Download To divide by any nonzero number, multiply by its reciprocal. Since 0

Name __________________________________
Period __________
Date:
Topic: 1-6 Quotients
Essential Question: Does division have distributive
properties like multiplication? If so, explain why and give
in example. If not, explain why not.
Standard:9-12.A.1.12
Explain and use equivalent representations for algebraic
expressions (e.g., simplify using the distributive property).
Objective:
To review rules for dividing real numbers.
Subtraction is defined in terms of addition and opposites.
Similarly, division is defined in terms of multiplication and
reciprocals.
Definition of
Division:
For every real number a and every nonzero real number b, the
quotient a divided by b is written,
or
To divide by any nonzero number, multiply by
its reciprocal. Since 0 has no reciprocal,
division by 0 is undefined.
Summary
Example 1:
Simplify:
1.
2.
(
3.
Exercise 1:
) (
(
)
(
)
)
(
)
Simplify:
1. (
2.
)
(
)
(
)
3. (
)
(
(
)
)
2
A number and its reciprocal have the same sign. Therefore, the
sign of a quotient of real numbers follows the same rules as the
sign of a product.
Rules for Division:
1. The quotient of two positive numbers or two negative
numbers is a positive
number.
2. The quotient of two numbers when one is positive and
the other negative is
a negative number.
Example 2:
Simplify
(
) (
(
)
)
(
( )(
Exercise 2:
)
)
Simplify
(
)
3
Distributive
Property:
Notice,
(
)
For all real numbers a and b and nonzero real numbers c,
and
Caution!
For example,
Since,
4
Example 3:
Simplify
(
Exercise 3:
)
Simplify
Class work:
page 34 Oral Exercises: 1-19
Homework:
page 35 Written Exercises: 2-28 even, 29-31
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