Holt McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

Warm Up Multiply or divide.

1. 6(7)

3. 42 7 ÷

4. 2.

6. Write as an improper fraction.

5. Write as a mixed number.

Holt McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

Warm Up Multiply 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.

Holt McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

Multiply real numbers. Divide real numbers.

Objectives

Holt McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

reciprocal multiplicative inverse

Vocabulary

Holt McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

When you multiply two numbers, the signs of the numbers you are multiplying determine whether the 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 McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

WORDS

Multiplying and Dividing Numbers with the Same Sign If two numbers have the same sign, their product or quotient is positive.

NUMBERS 4 • 5 = 20

–15 ÷ (–3) = 5

Multiplying and Dividing Signed Numbers

Holt McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

WORDS

Multiplying and Dividing Numbers with Different Signs If two numbers have different signs, their product or quotient is negative.

NUMBERS 6(–3) = –18

Multiplying and Dividing Signed Numbers

–18 ÷ 2 = –9

Holt McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

Find the value of each expression.

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

Example 1: Multiplying and Dividing Signed Numbers

A.

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

B.

Holt McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

Find the value of the expression.

The quotient of two numbers with different signs is negative.

Multiply.

= –2

C.

Additional Example 1: Multiplying and Dividing Signed Numbers

Holt McDougal 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 McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

10 ÷ 5 = 2 10 ∙ = = 2 1 5

10 5

Multiplicative inverses

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

Holt McDougal 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 McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

Example 2 Dividing by Fractions Example 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 McDougal 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 McDougal 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 McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

Properties of Zero

WORDS

NUMBERS

ALGEBRA

Multiplication by Zero The product of any number and 0 is 0.

1 3 · 0 = 0 0(–17) = 0

a · 0 = 0 0 · a = 0

Holt McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

Properties of Zero

WORDS

NUMBERS

ALGEBRA

Zero Divided by a Number The quotient of 0 and any nonzero number is 0.

0 6 = 0

0 ÷ a = 0

0 ÷ 2 3 = 0

0 a = 0

Holt McDougal 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 a 0

12 ÷ 0 Undefined

–5 0

Undefined

Holt McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

Example 3: Multiplying and Dividing with Zero

Multiply or divide.

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 an number and 0 is 0.

0

Holt McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

rate

33 4

times

•

time

1 1 3

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.

3 4

1 3

The speed of a hot-air balloon is 3 mi/h. It travels in a straight line parallel to the ground for 1 hour before landing. How many miles away from the liftoff site does the balloon land?

1 3

3 4

Holt McDougal Algebra 1

1-3 Multiplying and Dividing Real Numbers

Example 4: Recreation Application

3 3 4 • 1 1

3 = 15 4 • 4

3 Write and as improper fractions. 3 4 3 1 1

3

15(4) 4(3) = 60

12

= 5

Multiply the numerators and multiply the denominators.

3 3 4 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 McDougal 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 parallel to the ground. 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.