Transcript 1-3 Multiplying and Dividing Real Numbers Warm Up California Standards

1-3 Multiplying and Dividing Real Numbers
Preview
Warm Up
California Standards
Lesson Presentation
1-3 Multiplying and Dividing Real Numbers
Warm Up
Multiply or divide.
1. 6(7)
2.
42
3. 42 ÷ 7 6
4.
4
5. Write
as a mixed number.
6. Write
as an improper fraction.
1-3 Multiplying and Dividing Real Numbers
California
Standards
2.0 Students understand and use such
operations as taking the opposite, finding the
reciprocal, taking a root, and raising to a
fractional power. They understand and use the
rules of exponents.
1-3 Multiplying and Dividing Real Numbers
Vocabulary
reciprocal
multiplicative inverse
1-3 Multiplying and Dividing Real Numbers
When you multiply or divide two numbers, the
signs of the numbers determine whether the
result is positive or negative.
Numbers
Product/Quotient
Both positive
Positive
One negative
Negative
Both negative
Positive
1-3 Multiplying and Dividing Real Numbers
1-3 Multiplying and Dividing Real Numbers
Additional 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.
1-3 Multiplying and Dividing Real Numbers
Additional Example 1: Multiplying and Dividing
Signed Numbers
Find the value of each expression.
C.
Multiply.
The quotient of two numbers
with different signs is negative.
1-3 Multiplying and Dividing Real Numbers
Check It Out! Example 1
Find the value of each expression.
1a. 35  (–5)
–7
The quotient of two numbers
with different signs is negative.
1b. –11(–4)
44
The product of two numbers
with the same sign is positive.
1c. –6(7)
–42
The product of two numbers with
different signs is negative.
1-3 Multiplying and Dividing Real Numbers
Two numbers are reciprocals if their product is 1.
A number and its reciprocal are called multiplicative
inverses.
To divide by a number, you can multiply by its
multiplicative inverse.
1-3 Multiplying and Dividing Real Numbers
Additional Example 2A: Dividing with 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.
1-3 Multiplying and Dividing Real Numbers
Additional Example 2B: Dividing with Fractions
Divide.
Write
as an improper fraction.
To divide by
and
, multiply by
have different signs,
so the quotient is negative.
.
1-3 Multiplying and Dividing Real Numbers
Helpful Hint
You can write the reciprocal of a number by
switching the numerator and denominator. A
number written without a denominator has a
denominator of 1.
1-3 Multiplying and Dividing Real Numbers
Check It Out! Example 2a
Divide.
Write
as an improper fraction.
To divide by
, multiply by
and –9 have the same signs,
so the quotient is positive.
.
1-3 Multiplying and Dividing Real Numbers
Check It Out! Example 2b
Divide.
To divide by
, multiply by
.
Multiply the numerators and
multiply the denominators.
and
have different signs,
so the quotient is negative.
1-3 Multiplying and Dividing Real Numbers
Check It Out! Example 2c
Divide.
Write
as an improper fraction.
To divide by
multiply by
.
The signs are different, so the
quotient is negative.
1-3 Multiplying and Dividing Real Numbers
The number 0 has special properties
for multiplication and division.
1-3 Multiplying and Dividing Real Numbers
1-3 Multiplying and Dividing Real Numbers
Additional Example 3: Multiplying and Dividing
with Zero
Multiply or divide if possible.
0
A. 15
Zero is divided by a nonzero number.
0
B. –22  0
undefined
C. –8.45(0)
0
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 any number and 0 is 0.
1-3 Multiplying and Dividing Real Numbers
Check It Out! Example 3
Multiply or divide.
3a.
Zero is divided by a nonzero number.
0
3b. 0 ÷ 0
undefined
The quotient of zero and any nonzero
number is 0.
A number is divided by zero.
A number divided by 0 is undefined.
3c. (–12.350)(0) A number is multiplied by zero.
0
The product of any number
and 0 is 0.
1-3 Multiplying and Dividing Real Numbers
Additional 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 hours before
3
landing. How many miles away from the liftoff
site will 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.
rate
times
3
34

time
11
3
1-3 Multiplying and Dividing Real Numbers
Additional Example 4 Continued
3
3 • 1
15 • 4
1 =
4
3
4 3
15(4)
60
=
4(3)
12
=5
1
Write 3 3 and 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.
1-3 Multiplying and Dividing Real Numbers
Check It Out! Example 4
What if…? On another hot-air balloon trip,
the wind speed is 5.25 mi/h. The trip is
planned for 1.5 hours. The balloon travels in a
straight line parallel to the ground. How many
miles away from the liftoff site will the
balloon land?
5.25(1.5)
Rate times time equals distance.
= 7.875 mi
Distance traveled.
1-3 Multiplying and Dividing Real Numbers
Lesson Quiz
Find the value of each expression.
1.
35 –5
–7
2. 2(–6) –12
Multiply or divide if possible.
3. –3 ÷ 1 3 – 12
4
7
4. –2 1 (0) 0
3
5. – 3  0
4
undefined
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