Lesson 11Dividing Rational Numbers
Learning Goal
Let’s divide signed numbers.
Learning Targets
I can divide rational numbers.
Lesson Terms
- solution to an equation
Warm Up: Tell Me Your Sign
Problem 1
Consider the equation:
Without computing:
Is the solution to this equation positive or negative?
Are either of these two numbers solutions to the equation?
Activity 1: Multiplication and Division
Problem 1
Find the missing values in the equations
Problem 2
Rewrite the unknown factor problems as division problems.
Problem 3
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:
Problem 4
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?
Problem 1
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:
0 | 1 | 2 | 3 | |
---|---|---|---|---|
0 | ||||
1 | ||||
2 | ||||
3 |
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
?
Activity 2: Drilling Down
Problem 1
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?
Print Version
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 Summary
Any division problem is actually a multiplication problem:
because because because because
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.
A number that can be used in place of the variable that makes the equation true is called a solution to the equation. For example, for the equation