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

1-3 Multiplying and Dividing Real Numbers

Warm UpWarm Up

Lesson PresentationLesson Presentation

California Standards

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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.


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.

California Standards


reciprocalmultiplicative inverse

Vocabulary


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

One negative

Both negative

Positive

Negative

Positive


Find the value of each expression.

–5The product of two numbers with different signs is negative.

Additional Example 1: Multiplying and Dividing Signed Numbers

A.

12 The quotient of two numbers with the same sign is positive.

B.


The quotient of two numbers with different signs is negative.

Multiply.

C.


Additional Example 1: Multiplying and Dividing Signed Numbers



–7 The quotient of two numbers with different signs is negative.

Check It Out! Example 1

1a. 35 (–5)

44 The product of two numbers with the same sign is positive.

1b. –11(–4)

1c. –6(7)

–42 The product of two numbers with

different signs is negative.


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.


Example 2 Dividing by FractionsAdditional Example 2A: Dividing with Fractions

Divide.

To divide by , multiply by .

Multiply the numerators and multiply the denominators.

and have the same sign, so the quotient is positive.


Additional Example 2B: Dividing with Fractions

Divide.

Write as an improper fraction.


and have different signs,

so the quotient is negative.


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.

Helpful Hint


Check It Out! Example 2a

Divide.



and –9 have the same signs,

so the quotient is positive.


Check It Out! Example 2b

Divide.



and have different signs,

so the quotient is negative.


Check It Out! Example 2c

Divide.


To divide by multiply by .

The signs are different, so the quotient is negative.


The number 0 has special properties for multiplication and division.


Additional Example 3: Multiplying and Dividing with Zero

Multiply or divide if possible.

A. 15

0

B. –22 0

undefined

C. –8.45(0)

0

Zero is divided by a nonzero number.

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.

0



Multiply or divide.

3a.

0

Zero is divided by a nonzero number.

The quotient of zero and any nonzero number is 0.

3b. 0 ÷ 0

undefined A number divided by 0 is undefined.

3c. (–12.350)(0)

0 The product of any number and 0 is 0.

A number is divided by zero.

A number is multiplied by zero.


rate

334

times

time

113

Additional 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 hours before

landing. How many miles away from the liftoff

site will the balloon land?

13

34


Additional Example 4 Continued

3 34 • 1 1

3 = 15 4 • 4

3Write and as improper fractions.3

43 1 13

15(4) 4(3)

= 6012

= 5


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.


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. 35–7

–5 2. 2(–6) –12

Lesson Quiz

Multiply or divide if possible.

3. –3 ÷ 1 34

(0)4. –213 5. – 03

4– 12

70

undefined

15 miles

6. A cyclist traveled on a straight road for 1 hours at a speed of 12 mi/h. How many miles did the cyclist travel?

14

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

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