Holt Algebra 1 1-3 Multiplying and Dividing Real Numbers 1-3 Multiplying and Dividing Real Numbers Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson

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


Students will be able to Multiply real numbers. And divide real numbers.

Learning Target

Holt Algebra 1


reciprocalmultiplicative inverse

Vocabulary

Holt Algebra 1


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


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


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



–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



–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


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


10 ÷ 5 = 2 10 ∙ = = 215

105

Multiplicative inverses

Dividing by 5 is the same as multiplying by thereciprocal of 5, .

Holt Algebra 1


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


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


Example 2B: Dividing by Fractions

Divide.

Write as an improper fraction.


and have different signs,

so the quotient is negative.

Holt Algebra 1


Check It Out! Example 2a

Divide.



and have the same signs,

so the quotient is positive.

Holt Algebra 1


Check It Out! Example 2b

Divide.

Write the reciprocal of .


and have different signs,

so the quotient is negative.

Holt Algebra 1


Check It Out! Example 2c

Divide.


To divide by multiply by .

The signs are different so the quotient is negative.

Holt Algebra 1


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


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


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


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


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


Check It Out! Example 3a

Divide:

Multiply by the reciprocal.

Any number multiplied by0 equals 0.

Turn into an improperfraction.

Holt Algebra 1


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


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


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


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


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.

Documents

Holt Algebra 1 1-3 Multiplying and Dividing Real Numbers 1-3 Multiplying and Dividing Real Numbers Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson