ch 1 sec 6: slide #1 columbus state community college chapter 1 section 6 multiplying integers
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Ch 1 Sec 6: Slide #1
Columbus State Community College
Chapter 1 Section 6
Multiplying Integers
Ch 1 Sec 6: Slide #2
Multiplying Integers
1. Use a raised dot or parentheses to express multiplication.
2. Multiply integers.
3. Identify properties of multiplication.
Ch 1 Sec 6: Slide #3
Arithmetic vs. Algebra
Arithmetic
4 x 7 = 28
Factors
Algebra
4 • 7 = 28 or 4 ( 7 ) = 28 or ( 4 ) ( 7 ) = 28
Product
Factors Product Factors Product Factors Product
Ch 1 Sec 6: Slide #4
Expressing Multiplication in Algebra
EXAMPLE 1 Expressing Multiplication in Algebra
Rewrite each multiplication in three different ways, using a dot or parentheses. Also identify the factors and the product.
(a) 8 x 9
8 • 9 = 72 or 8 ( 9 ) = 72 or ( 8 ) ( 9 ) = 72
The factors are 8 and 9. The product is 72.
(b) 5 x 30
5 • 30 = 150 or 5 ( 30 ) = 150 or ( 5 ) ( 30 ) = 150
The factors are 5 and 30. The product is 150.
Ch 1 Sec 6: Slide #5
Using Parentheses
NOTE
Parentheses are used to show several different things in algebra. When we discussed the associative property of addition earlier in this chapter, we used parentheses as shown below.
7 + (–5 + 5)
7 + 0
7
Now we are using parentheses to indicate multiplication, as in 4 ( 7 ) or ( 4 )( 7 ).
Ch 1 Sec 6: Slide #6
Multiplying Two Integers
Multiplying Two Integers
If two factors have different signs, the product is negative. For example,
–9 • 4 = –36 and 2 • –6 = –12
If two factors have the same sign, the product is positive. For example,
5 • 8 = 40 and –3 • –7 = 21
Ch 1 Sec 6: Slide #8
Multiplying Two Integers
EXAMPLE 2 Multiplying Two Integers
Find each product.
(a) –5 • 6 = –30If two factors have different signs, the product is negative.
(b) (–7)(–8) = 56If two factors have the same sign, the product is positive.
(c) 2(–12) = –24If two factors have different signs, the product is negative.
Ch 1 Sec 6: Slide #9
Multiplying Several Integers
EXAMPLE 3 Multiplying Several Integers
Multiply.
(a) –2 • ( 4 • –8 )
Parentheses tell you to multiply 4 • –8 first.Both factors have different signs, so the product is negative.
–2 • ( –32 )
64 Now multiply –2 • –32. Both factors have the same sign, so the product is positive.
Ch 1 Sec 6: Slide #10
Multiplying Several Integers
EXAMPLE 3 Multiplying Several Integers
Multiply.
(b) –5 • –3 • –6
There are no parentheses, so multiply –5 • –3 first. Both factors have the same sign, so the product is positive.
15 • –6
–90 Now multiply 15 • –6. The factors have different signs, so the product is negative.
Ch 1 Sec 6: Slide #11
CAUTION
CAUTION
In Example 3(b) you may be tempted to think that the final product will be positive because all the factors have the same sign. Be careful to work with just two factors at a time and keep track of the sign at each step.
Ch 1 Sec 6: Slide #12
Calculator Tip – TI-30X IIS
(–)
(–)
Example 3(b): –5 • –3 • –6
Calculator Tip You can use the negative sign keyon your TI-30X IIS calculator for multiplication and division.
(–) x x5 3 6 =(–) (–)
–90
Ch 1 Sec 6: Slide #14
Multiplication Property of 0
Multiplication Property of 0
Multiplying any number by 0 gives a product of 0.Some examples are shown below.
–1 • 0 = 0 ( 0 )( 6 ) = 0 5,928 • 0 = 0
Ch 1 Sec 6: Slide #15
Multiplication Property of 1
Multiplication Property of 1
Multiplying any number by 1 leaves the number unchanged.Some examples are shown below.
–8 • 1 = –8 ( 1 )( 27 ) = 27 44 • 1 = 44
Ch 1 Sec 6: Slide #16
Using Properties of Multiplication
EXAMPLE 4 Using Properties of Multiplication
Multiply. Then name the property illustrated by each example.
(a) ( 0 ) • ( –5 ) Illustrates the multiplication property of 0.
(b) 314 • ( 1 ) Illustrates the multiplication property of 1.
= 0
= 314
Ch 1 Sec 6: Slide #17
Commutative Property of Multiplication
Commutative Property of Multiplication
Changing the order of two factors does not change the product.For example,
4 • 5 = 5 • 4 and 2 • –7 = –7 • 2
Ch 1 Sec 6: Slide #18
Associative Property of Multiplication
Associative Property of Multiplication
Changing the grouping of two factors does not change the product.For example,
6 • ( 5 • 2 ) = ( 6 • 5 ) • 2
6 • ( 10 )
60
= 30 • 2
= 60
Ch 1 Sec 6: Slide #19
Using the Commutative and Associative Properties
EXAMPLE 5 Using the Commutative and Associative Properties
Show that the product is unchanged and name the property that is illustrated in each case.
(a) 9 • 4 = 4 • 9
This example illustrates the commutative property of multiplication.
36 = 36
(b) ( 3 • 8 ) • 2 = 3 • ( 8 • 2 )
This example illustrates the associative property of multiplication.
24 • 2 = 3 • 16
48 = 48
Ch 1 Sec 6: Slide #20
Distributive Property
Distributive Property
Multiplication distributes over addition. An example is shown below.
4 ( 3 + 5 ) = 4 • 3 + 4 • 5
4 ( 8 )
32
= 12 + 20
= 32
4 ( 3 + 5 ) = 4 • 3 + 4 • 5
Ch 1 Sec 6: Slide #21
Using the Distributive Property
EXAMPLE 6 Using the Distributive Property
Rewrite each product using the distributive property. Show that the result is unchanged.
(a) 2 ( 9 + 3 )
2 ( 12 )
2 ( 9 + 3 ) = 2 • 9 + 2 • 3
24
= 18 + 6
= 24
Ch 1 Sec 6: Slide #22
Using the Distributive Property
EXAMPLE 6 Using the Distributive Property
Rewrite each product using the distributive property. Show that the result is unchanged.
(b) –3 ( –8 + 1 )
–3 ( –7 )
–3 ( –8 + 1 ) = –3 • –8 + –3 • 1
21
= 24 + –3
= 21
Ch 1 Sec 6: Slide #23
Multiplying Integers
Chapter 1 Section 6 – End
Written by John T. Wallace