IM: 7.5.11: Dividing Rational Numbers (Lesson)

Consider the equation: -27x=-35 

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Is the solution to this equation positive or negative?

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Is \frac{35}{27} a solution to the equation?

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Is -\frac{35}{27} a solution to the equation?

Find the missing values in the equations

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-3\cdot4=?

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-3\cdot?=12

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3\cdot?=12

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?\cdot-4=12

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?\cdot4=-12

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Rewrite the unknown factor problems as division problems.

Complete the sentences. Be prepared to explain your reasoning.

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The sign of a positive number divided by a positive number is always:

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The sign of a positive number divided by a negative number is always:

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The sign of a negative number divided by a positive number is always:

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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.

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Where is each person 10 seconds before they meet up?

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When is each person at the position -10 feet from the meeting place?

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: 1\otimes2=2. The table shows some of the products.

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In this system, 1\otimes3=3 and 2\otimes3=2. How can you see that in the table?

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What do you think 2\otimes1 is?

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What about 3\otimes3?

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What do you think the solution to 3\otimes n=2 is?

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What about 2\otimes n=3?

A water well drilling rig has dug to a height of -60 feet after one full day of continuous use.

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Assuming the rig drilled at a constant rate, what was the height of the drill after 15 hours?

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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 in the applet to show the drill’s progress:

https://curriculum.illustrativemathematics.org/MS/students/2/5/11/index.html
[Scroll to the tool under "11.3: Drilling Down"]

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Is the solution to this equation positive or negative?

Is \frac{35}{27} a solution to the equation?

Is -\frac{35}{27} a solution to the equation?

-3\cdot4=?

-3\cdot?=12

3\cdot?=12

?\cdot-4=12

?\cdot4=-12

Rewrite the unknown factor problems as division problems.

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:

Where is each person 10 seconds before they meet up?

When is each person at the position -10 feet from the meeting place?

In this system, 1\otimes3=3 and 2\otimes3=2. How can you see that in the table?

What do you think 2\otimes1 is?

What about 3\otimes3?

What do you think the solution to 3\otimes n=2 is?

What about 2\otimes n=3?

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?

At this rate, how many hours will it take until the drill reaches -250 feet?