1 3 Multiplying and Dividing Real Numbers Preview

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

1 -3 Multiplying and Dividing Real Numbers Warm Up Multiply or divide. 1. 6(7) 2. 42 3. 42 ÷ 7 6 4. 4 5. Write as a mixed number. 6. Write as an improper fraction.

1 -3 Multiplying and Dividing Real Numbers California Standards 2. 0 Students understand use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand use the rules of exponents.

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

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. Numbers Product/Quotient Both positive Positive One negative Negative Both negative Positive

1 -3 Multiplying and Dividing Real Numbers

1 -3 Multiplying and Dividing Real Numbers Additional 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.

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

1 -3 Multiplying and Dividing Real Numbers Check It Out! Example 1 Find the value of each expression. 1 a. 35 (– 5) – 7 The quotient of two numbers with different signs is negative. 1 b. – 11(– 4) 44 The product of two numbers with the same sign is positive. 1 c. – 6(7) – 42 The product of two numbers with different signs is negative.

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.

1 -3 Multiplying and Dividing Real Numbers Additional Example 2 A: Dividing with 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.

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

1 -3 Multiplying and Dividing Real Numbers Helpful Hint 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.

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

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

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

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

1 -3 Multiplying and Dividing Real Numbers

1 -3 Multiplying and Dividing Real Numbers Additional Example 3: Multiplying and Dividing with Zero Multiply or divide if possible. 0 A. 15 Zero is divided by a nonzero number. 0 B. – 22 0 undefined C. – 8. 45(0) 0 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.

1 -3 Multiplying and Dividing Real Numbers Check It Out! Example 3 Multiply or divide. 3 a. Zero is divided by a nonzero number. 0 3 b. 0 ÷ 0 undefined The quotient of zero and any nonzero number is 0. A number is divided by zero. A number divided by 0 is undefined. 3 c. (– 12. 350)(0) A number is multiplied by zero. 0 The product of any number and 0 is 0.

1 -3 Multiplying and Dividing Real Numbers Additional 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 hours before landing. How many miles away from the liftoff site will 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. rate times 3 34 time 11 3

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

1 -3 Multiplying and Dividing Real Numbers Check It Out! Example 4 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? 5. 25(1. 5) Rate times time equals distance. = 7. 875 mi Distance traveled.

1 -3 Multiplying and Dividing Real Numbers Lesson Quiz Find the value of each expression. 1. 35 – 7 2. 2(– 6) – 12 Multiply or divide if possible. 3. – 3 ÷ 13 – 12 4 7 4. – 2 1 (0) 0 3 5. – 3 0 4 undefined 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