1. CONFIDENTIAL 1 Multiplying and Dividing Real Numbers Multiplying and Dividing Real Numbers

2. CONFIDENTIAL 2 Warm Up 1)12 - 18 2)-6 + 14 3)3 - (-5) 4)11 + (-8) Add or subtract:

3. CONFIDENTIAL 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. This is true for division also.

4. CONFIDENTIAL 4 Multiplying and Dividing Signed Numbers

5. CONFIDENTIAL 5 B) 8x for x = -5 4 8x = 8 x -5 4 = 8(-5) 4 = -40 = -10 4 First substitute - 5 for x. 4 Multiply. The quotient of two numbers with different signs is negative. Multiplying and Dividing Signed Numbers Find the value of each expression. A) -12 · 5 = -60 The product of two numbers with different signs is negative.

6. CONFIDENTIAL 6 Find the value of each expression. Now you try! 1a) 35 ÷ (-5) 1b) -11 (-4) 1c) -6x for x = 7

7. CONFIDENTIAL 7 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.

8. CONFIDENTIAL 8 Dividing by Fractions Divide. To divide by - 8, multiply by -15. 15 8 Multiply the numerators and multiply the denominators. - 4, multiply by -8 have the same sign, 5 15 so the quotient is positive.

9. CONFIDENTIAL 9 Write 4 as a fraction with a denominator of 1. Write 1 as an improper fraction. 4 To divide by 37, multiply by 4. 4 37 - 4 and 1 have different signs, 4 so the quotient is negative. 9 9

10. CONFIDENTIAL 10 Divide. Now you try! 2a) 2b) 2c)

11. CONFIDENTIAL 11 No number can be multiplied by 0 to give a product of 1, so 0 has no reciprocal. Because of this, division by 0 is not possible. We say that division by 0 is undefined.

12. CONFIDENTIAL 12 Properties of Zero

13. CONFIDENTIAL 13 Multiplying and Dividing with Zero A ) 0 ÷ 16.568 = 0 B) 63 7 ÷ 0 8 = undefined C) 1 · 0 = 0 Multiply or divide if possible. 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.

14. CONFIDENTIAL 14 Multiply or divide. Now you try! 3a) 3b) 3c)

15. CONFIDENTIAL 15 Recreation Application A hot-air balloon is taken for a 2.5-hour trip. The wind speed (and the speed of the balloon) is 4.75 mi/h. The balloon travels in a straight line. How many miles away from the liftoff site will the balloon land? Find the distance traveled at a rate of 4.75 mi/h for 2.5 hours. To find distance, multiply rate by time. rate times time 4.75 · 2.5 = 11.875 The hot-air balloon will land 11.875 miles from the liftoff site.

16. CONFIDENTIAL 16 4) 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? Now you try!

17. CONFIDENTIAL 17 Assessment Find the value of each expression. 1) -72 ÷ (-9) 2) 11 (-11) 3)-7.2 ÷ x for x = 3.6

18. CONFIDENTIAL 18 Divide: 4) 5) 6)

19. CONFIDENTIAL 19 Multiply or divide if possible. 7) 3.8 ÷ 0 8) 0 (-27) 9) 0 ÷ 2 3

20. CONFIDENTIAL 20 10) It is estimated that 7 million people saw off-Broadway shows in 2002. Assume that the average price of a ticket was $30. How much money was spent on tickets for off-Broadway shows in 2002?

21. CONFIDENTIAL 21 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. This is true for division also. Let’s review

22. CONFIDENTIAL 22 Multiplying and Dividing Signed Numbers

23. CONFIDENTIAL 23 B) 8x for x = -5 4 8x = 8 x -5 4 = 8(-5) 4 = -40 = -10 4 First substitute - 5 for x. 4 Multiply. The quotient of two numbers with different signs is negative. Multiplying and Dividing Signed Numbers Find the value of each expression. A) -12 · 5 = -60 The product of two numbers with different signs is negative.

24. CONFIDENTIAL 24 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.

25. CONFIDENTIAL 25 Dividing by Fractions Divide. To divide by - 8, multiply by -15. 15 8 Multiply the numerators and multiply the denominators. - 4, multiply by -8 have the same sign, 5 15 so the quotient is positive.

26. CONFIDENTIAL 26 Properties of Zero

27. CONFIDENTIAL 27 Multiplying and Dividing with Zero A ) 0 ÷ 16.568 = 0 B) 63 7 ÷ 0 8 = undefined C) 1 · 0 = 0 Multiply or divide if possible. 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.

28. CONFIDENTIAL 28 Recreation Application A hot-air balloon is taken for a 2.5-hour trip. The wind speed (and the speed of the balloon) is 4.75 mi/h. The balloon travels in a straight line. How many miles away from the liftoff site will the balloon land? Find the distance traveled at a rate of 4.75 mi/h for 2.5 hours. To find distance, multiply rate by time. rate times time 4.75 · 2.5 = 11.875 The hot-air balloon will land 11.875 miles from the liftoff site.

29. CONFIDENTIAL 29 You did a great job today!