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6-8 Accelerated 6 Unit 7 Lesson 16

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K-5 Math •6-8 Math 9-12 Math

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•Accelerated 6 Accelerated 7

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Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 •Unit 7 Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 •Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20 Lesson 21 Lesson 22 Lesson 23

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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?

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16.2

Activity

Multiplication and Division

Standards Alignment

Building On

Addressing

7.NS.2.b

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

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Building Toward

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

Standards Alignment

Building On

Addressing

7.NS.2.b

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

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Building Toward

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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Standards Alignment

Building On

7.NS.2

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

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Addressing

Building Toward

7.EE.4.a

Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

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