1 3 Multiplying and Dividing Real Numbers Holt

1 -3 Multiplying and Dividing Real Numbers Holt Algebra 1

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

1 -3 Multiplying and Dividing Real Numbers Warm Up Multiply or divide. 1. 6(7) 2. 42 3. 42 ÷ 7 4. 4 5. Write as a mixed number. 6. Write as an improper fraction. Holt Algebra 1 6

1 -3 Multiplying and Dividing Real Numbers Objectives Multiply real numbers. Divide real numbers. Holt 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 15 3(– 5) One negative – 15 – 3(– 5) Both negative This is true for division also. Holt Algebra 1 15 Positive Negative Positive

1 -3 Multiplying and Dividing Real Numbers Multiplying and Dividing Signed Numbers Multiplying and Dividing Numbers with the Same Sign WORDS NUMBERS If two numbers have the same sign, their product or quotient is positive. 4 5 = 20 – 15 ÷ (– 3) = 5 Holt Algebra 1

1 -3 Multiplying and Dividing Real Numbers Multiplying and Dividing Signed Numbers Multiplying and Dividing Numbers with Different Signs WORDS NUMBERS Holt Algebra 1 If two numbers have different signs, their product or quotient is negative. 6(– 3) = – 18 ÷ 2 = – 9

1 -3 Multiplying and Dividing Real Numbers Check It Out! Example 1 a and 1 b Find the value of each expression. 1 a. 35 (– 5) – 7 The quotient of two numbers with different signs is negative. 1 b. – 11(– 4) 44 Holt Algebra 1 The product of two numbers with the same sign is positive.

1 -3 Multiplying and Dividing Real Numbers Check It Out! Example 1 c Find the value of each expression. 1 c. – 6 x for x = 7 – 6 x = – 6(7) = – 42 Holt Algebra 1 First substitute 7 for x. 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. 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 Multiplicative inverses 1 10 10 ∙ 5 = 2 10 ÷ 5 = 2 Dividing by 5 is the same as multiplying by the reciprocal of 5, Holt Algebra 1 .

1 -3 Multiplying and Dividing Real Numbers Helpful Hint You can write the reciprocal of a number by switching the numerator and denominator. A whole number has a denominator of 1. Holt Algebra 1

1 -3 Multiplying and Dividing Real Numbers Check It Out! Example 2 a Divide. Write as an improper fraction. To divide by and , multiply by have the same signs, so the quotient is positive. Holt Algebra 1 .

1 -3 Multiplying and Dividing Real Numbers Check It Out! Example 2 b Divide. Write the reciprocal of To divide by and . , multiply by have different signs, so the quotient is negative. Holt Algebra 1 .

1 -3 Multiplying and Dividing Real Numbers Check It Out! Example 2 c 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 Multiplication by Zero The product of any number and 0 is 0. NUMBERS 1 · 0=0 3 ALGEBRA a· 0=0 Holt Algebra 1 0(– 17) = 0 0·a=0

1 -3 Multiplying and Dividing Real Numbers Properties of Zero WORDS NUMBERS ALGEBRA Holt Algebra 1 Zero Divided by a Number The quotient of 0 and any nonzero number is 0. 0 =0 6 0 =0 a 0÷ 2 =0 3 0÷a=0

1 -3 Multiplying and Dividing Real Numbers Properties of Zero Division by Zero WORDS NUMBERS ALGEBRA Division by 0 is undefined. 12 ÷ 0 Undefined a÷ 0 Undefined Holt Algebra 1 – 5 0 a 0

1 -3 Multiplying and Dividing Real Numbers Lesson Quiz Find the value of each expression. 1. 35 – 7 2. 2 x for x = – 6 – 12 Multiply or divide if possible. 3. – 3 ÷ 13 – 12 4 7 4. – 2 1 (0) 0 3 undefined 5. – 3 0 4 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 Holt Algebra 1

1 -3 Multiplying and Dividing Real Numbers Homework Due Friday, September 18 th Page 23: 1 -12; 21 -46 Reminder: Homework Quiz tomorrow and turn in assignment sheets! Holt Algebra 1