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IM: 7.5.11: Dividing Rational Numbers (Lesson)

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Last updated 11 months ago
23 questions
11.1: Tell Me Your Sign
Consider the equation: -27x=-35
1
1
1
11.2: Multiplication and Division
11.3: Drilling Down
Question 1
1.

Is the solution to this equation positive or negative?

Question 2
2.

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

Question 3
3.

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

Find the missing values in the equations
1
Question 4
4.

-3\cdot4=?

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Question 5
5.

-3\cdot?=12

1
Question 6
6.

3\cdot?=12

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1
1
Complete the sentences. Be prepared to explain your reasoning.
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Question 10
10.

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

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Question 11
11.

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

1
Question 12
12.

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

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Question 13
13.

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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Question 14
14.

Where is each person 10 seconds before they meet up?

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Question 15
15.

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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Question 16
16.

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

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Question 17
17.

What do you think 2\otimes1 is?

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Question 18
18.

What about 3\otimes3?

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1
A water well drilling rig has dug to a height of -60 feet after one full day of continuous use.
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Question 21
21.

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

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Question 22
22.

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"]
1
Question 23
23.

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

Question 7
7.

?\cdot-4=12

Question 8
8.

?\cdot4=-12

Question 9
9.

Rewrite the unknown factor problems as division problems.

Question 19
19.

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

Question 20
20.

What about 2\otimes n=3?