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Lesson 2-3
Multiplying and Dividing Rational Numbers
1
Multiply real numbers
NAEP 2005 Strand: Number Properties and Operations
Topic: Number Operations
2
Divide real numbers
Local Standards: ____________________________________
Lesson Objectives
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Vocabulary and Key Concepts.
Identity Property of Multiplication
For every real number n,
Examples 1 ? 5 1 ? (5) Multiplication Property of 1
For every real number n,
Examples 1 ? 5 .
Multiplication Property of Zero
For every real number n,
Examples 35 ? 0 35 ? 0 .
–1 ? (5) Multiplying Numbers With the Same Sign
The product of two positive numbers or two negative numbers is
Examples 5 ? 2 .
.
5(2) © Pearson Education, Inc., publishing as Pearson Prentice Hall.
Multiplying Numbers With Different Signs
The product of a positive number and a negative number, or a negative
number and a positive number, is
Examples 3(6) .
3 ? 6 Dividing Numbers With the Same Sign
The quotient of two positive numbers or two negative numbers is
Examples 6 3 .
6 (3) Dividing Numbers With Different Signs
The quotient of a positive number and a negative number, or a negative
number and a positive number, is
Examples 6 3 =
.
6 (3) =
Inverse Property of Multiplication
For every nonzero real number a, there is a multiplicative inverse 1a such
that
.
Examples 5(15) –5(15) The multiplicative inverse of a nonzero rational number ba is
A reciprocal is
Daily Notetaking Guide
Algebra 1 Lesson 2-3
23
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Examples.
1 Multiplying Numbers Simplify the expression 6(34).
The product of a positive number and
()
6 34 a negative number is
Write .
as a mixed number.
a
2 Evaluating Expressions Use the function t 5.5(1,000
)°F to calculate the
(
1,000
5.5
(
)
Divide within parentheses.
F
Multiply.
t 5.5
)
Substitute
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change in temperature t for an increase in altitude a of 7,200 ft.
for a.
3 Simplifying Exponential Expressions Use the order of operations to
simplify each expression.
?
?
?
)
b. (0.2)4 (
Write as repeated multiplication.
Simplify.
)?(
)?(
)?(
)
Write as repeated multiplication.
Simplify.
Quick Check.
1. Simplify each expression.
a. 4(6)
c. 4.9(8)
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Algebra 1 Lesson 2-3
b. 10(5)
d. 23(34)
Daily Notetaking Guide
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(
a. 0.24 Name_____________________________________ Class____________________________ Date ________________
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
All rights reserved.
2. Use the expression in Example 2 to find the change in temperature if a balloon
rises 4,500 ft from the ground.
Daily Notetaking Guide
Algebra 1 Lesson 2-3
25
Name_____________________________________ Class____________________________ Date ________________
Examples.
4 Dividing Numbers Simplify the expression 54 (9).
54 (9) The quotient of a negative number and a negative number is
.
5 Evaluating Expressions Evaluate xy 4z2 for x 4, y 2,
and z 4.
(
)2
Substitute
(
)
Simplify the power.
4
4
2
(
)
for x,
for y, and
for z.
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( )
( )
xy 4z Divide and multiply.
Subtract.
p
6 Division Using the Reciprocal Evaluate r for p 32 and r 34.
32
( )
( )
Rewrite the equation.
Substitute
Multiply by
for p and
for r.
, the reciprocal of 3 .
4
Simplify.
Quick Check.
Simplify each expression.
3. a. 43
b. (2)4
5. Evaluate each expression for x 8, y 5,
and z 3.
a. 3x (2z) y 10
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Algebra 1 Lesson 2-3
b.
2z x
2y
4. a. 42 7
b. 8 (2)
x
6. Evaluate y for x 8 and
y 2 4
5
Daily Notetaking Guide
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
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r