Multiplying and Dividing Real Numbers Section 1-6

Goals Goal To Find products and quotients of real numbers. Rubric Level 1 – Know the goals. Level 2 – Fully understand the goals. Level 3 – Use the goals to solve simple problems. Level 4 – Use the goals to solve more advanced problems. Level 5 – Adapts and applies the goals to different and more complex problems.

Vocabulary Multiplicative Inverse Reciprocal

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 15 Positive –15 Negative 15 Positive This is true for division also. Multiplying Real Numbers

Rules for Multiplying and Dividing

Find the value of each expression. –5–5 The product of two numbers with different signs is negative. A. 12 The quotient of two numbers with the same sign is positive. B. Example: Multiplying and Dividing Real Numbers

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

Find the value of each expression. –7–7 The quotient of two numbers with different signs is negative. a. 35  (–5) 44 The product of two numbers with the same sign is positive. b. –11(–4) c. –6(7) – 42 The product of two numbers with different signs is negative. Your Turn:

Reciprocals 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.

10 ÷ 5 = 210 ∙ = = Multiplicative inverses Dividing by 5 is the same as multiplying by the reciprocal of 5,. Reciprocals

You can write the reciprocal of a number by switching the numerator and denominator. A whole number has a denominator of 1. Helpful Hint

Example 2 Dividing by Fractions Divide. Example: Dividing with Fractions To divide by, multiply by. Multiply the numerators and multiply the denominators. and have the same sign, so the quotient is positive.

Divide. Write as an improper fraction. To divide by, multiply by. and have different signs, so the quotient is negative. Example: Dividing with Fractions

Divide. Write as an improper fraction. To divide by, multiply by. and –9 have the same signs, so the quotient is positive. Your Turn:

Divide. To divide by, multiply by. Multiply the numerators and multiply the denominators. and have different signs, so the quotient is negative. Your Turn:

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.

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

Multiply or divide if possible. A 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 Example: Multiplying & Dividing with Zero

Multiply or divide. a. 0 Zero is divided by a nonzero number. The quotient of zero and any nonzero number is 0. b. 0 ÷ 0 undefined A number divided by 0 is undefined. c. (–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. Your Turn:

rate times  time Find the distance traveled at a rate of 3 mi/h for 1 hour. To find distance, multiply rate by time 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? Example: Application

= Write and as improper fractions (4) 4(3) = = 5 Multiply the numerators and multiply the denominators and have the same sign, so the quotient is positive The hot-air balloon lands 5 miles from the liftoff site. Example: Continued

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. = mi Distance traveled. Your Turn:

Joke Time What’s a fish with no eyes? A fsh. What do you call a nun that walks in her sleep? A roamin’ Catholic. Why did the cookie go to the doctor? Because he was feeling crummy.

Assignment 1.6 Exercises Pg. 49 – 51: #8 – 74 even.