Download Rules for Multiplication

Rules for Multiplication
September 12, 2011
Rules for Multiplication
Objective To multiply real numbers.
Identity Property of Multiplication
When you multiply any given real number
by 1, the product is equal to the
given
number. For example:
4 ∙ 1 = 4 and 1 ∙ 4 = 4
The identity element for multiplication is 1.
Identity Property of Multiplication
There is a unique real number 1 such that
for every real number a,
𝒂 ∙ 𝟏 = 𝒂 and 𝟏 ∙ 𝒂 = 𝒂
Multiplicative Property of Zero
The equations 4 ∙ 0 = 0 and 0 ∙ 4 = 0
illustrate the multiplicative property of
zero: When one (or at least one) of
the
factors of a product is zero, the product
itself is zero.
Multiplicative Property of Zero
For every real number a:
𝒂 ∙ 𝟎 = 𝟎 and 𝟎 ∙ 𝒂 = 𝟎
Multiplicative Property of 1
What is 4 −1 ?
4 −1 = −1 + −1 + −1 + −1 = −4
Multiplying any real number by 1 produces
the opposite of the number.
Multiplicative Property of1
For every real number a:
𝒂 −𝟏 = −𝒂 and
−𝟏 𝒂 = −𝒂
Multiplicative Property of1
A special case of this property occurs when
the value of a is 1.
−1 −1 = 1
Using the multiplicative property of 1 with
the familiar multiplication facts for positive
numbers and properties that you have
learned, you can compute the product of
any two real numbers.
Example 1
Multiply:
4 7
28
4 −7
−28
−4 7
−28
−4 −7
28
Property of Opposites in Products
For all real numbers a and b:
−𝒂 𝒃 = −𝒂𝒃
𝒂 −𝒃 = −𝒂𝒃
−𝒂 −𝒃 = 𝒂𝒃
Rules for Multiplication
Practice in computing products will suggest
to you the following rules
for multiplication
of positive and negative numbers.
1. If two numbers have the same sign, their
product is positive.
2. If two numbers have opposite signs, their
product is negative.
Rules for Multiplication
For multiplication with multiple negative
numbers,
1. The product of an even number of
negative numbers is positive.
2. The product of an odd number of
negative numbers is negative.
Example 2
Multiply:
4 −6 −7 −5
−840
−2 −8 −7 5 −6
3360
−9 3 0 −5
0
Example 3a
Simplify: −3𝑥 −4𝑦
−3𝑥 −4𝑦 = −3 𝑥 −4 𝑦
= −3 −4 𝑥𝑦
= 12𝑥𝑦
Example 3b
Simplify: 4𝑝 + −5
4𝑝 + −5 = 4 + −5 𝑝
= −1 𝑝
= −𝑝
Example 4a
Simplify: −2 𝑥 − 3𝑦
−2 𝑥 − 3𝑦 = −2𝑥 − −2 3𝑦
= −2𝑥 − −6𝑦
= −2𝑥 + 6𝑦
Example 4b
Simplify: 3𝑝 − 4 𝑝 − 2
3𝑝 − 4 𝑝 − 2 = 3𝑝 − 4𝑝 − 4 ∙ 2
= 3𝑝 − 4𝑝 − 8
= 3𝑝 − 4𝑝 + 8
= −𝑝 + 8
Classwork: page 72
Oral Exercises: 1-30
Homework: page 72:
2-34 even, 36-51  3
page 73: Mixed Review