think of the first
integer as the number of groups, or repeated jumps, and the second
integer as the interval, or distance, of those jumps. Remember to
always start the jumps at zero.
Examples: Show 4 x -3 on a number line.
4 x -3 means “four groups of -3” or “four jumps of intervals of -3”
Examples: Show -3 x -2 on a number line.
3 x -2 means “three groups of -2” or “three jumps of intervals of -2”, so
-3 x -2 means “ the opposite of three groups of -2” or “the opposite of
three jumps of intervals of -2”
PRE-ALGEBRA
Multiplying Integers
LESSON 2-4
Additional Examples
Use a number line to find 5 • (–2).
Start at 0. Make 5 groups
of –2 on the number line.
The sum of 5 groups of –2 is –10. So, 5 • (–2) = –10.
PRE-ALGEBRA
Multiplying and Dividing Integers
LESSON 1-9
Additional Examples
A diver is descending from the surface of the water at
a rate of 5 ft/s. Write an expression with repeated addition to
show how far the diver is from the surface of
the water after four seconds.
Use a number line to show repeated addition.
4 (–5) = (–5) + (–5) + (–5) + (–5) = –20
The diver is 20 feet below the surface of the water.
PRE-ALGEBRA
Multiplying and Diving
Integers (1-9)
How can you use a
pattern to multiply
integers?
To use a pattern to multiply integers, start with products you know to help
you figure out those you don’t.
Examples: Use a pattern to multiply -2(5) and -2(-5)..
PRE-ALGEBRA
Multiplying and Dividing Integers
LESSON 1-9
Additional Examples
Use a pattern to find each product.
a. –2(7)
2(7) = 14
Start with products you know.
1(7) = 7
0(7) = 0
–1(7) = –7
Continue the pattern.
–2(7) = –14
PRE-ALGEBRA
Multiplying and Dividing Integers
LESSON 1-9
Additional Examples
(continued)
b. –2(–7)
2(–7) = –14
Start with products you know.
1(–7) = –7
0(–7) = 0
–1(–7) = 7
Continue the pattern.
–2(–7) = 14
PRE-ALGEBRA
Multiplying and Dividing Integers
LESSON 1-9
Additional Examples
Multiply 6(–2)(–3).
6(–2)(–3) = (–12)(–3)
= 36
Multiply from left to right. The product of
a positive integer and a negative integer
is negative.
Multiply. The product of two negative integers
is positive.
PRE-ALGEBRA
Multiplying and Diving
Integers (1-9)
What are the rules for
multiplying positive and
negative numbers?
Rule: Multiplying Numbers With the Same Sign – The product of two
positive or two negative numbers is positive.
Examples:
5 x 2 = 10
-5 (-2) = 10
Rule: Multiplying Numbers With Different Signs – The product of two
numbers with opposite signs (a “+” number times a “–” number or a “-”
number with a “+” number) is negative.
Examples:
3 x -6 = -18
-3 (6) = 18
The following patterns are true when multiplying numbers with the same
or different signs.
PRE-ALGEBRA
Multiplying and Diving
Integers (1-9)
What are the rules for
dividing positive and
negative numbers?
NOTE: You can use same rules for multiplying positives and
negatives.
Rule: Dividing Numbers With the Same Sign – The quotient of two
positive or two negative numbers is positive.
Examples:
6÷3=2 :
-6 ÷ (-3) = 2
Rule: Multiplying Numbers With Different Signs – The quotient of two
numbers with opposite signs (a “+” number divided by a “–” number or a
“-” number divided by a “+” number) is negative.
Examples:
-6 ÷ 3 = -2 :
6 ÷ -3 = -2
PRE-ALGEBRA
Multiplying and Dividing Integers
LESSON 1-9
Additional Examples
Use the table to find the average of the differences
in the values of a Canadian dollar and a U.S. dollar for
2003–2005.
–29 + (–23) + (–17)
3
Write an expression for
the average.
PRE-ALGEBRA
Multiplying and Dividing Integers
LESSON 1-9
Additional Examples
(continued)
=
–69
3
= –23
Use the order of operations.
The fraction bar acts as a
grouping symbol.
The quotient of a negative integer
and a positive integer is negative.
For 2003–2005, the average difference was –23¢.
PRE-ALGEBRA
Multiplying and Dividing Integers
LESSON 1-9
Lesson Quiz
Find each product or quotient.
1. –7(–3)
2. –36 ÷ (–9)
21
4
3. –12 • 2
4. 7(–3)
–24
–21
5. –6 • (–2) • (–1)
–12
PRE-ALGEBRA