1. 1-3 Multiplying and Dividing Real Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview

2. 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.

3. 1-3 Multiplying and Dividing Real Numbers 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. California Standards

4. 1-3 Multiplying and Dividing Real Numbers reciprocal multiplicative inverse Vocabulary

5. 1-3 Multiplying and Dividing Real Numbers When you multiply or divide two numbers, the signs of the numbers determine whether the result is positive or negative. NumbersProduct/Quotient Both positive One negative Both negative Positive Negative Positive

6. 1-3 Multiplying and Dividing Real Numbers

7. 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. Additional Example 1: Multiplying and Dividing Signed Numbers A. 12 The quotient of two numbers with the same sign is positive. B.

8. 1-3 Multiplying and Dividing Real Numbers The quotient of two numbers with different signs is negative. Multiply. C. Find the value of each expression. Additional Example 1: Multiplying and Dividing Signed Numbers

9. 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 1 1a. 35  (–5) 44 The product of two numbers with the same sign is positive. 1b. –11(–4) 1c. –6(7) – 42 The product of two numbers with different signs is negative.

10. 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.

11. 1-3 Multiplying and Dividing Real Numbers Example 2 Dividing by Fractions Additional Example 2A: Dividing with Fractions Divide. To divide by, multiply by. Multiply the numerators and multiply the denominators. and have the same sign, so the quotient is positive.

12. 1-3 Multiplying and Dividing Real Numbers Additional Example 2B: Dividing with Fractions Divide. Write as an improper fraction. To divide by, multiply by. and have different signs, so the quotient is negative.

13. 1-3 Multiplying and Dividing Real Numbers You can write the reciprocal of a number by switching the numerator and denominator. A number written without a denominator has a denominator of 1. Helpful Hint

14. 1-3 Multiplying and Dividing Real Numbers Check It Out! Example 2a Divide. Write as an improper fraction. To divide by, multiply by. and –9 have the same signs, so the quotient is positive.

15. 1-3 Multiplying and Dividing Real Numbers Check It Out! Example 2b Divide. To divide by, multiply by. Multiply the numerators and multiply the denominators. and have different signs, so the quotient is negative.

16. 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. 1-3 Multiplying and Dividing Real Numbers The number 0 has special properties for multiplication and division.

18. 1-3 Multiplying and Dividing Real Numbers

19. 1-3 Multiplying and Dividing Real Numbers Additional Example 3: Multiplying and Dividing with Zero Multiply or divide if possible. 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 any number and 0 is 0. 0

20. 1-3 Multiplying and Dividing Real Numbers Check It Out! Example 3 Multiply or divide. 3a. 0 Zero is divided by a nonzero number. The quotient of zero and any nonzero number is 0. 3b. 0 ÷ 0 undefined A number divided by 0 is undefined. 3c. (–12.350)(0) 0 The product of any number and 0 is 0. A number is divided by zero. A number is multiplied by zero.

21. 1-3 Multiplying and Dividing Real Numbers rate 3 3434 times  time 1 1313 Additional 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 hours before landing. How many miles away from the liftoff site will the balloon land? 1313 3434

22. 1-3 Multiplying and Dividing Real Numbers Additional Example 4 Continued 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.

23. 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 parallel to the ground. How many miles away from the liftoff site will the balloon land? Check It Out! Example 4 5.25(1.5)Rate times time equals distance. = 7.875 mi Distance traveled.

24. 1-3 Multiplying and Dividing Real Numbers Find the value of each expression. 1. 35 –7 –5 2. 2(–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