Multiplying and Dividing Real Numbers 1 3 Real

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 Vocabulary reciprocal multiplicative inverse Holt Algebra 1

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 Example 1: Multiplying and Dividing Signed Numbers Find the value of each expression. A. – 5 The product of two numbers with different signs is negative. 12 The quotient of two numbers with the same sign is positive. B. Holt Algebra 1

1 -3 Multiplying and Dividing Real Numbers Example 1 C: Multiplying and Dividing Signed Numbers Find the value of the expression. First substitute for x. The quotient of two numbers with different signs is negative. Holt Algebra 1

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 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 Example 2 A: Dividing by Fractions Example 2 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 2 B: Dividing by Fractions Divide. Write as an improper fraction. 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 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 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 Example 3: Multiplying and Dividing with Zero Multiply or divide. 0 A. 15 Zero is divided by a nonzero number. 0 B. – 22 0 undefined C. – 8. 45(0) 0 Holt Algebra 1 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.

1 -3 Multiplying and Dividing Real Numbers Example 4: Recreation Application The speed of a hot-air balloon is 3 3 mi/h. It 4 1 travels in a straight line for 1 3 hour before landing. How many miles away from the liftoff site does the balloon land? 1 hour. Find the distance traveled at a rate of 3 3 mi/h for 1 4 3 To find distance, multiply rate by time. Holt Algebra 1 rate times 3 34 time 11 3

1 -3 Multiplying and Dividing Real Numbers Example 4: Recreation Application 3 3 • 1 1 = 15 • 4 4 3 15(4) 60 = 4(3) 12 =5 Write 3 3 and 1 1 as improper fractions. 3 4 Multiply the numerators and multiply the denominators. 3 3 and 1 1 have the same sign, so 4 3 the quotient is positive. The hot-air balloon lands 5 miles from the liftoff site. Holt Algebra 1

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. 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