Grade 7, Unit 5.11 - Open Up Resources

Consider the equation: $\text- 27x = \text- 35$

Without computing:

Is the solution to this equation positive or negative?
Are either of these two numbers solutions to the equation?

$\frac{35}{27}$

$\text-\frac{35 }{ 27}$

Find the missing values in the equations
1. $\text-3 \boldcdot 4 = \text{?}$
2. $\text-3 \boldcdot \text{?} = 12$
3. $3 \boldcdot \text{?} = 12$
4. $\text{?} \boldcdot \text-4 = 12$
5. $\text{?} \boldcdot 4 = \text-12$
Rewrite the unknown factor problems as division problems.
Complete the sentences. Be prepared to explain your reasoning.
1. The sign of a positive number divided by a positive number is always:
2. The sign of a positive number divided by a negative number is always:
3. The sign of a negative number divided by a positive number is always:
4. 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.
1. Where is each person 10 seconds before they meet up?
2. 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: $1 \otimes 2 = 2$ . The table shows some of the products.

$\otimes$	0	1	2	3
0	0	0	0	0
1		1	2	3
2			0	2
3

In this system, $1 \otimes 3 = 3$ and $2 \otimes 3 = 2$ . How can you see that in the table?
What do you think $2 \otimes 1$ is?
What about $3\otimes 3$ ?
What do you think the solution to $3\otimes n = 2$ is?
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.

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?

US Navy 090226-N-9584H-018 Construction Electrician Constructionman Greg Langdon, assigned to Naval Mobile Construction Battalion (NMCB) 1, installs a new section of drill steel during a water well drilling operation Copyright Owner: Mass Communication Specialist Seaman Ernesto Hernandez Fonte License: Public Domain Via: Wikimedia Commons

Use the coordinate grid to show the drill’s progress.

GeoGebra Applet bz7v4QgM
At this rate, how many hours will it take until the drill reaches -250 feet?

Summary

Any division problem is actually a multiplication problem:

$6 \div 2 = 3$ because $2 \boldcdot 3 = 6$
$6 \div \text- 2 = \text-3$ because $\text-2 \boldcdot \text-3 = 6$
$\text-6 \div 2 = \text-3$ because $2 \boldcdot \text-3 = \text-6$
$\text-6 \div \text-2 = 3$ because $\text-2 \boldcdot 3 = \text-6$

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: Dividing Rational Numbers

11.1: Tell Me Your Sign

11.2: Multiplication and Division

Are You Ready For More?

11.3: Drilling Down

Summary

Practice Problems ▶