Multiplying Rational Numbers

Warmup

• Click on  to begin.â€‹
• After you provide an answer to a question, click on  to continue.
• Then “New Question“.

Activity #1

Analyze Speed and Time Data.

A traffic safety engineer was studying travel patterns along a highway. She set up a camera and recorded the speed and direction of cars and trucks that passed by the camera. Positions to the east of the camera are positive, and to the west are negative.

Here are some positions and times for one car:

• Based on the traffic data above, answer the following questions:

(1.) In what direction is this car traveling?

(2.) What is its velocity?

(3.) What does it mean when the time is zero?

(4.) What could it mean to have a negative time?

Here below are the positions and times for a different car whose velocity is -50 feet per second:

• Complete the table with the rest of the positions.

(1.) In what direction is this car traveling?

(2.) Explain how you know.

• Complete the table below for several different cars passing the camera.

(1.) If a car is traveling west when it passes the camera, will its position be positive or negative 60 seconds before it passes the camera?

(2.) If we multiply a positive number and a negative number, is the result positive or negative?

(3.) If we multiply two negative numbers, is the result positive or negative?

Activity #2

Complete a Table of Speed and Time.

Around noon, a car was traveling -32 meters per second down a highway. At exactly noon (when time was 0), the position of the car was 0 meters.

• Use the information above to complete this table.
• Graph the relationship between the time and the car’s position.

(1.) What was the position of the car at -3 seconds?

(2.) What was the position of the car at 6.5 seconds?

Activity #3

Read Temperature at Different Conditions.

• Read the information below and answer the questions that follow.

A weather station on the top of a mountain reports that the temperature is currently 0Â°C and has been falling at a constant rate of 3Â°C per hour. If it continues to fall at this rate, find each indicated temperature. In each case, explain or show your reasoning.

Challenge #1

Find the missing numbers in each equation below.

Challenge #2

Choose the correct answer for each expression below.

Challenge #3

Look at the patterns along the rows and columns and continue those patterns to complete the table. When you have filled in all the boxes you can see, click on the “More Boxes” button.

What does this tell you about multiplication by a negative?

Quiz Time