Download Chapter 1: Introduction to Algebra: Integers

1
Introduction to Algebra:
Integers
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 1
1.6 Multiplying Integers
R.1 Fractions
Objectives
1. Use a raised dot or parentheses to express
multiplication.
2. Multiply integers.
3. Identify properties of multiplication.
4. Estimate answers to application problems
involving multiplication.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 2
Use a raised dot or parentheses to
express multiplication.

Numbers being multiplied are called
factors and the answer is called the
product.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 3
Use a raised dot or parentheses to
express multiplication.
Example Rewrite the multiplication in
three different ways. Identify the factor and
the product.
10 × 7
The factors are 10 and 7 and the product is 70.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 4
Multiply integers.
Multiply Two Integers
If two factors have different signs, the product
is negative.
For example,
and
4  ( 5)  20
2  6  12
If two factors have the same sign, the product
is positive. For example,
7  3  21
and  3  ( 10)  30
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 5
Multiply integers.
Example Multiply the integers.
2 • 8
2  8  16


Positive
Negative
The factors have
different signs, so the
product is negative.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 6
Multiply integers.
Example Multiply the integers.
10( 6)
10( 6)  60
The factors have the
same sign, so the
product is positive.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 7
Multiply integers.
Example Multiply the integers.
3 • (4 • 5)
3  (4  5)
Multiply numbers in
parentheses first.
3  20
60
Then multiply the resulting pair
of numbers.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 8
Multiply integers.
Example Multiply the integers.
2  ( 2)  ( 2)
2  ( 2)  ( 2)
Multiply the first pair of
numbers.
4  ( 2)
8
Then multiply the resulting pair
of numbers.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 9
Identify properties of multiplication.
Multiplication Property of 0
Multiplying any number by 0 gives a product
of 0.
Some examples are shown below.
16(0) = 0
(0)(5) = 0
32,977(0) = 0
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 10
Identify properties of multiplication.
Multiplication Property of 1
Multiplying a number by 1 leaves the number
unchanged.
Some examples are shown below.
6(1) = 6 –12(1) = –12 (1)(5876) = 5876
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 11
Identify properties of multiplication.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 12
Identify properties of multiplication.
Example Show that the product is
unchanged and name the property that is
illustrated.
7  ( 4)  4  ( 7)
Both products are 28.
Commutative property of multiplication
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 13
Identify properties of multiplication.
Example Show that the product is
unchanged and name the property that is
illustrated.
5  (10  2)  (5  10)  2
5  20  50  2
100  100
Both products are 100.
Associative property of multiplication
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 14
Identify properties of multiplication.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 15
Identify properties of multiplication.
Example Rewrite the product, using the
distributive property. Show that the result is
unchanged. 2( 5  1)
2( 5  1)  ( 2)  ( 5)  ( 2)  (1)
2( 4)  10  ( 2)
88
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 16
Estimate answers to application
problems involving multiplication.
Example Last year Videoland had to replace
392 defective DVDs at a cost of $19 each. How
much money was lost on defective DVDs?
Estimate: Use front end rounding: 392 rounds to
400 and –$19 rounds to –$20.
400  ( $20)  $8000
Exact: 392  ( $19)  $7448
Videoland lost $7448 in defective DVDs.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Slide 17