1. Algebra 1 Chapter 1 Section 3 Multiplying and Dividing Real Numbers

2. When you multiply or divide two numbers, the signs of the numbers determine whether the result is positive or negative.

4. Example 1: Multiplying and Dividing Real Numbers Find the value of each expression. A) -12 · 5 -60 B) 8(-5/4) (8/1)(-5/4) -40/4 -10 The product of two numbers with different signs is negative. First, change the whole number to an improper fraction by placing a one under the 8. Then, multiply top times top and bottom times bottom. Last, divide. The quotient of two numbers with different signs is negative.

5. You Try: Find the value of each expression. 1a) 35 ÷ (-5) 1b) -11(-4) 1C) -6(7)

6. Answers: 1a) -7 1b) 44 1c) -42

7. Two numbers are reciprocals if their product is 1. A number and its reciprocal are called multiplicative inverses. To find the reciprocal of a fraction you flip it over. ex) 2/3 the reciprocal is 3/2

8. To find the reciprocal of a whole number, you first put a 1 under it, then flip it over. ex) 4 first change it to 4/1 the reciprocal of 4 is ¼.

9. To divide by a number, you can multiply by its multiplicative inverse (reciprocal).

10. Example 2: Dividing with fractions. Divide. A) -4/5 ÷ (-8/15) -4/5 · (-15/8) (-4)(-15) 5(8) 60 = 3 40 2 To divide fractions, you bring down the first fraction, change to multiplication and flip over the second fraction. Then you multiply top times top and bottom times bottom. Always reduce your fraction by the largest number you can. (20)

11. B) -4 ÷ 9 ¼ -4/1 ÷ 37/4 -4/1 · 4/37 -4(4) 1(37) -16 37 Write 4 as a fraction by putting a 1 in the denominator. Also, change 9 ¼ to an improper fraction by multiplying the denominator with the whole number and adding the numerator. Bring down the first fraction, change multiplication and flip over the second fraction. Now, multiply. Top times top, and bottom times bottom. This fraction cannot be reduced or simplified.

12. You Try: Divide: 2a) -3/4 ÷ (-9) 2b) 3/10 ÷ (-6/5) 2c) -5/6 ÷ 1 2/3

13. Answers: 2a) -3/4 ÷ (-9) -3/4 ÷ (-9)/1 -3/4 · 1/(-9) (-3)(1) 4(-9) -3 = 1 -36 12 Change the whole number to a fraction. Bring down the first fraction, change to multiplication, flip over the second fraction. Now, multiply. Top times top and bottom times bottom. Simplify by reducing (by 3). A negative divided by a negative is positive.

14. The number 0 has special properties for multiplication and division.

15. Example 3: Multiplying and Dividing with Zero Multiply or divide if possible. A) 0 ÷ 16,568 0 B) 63 7/8 ÷ 0 undefined C) 1 · 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 any number and 0 is 0.

16. You Try: Multiply or Divide. 3a) 0 ÷ (-8 1/6) 3b) 2.04 ÷ 0 3C) (-12.350)(0)

17. Answers: 3a) 0 3b) undefined 3c) 0

18. Example 4: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 parallel to the ground. How many miles away fro the liftoff site will the balloon land?

19. Find the distance traveled at a rate of 4.75 mi/h for 2.5 hours. To find distance, multiply rate by time. (distance = rate times time). rate (speed) times time 4.75 ·2.5 11.875