Download Multiply or divide. A.

Multiplying and Dividing
1-3
1-3 Multiplying and Dividing Real Numbers
Real Numbers
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Warm Up
Multiply or divide.
1. 6(7)
2.
42
3. 42 ÷ 7
4.
4
5. Write
as a mixed number.
6. Write
as an improper fraction.
Holt Algebra 1
6
1-3 Multiplying and Dividing Real Numbers
Objectives
Multiply real numbers.
Divide real numbers.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Vocabulary
reciprocal
multiplicative inverse
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Multiplying and Dividing Signed Numbers
Multiplying and Dividing
Numbers with the Same Sign
WORDS
NUMBERS
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 Signed Numbers
Multiplying and Dividing
Numbers with Different Signs
WORDS
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
Example 1: Multiplying and Dividing Signed Numbers
Find the value of each expression.
A.
–5
The product of two numbers
with different signs is negative.
12
The quotient of two numbers
with the same sign is positive.
B.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Example 1C: Multiplying and Dividing Signed Numbers
Find the value of the expression.
First substitute
for x.
The quotient of two numbers
with different signs is negative.
Holt Algebra 1
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
Multiplicative inverses
10 ÷ 5 = 2
1
10
10 ∙ 5 = 5 = 2
Dividing by 5 is the same as multiplying by the
reciprocal of 5, .
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Helpful Hint
You can write the reciprocal of a number by
switching the numerator and denominator. A
whole number has a denominator of 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
Example 2B: Dividing by Fractions
Divide.
Write
as an improper fraction.
To divide by
and
, multiply by
have different signs,
so the quotient is negative.
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
Properties of Zero
WORDS
Multiplication by Zero
The product of any number
and 0 is 0.
NUMBERS
1
·0=0
3
ALGEBRA
a·0=0
Holt Algebra 1
0(–17) = 0
0·a=0
1-3 Multiplying and Dividing Real Numbers
Properties of Zero
WORDS
NUMBERS
ALGEBRA
Holt Algebra 1
Zero Divided by a Number
The quotient of 0 and any
nonzero number is 0.
0
=0
6
0 =0
a
0÷ 2 =0
3
0÷a=0
1-3 Multiplying and Dividing Real Numbers
Properties of Zero
Division by Zero
WORDS
NUMBERS
ALGEBRA
Division by 0 is undefined.
12 ÷ 0
Undefined
a÷0
Undefined
Holt Algebra 1
–5
0
a
0
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. –8.45(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.
1-3 Multiplying and Dividing Real Numbers
Example 4: Recreation Application
The speed of a hot-air balloon is 3 3 mi/h. It
4
1
travels in a straight line for 1 hour before
3
landing. How many miles away from the liftoff
site does the balloon land?
1 hour.
Find the distance traveled at a rate of 3 3
mi/h
for
1
4
3
To find distance, multiply rate by time.
Holt Algebra 1
rate
times
3
34

time
11
3
1-3 Multiplying and Dividing Real Numbers
Example 4: Recreation Application
3 3 • 1 1 = 15 • 4
4
3
4 3
15(4)
60
=
4(3)
12
=5
Write 3 3 and 1 1 as improper fractions.
4
3
Multiply the numerators and
multiply the denominators.
3 3 and 1 1 have the same sign, so
4
3
the quotient is positive.
The hot-air balloon lands 5 miles from the liftoff site.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Lesson Quiz
Find the value of each expression.
1.
35 –5
–7
2. 2x for x = –6 – 12
Multiply or divide.
3. –3 ÷ 1 3 – 12
4
7
4. –2 1 (0) 0
3
undefined
5. – 3  0
4
1
6. A cyclist traveled on a straight road for 1 4
hours at a speed of 12 mi/h. How many
miles did the cyclist travel?
15 miles
Holt Algebra 1