Download mgpia3e_ppt_01_05

1.5
Multiplying Whole
Numbers and Area
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Multiplication
Multiplication is repeated addition with a different
notation.
4 + 4 + 4 + 4 + 4 = 5 ∙ 4 = 20
5 fours
factor product
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
2
Multiplication Property of 0
The product of 0 and any number is 0.
90=0
06=0
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
3
Multiplication Property of 1
The product of 1 and any number is that same number.
91=9
16=6
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
4
Commutative Property of
Multiplication
Changing the order of two factors does not change
their product.
6 • 3 = 18 and 3 • 6 = 18
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
5
Associative Property of
Multiplication
Changing the grouping of factors does not change
their product.
5 • ( 2 • 3) = 5 • 6 = 30
and
(5 • 2) • 3 = 10 • 3 = 30
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
6
Distributive Property
Multiplication distributes over addition.
5(3 + 4) = 5 • 3 + 5 • 4
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
7
Area
1 square inch
1
5 inches
1
3 inches
Area of a rectangle = length  width
= (5 inches)(3 inches)
= 15 square inches
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
8
Helpful Hint
Remember that perimeter (distance around a plane figure) is
measured in units. Area (space enclosed by a plane figure) is
measured in square units.
Perimeter =
5 inches + 4 inches + 5
inches + 4 inches = 18
inches
5 inches
Rectangle
4 inches
Area = (5 inches)(4 inches) = 20 square inches
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
9
Multiplication Words
There are several words or phrases that indicate the
operation of multiplication. Some of these are as follows:
Key Words
Examples
Symbols
multiply
multiply 4 by 3
4•3
product
times
the product of 2 and 5
7 times 6
2•5
7•6
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
10