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6-8 Accelerated 6 Unit 7 Lesson 16

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IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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Lesson 16

16.1 Warm-up 16.2 Activity 16.3 Activity Student Lesson Summary Glossary

Unit 7, Lesson 16

Dividing Rational Numbers

Accelerated 6

16.1

Warm-up

Tell Me Your Sign

Consider the equation:

Without computing:

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

Are You Ready for More?

16.2

Activity

Multiplication and Division

Find the unknown value in each equation.
Rewrite each unknown factor problem (the last four equations of the previous problem) as a division problem.
Complete the sentences. Be prepared to explain your reasoning.
1. A positive number divided by a positive number equals a _______________________.
2. A positive number divided by a negative number equals a _______________________.
3. A negative number divided by a positive number equals a _______________________.
4. A negative number divided by a negative number equals a _______________________.
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?

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16.3

Activity

Drilling Down

A water well drilling rig has dug to a height of -60 feet after 24 hours 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.
A coordinate grid. The origin is labeled “O.” The horizontal axis is labeled “hours” and, starting at the origin, the numbers 10 through 100, in increments of 10, are indicated. There are gridlines midway between. The vertical axis is labeled “feet” and, starting at the origin, the numbers negative 50 through negative 250, in increments of 50, are indicated. There are gridlines midway between.
At this rate, how many hours will it take until the drill reaches -250 feet?

<p>Image of a water well drilling rig.</p>

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Student 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.

A positive number divided by a negative number always results in a negative number.
A negative number divided by a positive number always results in a negative number.
A negative number divided by a negative number always results in a positive number.

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 , the solution is -10 because it is true that .

Glossary

solution to an equation

A solution to an equation is a number that can be used in place of the variable to make the equation true.

The solution to the equation is 7, because it is true that .
The solution to is not 9, because does not equal 8.

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