Lesson 9
Multiplying Rational Numbers
Let's multiply signed numbers.
Problem 1
Fill in the missing numbers in these equations
 \(\text2 \boldcdot (\text4.5) = {?}\)
 \((\text8.7) \boldcdot (\text10) = {?}\)
 \((\text7) \boldcdot {?} = 14\)
 \({?} \boldcdot (\text10) = 90\)
Problem 2
A weather station on the top of a mountain reports that the temperature is currently \(0^\circ\text{C}\) and has been falling at a constant rate of \(3^\circ\text{C}\) 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?
Problem 3
Find the value of each expression.
 \(\frac14 \boldcdot (\text12)\)
 \(\text{}\frac {1}{3} \boldcdot 39\)
 \((\text{}\frac {4}{5}) \boldcdot (\text75)\)
 \(\text{}\frac {2}{5} \boldcdot (\text{}\frac {3}{4})\)
 \(\frac83 \boldcdot \text42\)
Problem 4
To make a specific hair dye, a hair stylist uses a ratio of \(1\frac18\) oz of red tone, \(\frac 34\) oz of gray tone, and \(\frac58\) oz of brown tone.

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?
Problem 5
 Here are the vertices of rectangle \(FROG\): \((\text2,5), (\text2,1), (6,5), (6,1)\).
Find the perimeter of this rectangle. If you get stuck, try plotting the points on a coordinate plane.  Find the area of the rectangle \(FROG\).
 Here are the coordinates of rectangle \(PLAY\): \((\text11, 20), (\text11, \text3), (\text1, 20), (\text1, \text3)\). Find the perimeter and area of this rectangle. See if you can figure out its side lengths without plotting the points.