Multiplying Rational Numbers: IM 7.5.9
[url=https://im.kendallhunt.com/MS/teachers/2/5/9/preparation.html]“Multiplying Rational Numbers”[/url] from IM Grade 7 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 7.5.9
- IM 7.5.9 Lesson: Multiplying Rational Numbers
- Practice 7.5.9
- IM 7.5.9 Practice: Multiplying Rational Numbers
IM 7.5.9 Lesson: Multiplying Rational Numbers
Where was the girl:
[list=1][*]5 seconds [i]after[/i] this picture was taken? Mark her approximate location on the picture.[/*][*]5 seconds [i]before[/i] this picture was taken? Mark her approximate location on the picture.[/*][/list]
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.
[size=150]Here are some positions and times for one car:[/size][br][center][img]data:image/png;base64,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[/img][/center][br]In what direction is this car traveling?
What is its velocity?
What does it mean when the time is zero?
What could it mean to have a negative time?
Here 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.[br][br]In what direction is this car traveling? Explain how you know.
Complete the table for several different cars passing the camera.
If we multiply a positive number and a negative number, is the result positive or negative?
If a car is traveling west when it passes the camera, will its position be positive or negative 60 seconds [i]before[/i] it passes the camera?
If we multiply two negative numbers, is the result positive or negative?
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. Complete the table.
Graph the relationship between the time and the car's position.
What was the position of the car at -3 seconds?
What was the position of the car at 6.5 seconds?
Find the value of these expressions without using a calculator.
[math](-1)^2[/math]
[math]\left(-1\right)^3[/math]
[math]\left(-1\right)^4[/math]
[math]\left(-1\right)^{99}[/math]
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?
IM 7.5.9 Practice: Multiplying Rational Numbers
Fill in the missing numbers in this equation.
[math]\left(-2\right)\cdot\left(-4.5\right)=?[/math]
[math]\left(-8.7\right)\cdot\left(-10\right)=?[/math]
[math]\left(-7\right)\cdot?=14[/math]
[math]?\cdot\left(-10\right)=90[/math]
A weather station on the top of a mountain reports that the temperature is currently 0°C and has been falling at a constant rate of 3°C per hour. If it continues to fall at this rate, find each indicated temperature. Explain or show your reasoning.
What will the temperature be in 2 hours?
What will the temperature be in 5 hours?
What will the temperature be in half an hour?
What was the temperature 1 hour ago?
What was the temperature 3 hours ago?
What was the temperature 4.5 hours ago?
Find the value of each expression.
[math]\frac{1}{4}\cdot\left(-12\right)[/math]
[math]-\frac{1}{3}\cdot39[/math]
[math]\Big(-\frac{4}{5}\Big)\cdot(-75)[/math]
[math]\left(-\frac{2}{5}\right)\cdot\left(-\frac{3}{4}\right)[/math]
[math]\frac{8}{3}\cdot\left(-42\right)[/math]
[size=150]To make a specific hair dye, a hair stylist uses a ratio of [math]1\frac{1}{8}[/math] oz of red tone, [math]\frac{3}{4}[/math] oz of gray tone, and [math]\frac{5}{8}[/math] oz of brown tone.[/size][br][br]If the stylist needs to make 20 oz of dye, how much of each dye color is needed?
If the stylist needs to make 100 oz of dye, how much of each dye color is needed?
Here are the vertices of rectangle FROG: (-2.5), (-2,1), (6,5), (6,1). Find the perimeter of this rectangle. If you get stuck, try plotting the points on a coordinate plane.
What is the perimeter of [math]FROG[/math]?
Find the area of the rectangle [math]FROG[/math].
Here are the coordinates of rectangle [math]PLAY[/math]: [math](-11,20),(-11,-3),(-1,20),(-1,-3)[/math].[br][br]What is the perimeter of [math]PLAY[/math]?[br][br]See if you can answer the question without plotting the points. But, if you get stuck, there is a graph below for you to use to help you answer this question.
What is the area of [math]PLAY[/math]?[br][br]See if you can answer the question without plotting the points. But, if you get stuck, there is a graph below for you to use to help you answer this question.