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1-3 Multiplying and Dividing Real Numbers
Objectives
Multiply real numbers.
Divide real numbers.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
When you multiply two numbers, the signs of the
numbers you are multiplying determine whether
the product is positive or negative.
Factors
Product
3(5) Both positive
15
3(–5) One negative
–15
–3(–5) Both negative
This is true for division also.
Holt Algebra 1
15
Positive
Negative
Positive
1-3 Multiplying and Dividing Real Numbers
Multiplying and Dividing Same Sign Numbers
WORDS
NUMBERS
Multiplying and Dividing
Numbers with the Same Sign
If two numbers have the same sign,
their product or quotient is positive.
4  5 = 20
–15 ÷ (–3) = 5
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Multiplying and Dividing Diff. Sign Numbers
WORDS
Multiplying and Dividing
Numbers with Different Signs
If two numbers have different signs,
their product or quotient is negative.
6(–3) = –18
NUMBERS
Holt Algebra 1
–18 ÷ 2 = –9
1-3 Multiplying and Dividing Real Numbers
Check It Out! Example 1a and 1b
Find the value of each expression.
1a. 35  (–5)
–7
The quotient of two numbers
with different signs is negative.
1b. –11(–4)
44
Holt Algebra 1
The product of two numbers
with the same sign is positive.
1-3 Multiplying and Dividing Real Numbers
Check It Out! Example 1c
Find the value of each expression.
1c. –6x for x = 7
–6x = –6(7)
= –42
Holt Algebra 1
First substitute 7 for x.
The product of two numbers with
different signs is negative.
1-3 Multiplying and Dividing Real Numbers
Example 1: Multiplying and Dividing Signed Numbers
Find the value of each expression.
Top number times whole number,
divided by bottom number
A.
–5
The product of two numbers
with different signs is negative.
B.
12
Holt Algebra 1
The quotient of two numbers
with the same sign is positive.
1-3 Multiplying and Dividing Real Numbers
Example 1C: Multiplying and Dividing Signed Numbers
Find the value of the expression.
First substitute
for x.
Whole number times top number,
divided by bottom number.
The quotient of two numbers
with different signs is negative.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Two numbers are reciprocals if their product is 1. (At
least one of the numbers will be a fraction).
Dividing fractions is the same as
Flip the Second Fraction and Multiply
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Multiplicative inverses
10 ÷ 5 = 2
1
10
10 ∙ 5 = 5 = 2
Dividing by 5 is the same as multiplying by the
reciprocal of 5, because 5 is really 5/1.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Example 2A: Dividing by Fractions
Example 2 Dividing by Fractions
Divide.
To divide by
, multiply by
.
Multiply the numerators and
multiply the denominators.
and
have the same sign,
so the quotient is positive.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Check It Out! Example 2a
Divide.
Write
as an improper fraction.
To divide by
and
, multiply by
have the same signs,
so the quotient is positive.
Holt Algebra 1
.
1-3 Multiplying and Dividing Real Numbers
Check It Out! Example 2b
Divide.
Write the reciprocal of
To divide by
and
.
, multiply by
have different signs,
so the quotient is negative.
Holt Algebra 1
.
1-3 Multiplying and Dividing Real Numbers
No number can be multiplied by 0 to give a
product of 1, so 0 has no reciprocal. Because
0 has no reciprocal, you can’t divide by 0.
Therefore, dividing by zero is undefined (it
doesn’t exist, there is no answer at all).
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Example 3: Multiplying and Dividing with Zero
Multiply or divide.
0
A. 15
Zero is divided by a nonzero number.
0
B. –22  0
undefined
C. –8(0)
0
Holt Algebra 1
The quotient of zero and any nonzero
number is 0.
A number is divided by zero.
Division by zero is undefined.
A number is multiplied by zero.
The product of an number and 0 is 0.