holt algebra 1 1-3 multiplying and dividing real numbers 1-3 multiplying and dividing real numbers...
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Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers1-3Multiplying and Dividing Real Numbers
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Add or subtract using a number line.
1. –2 + 9 7 2. –5 – (–3) –2
Add or subtract.
3. –23 + 42 19 4. 4.5 – (–3.7) 8.2
5.
Lesson Quiz
6. The temperature at 6:00 A.M. was –23°F.At 3:00 P.M. it was 18°F. Find the differencein the temperatures.41°F
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Students will be able to Multiply real numbers. And divide real numbers.
Learning Target
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
reciprocalmultiplicative inverse
Vocabulary
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
When you multiply two numbers, the signs of thenumbers you are multiplying determine whetherthe product is positive or negative.
Factors Product
3(5) Both positive
3(–5) One negative
–3(–5) Both negative
15 Positive
–15 Negative
15 Positive
This is true for division also.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Find the value of each expression.
–5The product of two numberswith different signs is negative.
Example 1: Multiplying and Dividing Signed Numbers
A.
12 The quotient of two numberswith the same sign is positive.
B.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Find the value of the expression.
The quotient of two numberswith different signs is negative.
Example 1C: Multiplying and Dividing Signed Numbers
First substitute for x.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Find the value of each expression.
–7The quotient of two numberswith different signs is negative.
Check It Out! Example 1a and 1b
1a. 35 (–5)
44 The product of two numberswith the same sign is positive.
1b. –11(–4)
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Find the value of each expression.
–6x = –6(7) First substitute 7 for x.
Check It Out! Example 1c
1c. –6x for x = 7
= –42 The product 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.A number and its reciprocal are called multiplicative inverses. To divide by a number, you can multiply by its multiplicative inverse.
Dividing by a nonzero number is the same as Multiplying by the reciprocal of the number.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
10 ÷ 5 = 2 10 ∙ = = 215
105
Multiplicative inverses
Dividing by 5 is the same as multiplying by thereciprocal of 5, .
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
You can write the reciprocal of a number by switching the numerator and denominator. A whole number has a denominator of 1.
Helpful Hint
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Example 2 Dividing by FractionsExample 2A: 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 , multiply by .
and 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 , multiply by .
and 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 , multiply by .
and have different signs,
so the quotient is negative.
Holt Algebra 1
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.
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, division by 0 is not possible. We say that division by zero is undefined.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Properties of Zero
WORDS
NUMBERS
ALGEBRA
Multiplication by ZeroThe product of any numberand 0 is 0.
13 · 0 = 0 0(–17) = 0
a · 0 = 0 0 · a = 0
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Properties of Zero
WORDS
NUMBERS
ALGEBRA
Zero Divided by a NumberThe quotient of 0 and any nonzero number is 0.
06 = 0
0 ÷ a = 0
0 ÷ 23 = 0
0a = 0
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Properties of Zero
WORDS
NUMBERS
ALGEBRA
Division by Zero
Division by 0 is undefined.
a ÷ 0 a0
12 ÷ 0Undefined
–5 0
Undefined
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Example 3: Multiplying and Dividing with Zero
Multiply or divide.
A. 15
0
B. –22 0undefined
C. –8.45(0)
0
Zero is divided by a nonzero number.
The quotient of zero and any nonzeronumber 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.
0
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Check It Out! Example 3a
Divide:
Multiply by the reciprocal.
Any number multiplied by0 equals 0.
Turn into an improperfraction.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Check It Out! Example 3b and 3c
Divide:
3b. 0 ÷ 0
0 ÷ 0 = undefined Any number divided by 0 is undefined.
3c. (–12.350)(0)
(–12.350)(0) = 0 The product of any number and 0 is 0.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
rate
334
times
time
113
Example 4: Recreation Application
Find the distance traveled at a rate of 3 mi/h for 1 hour.To find distance, multiply rate by time.
34
13
The speed of a hot-air balloon is 3 mi/h. It
travels in a straight line for 1 hour before
landing. How many miles away from the liftoff
site does the balloon land?
13
34
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Example 4: Recreation Application
3 34 • 1 1
3 = 15 4 • 4
3 Write and as improper fractions.343 1 1
3
15(4) 4(3) = 60
12
= 5
Multiply the numerators andmultiply the denominators.
3 34 and have the same sign, so
the quotient is positive.1 1
3
The hot-air balloon lands 5 miles from the liftoff site.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
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. How many miles away from the liftoff site will the balloon land?
Check It Out! Example 4
5.25(1.5) Speed times time equals distance.
= 7.875 mi Distance traveled.
Holt Algebra 1
1-3 Multiplying and Dividing Real Numbers
Warm UpMultiply or divide.
1. 6(7)
3. 42 7÷
4.2.
6. Write as an improper fraction.
42 6
4
5. Write as a mixed number.