1. Holt 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.

2. Holt Algebra 1 1-3 Multiplying and Dividing Real Numbers Multiply real numbers. Divide real numbers. Objectives

3. Holt Algebra 1 1-3 Multiplying and Dividing Real Numbers reciprocal multiplicative inverse Vocabulary

4. 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. FactorsProduct 3(5)Both positive 3(–5)One negative –3(–5) Both negative 15Positive –15 Negative 15 Positive This is true for division also.

5. Holt 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

6. Holt 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

7. Holt Algebra 1 1-3 Multiplying and Dividing Real Numbers Find the value of each expression. –5–5 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.

8. Holt 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. Example 1C: Multiplying and Dividing Signed Numbers First substitute for x.

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

10. Holt Algebra 1 1-3 Multiplying and Dividing Real Numbers Find the value of each expression. – 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.

11. Holt Algebra 1 1-3 Multiplying and Dividing Real Numbers 10 ÷ 5 = 210 ∙ = = 2 1 5 10 5 Multiplicative inverses Dividing by 5 is the same as multiplying by the reciprocal of 5,.

12. Holt 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.

13. Holt 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.

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

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

16. Holt Algebra 1 1-3 Multiplying and Dividing Real Numbers Check It Out! Example 2c Divide. Write as an improper fraction. To divide by multiply by. The signs are different so the quotient is negative.

17. 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.

18. Holt 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. 1313 · 0 = 0 0(–17) = 0 a · 0 = 00 · a = 0

19. Holt 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. 0606 = 0 0 ÷ a = 0 0 ÷ 2323 = 0 0a0a

20. Holt 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 a0a0 12 ÷ 0 Undefined –5 0 Undefined

21. Holt 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

22. Holt Algebra 1 1-3 Multiplying and Dividing Real Numbers Check It Out! Example 3a Divide: Multiply by the reciprocal. Any number multiplied by 0 equals 0. Turn into an improper fraction.

23. Holt Algebra 1 1-3 Multiplying and Dividing Real Numbers 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.

24. Holt Algebra 1 1-3 Multiplying and Dividing Real Numbers rate 3 3434 times  time 1 1313 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. 3434 1313 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? 1313 3434

25. Holt Algebra 1 1-3 Multiplying and Dividing Real Numbers Example 4: Recreation Application 3 3434 1 1313 = 15 4 4343 Write and as improper fractions. 3434 31 1313 15(4) 4(3) = 60 12 = 5 Multiply the numerators and multiply the denominators. 3 3434 and have the same sign, so the quotient is positive. 1 1313 The hot-air balloon lands 5 miles from the liftoff site.

26. Holt 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. 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.

27. Holt Algebra 1 1-3 Multiplying and Dividing Real Numbers Find the value of each expression. 1. 35 –7 –5 2. 2x for x = –6 – 12 Lesson Quiz Multiply or divide if possible. 3. –3 ÷ 1 3434 (0) 4. –2 1313 5. –  0 3434 – 12 7 0 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? 1414