What you should learn

To Divide Rational Numbers

NCTM Curriculm Standards 2, 4, 6 - 9

 

In doing this the teacher wants to make sure that the following words are incorporated into the introductory lesson:

Dimensional Analysis

Complex Fraction

Introduction: Vicki Van Meter had a lot to write in her report about her summer vacation of 1993. At 12 years old, inspired by Amelia Earhart, she became the youngest female to pilot a plane across the Atlantic Ocean. Vicki did all of the flying, navigation, and communication for her 3200-kilometer flight aboard a single-engine Cessna 210. She also had to be concerned about how supplies and fuel were loaded onto the plane.

Before any small aircraft can take off, the pilot must be sure that the aircraft is loaded so that the center of gravity is within certain safe limits. If it is, the pilot is ready for takeoff. If not, the weight must be rebalanced.

Use the table below to find the center of gravity for a particular aircraft. th esafe limit for this aircraft is 82.1. For each location, the weight and the arm are multiplied to find the moment.

Now add the moments, divide by the total weight, and round to the nearest tenth to find the center of gravity.

Total Moments Total Weight = Center of Gravity

250,585 3120 = 80.3

Since 80.3 is less than 82.1, the aircraft is safe and ready for takeoff.

You already know that the quotient of two positive numbers is positive. But how do you determine the sign of the quotient when negative numbers are involved? Since multiplicaiton and division are inverse operations, the rule for finding the sign of the quotient of two numbers is similar to the rule for finding the sign of the product. Study this pattern.

-40 8 = -5

These examples suggest the following rules.

Dividing Two Rational Numbers: The quotient of two numbers having the same sign is positive. The quotient of two numbers having the different signs is negative.

Exercise 1: Find each quotient.

a. -75 (-15)

This division problem may also be written as -75/-15 = 5

b. 72/-8

 

 

To divide by any nonzero number, multiply by the reciprocal of that number.

Exercise 2: Find each quotient.

a. (1/2)5

(1/2)5 = (1/2) * (1/5) = 1/10

b. (-6/7)3

 

 

When solving problems involving measurements, you need to use dimensional analysis. This is the process of carrying units throughout a computation.

If a fraction has one or more fractions in the numerator or denominator, it is called a complex fraction. To simplify a complex fraction, rewrite it as a division sentence.

Exercise 3: Write each fraction in simplest form.

a. (2/3)/8

Rewrite the fraction as (2/3)8, since fractions indicate division.

(2/3)8 = (2/3) * (1/8) = 2/24 = 1/12

b. -5/(3/7)

 

Exercise 4: Simplify (-3a + 16)/4

Activity: Three units of measure that nurses commonly use are cubic centimeters (cc), drops, and grains.

a.A doctor orders 1/400 of a grain of medicine to be given to a patient. The nurse has a vial labeled 1/200 grain per cc. How many cc of the medicine should the nurse give the patient?

b. The doctor also prescribes a 1000-cc intravenous (IV) pouch of fluid to be given to the patient over an 8-hour period. If there are 15 drops in 1 cc, for how many drops per minute should the nurse set the IV?

Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.

Homework: The homework to be assigned for tonight would be:15 - 43 odd, 44, 45, 47, 48 - 55

Alternative Homework: Enriched: 14 - 42 even, 44 - 55

Extra Practice: Students book page 761 Lesson 2-7

Extra Practice Worksheet: Click Here.

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