Lesson 11Dividing Rational Numbers
Let's divide signed numbers.
- I can divide rational numbers.
11.1 Tell Me Your Sign
Consider the equation:
- Is the solution to this equation positive or negative?
- Are either of these two numbers solutions to the equation?
11.2 Multiplication and Division
Find the missing values in the equations
- Rewrite the unknown factor problems as division problems.
Complete the sentences. Be prepared to explain your reasoning.
The sign of a positive number divided by a positive number is always:
The sign of a positive number divided by a negative number is always:
The sign of a negative number divided by a positive number is always:
The sign of a negative number divided by a negative number is always:
Han and Clare walk towards each other at a constant rate, meet up, and then continue past each other in opposite directions. We will call the position where they meet up 0 feet and the time when they meet up 0 seconds.
Han's velocity is 4 feet per second.
Clare's velocity is -5 feet per second.
Where is each person 10 seconds before they meet up?
When is each person at the position -10 feet from the meeting place?
Are you ready for more?
It is possible to make a new number system using only the numbers 0, 1, 2, and 3. We will write the symbols for multiplying in this system like this: . The table shows some of the products.
- In this system, and . How can you see that in the table?
- What do you think is?
- What about ?
- What do you think the solution to is?
- What about ?
11.3 Drilling Down
A water well drilling rig has dug to a height of -60 feet after one full day of continuous use.
- Assuming the rig drilled at a constant rate, what was the height of the drill after 15 hours?
- If the rig has been running constantly and is currently at a height of -147.5 feet, for how long has the rig been running?
Use the coordinate grid to show the drill’s progress.
At this rate, how many hours will it take until the drill reaches -250 feet?
Lesson 11 Summary
Any division problem is actually a multiplication problem:
Because we know how to multiply signed numbers, that means we know how to divide them.
- The sign of a positive number divided by a negative number is always negative.
- The sign of a negative number divided by a positive number is always negative.
- The sign of a negative number divided by a negative number is always positive.
Lesson 11 Practice Problems
Find the quotients:
Find the quotients.
Is the solution positive or negative?
Find the solution mentally.
In order to make a specific shade of green paint, a painter mixes quarts of blue paint, 2 cups of green paint, and gallon of white paint. How much of each color is needed to make 100 cups of this shade of green paint?
Here is a list of the highest and lowest elevation on each continent.
highest point (m) lowest point (m) Europe 4,810 -28 Asia 8,848 -427 Africa 5,895 -155 Australia 4,884 -15 North America 6,198 -86 South America 6,960 -105 Antarctica 4,892 -50
- Which continent has the largest difference in elevation? The smallest?
- Make a display (dot plot, box plot, or histogram) of the data set and explain why you chose that type of display to represent this data set.