Illustrative Mathematics Grade 7, Unit 5, Lesson 11: Dividing Rational Numbers

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Illustrative Math
Grade 7

Lesson 11: Dividing Rational Numbers

Let’s divide signed numbers.

Illustrative Math Unit 7.5, Lesson 11 (printable worksheets)

Lesson 11 Summary

The following diagram shows how to divide signed numbers.

Lesson 11.1 Tell Me Your Sign

Consider the equation:

-27x = -35
Without computing:

1. Is the solution to this equation positive or negative?
   
2. Are either of these two numbers solutions to the equation?
   35/27
   -35/27
   

• See Video for Whole Lesson

Lesson 11.2 Multiplication and Division

1. Find the missing values in the equations a. -3 · 4 = ? b. -3 · ? = 12 c. 3 · ? = 12 d. ? · -4 = 12 e. ? · 4 = 12
2. Rewrite the unknown factor problems as division problems.
3. Complete the sentences. Be prepared to explain your reasoning. a. The sign of a positive number divided by a positive number is always: b. The sign of a positive number divided by a negative number is always: c. The sign of a negative number divided by a positive number is always: d. The sign of a negative number divided by a negative number is always:
4. 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. a. Where is each person 10 seconds before they meet up? b. 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 ⊗ 2 = 2. The table shows some of the products.

• Show Answer

  

Lesson 11.3 Drilling Down

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

1. Assuming the rig drilled at a constant rate, what was the height of the drill after 15 hours?
2. 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?
3. Use the coordinate grid to show the drill’s progress.
   Open Applet
   
4. At this rate, how many hours will it take until the drill reaches -250 feet?

Lesson 11 Practice Problems

1. Find the quotients:
   24 ÷ 6
   -1.5 ÷ 0.3
   -4 ÷ -20
   
2. Find the quotients:
   a. 2/5 ÷ 3/4
   b. 9/4 ÷ - 3/4
   c. - 5/7 ÷ - 1/3
   d. -5/3 ÷ 1/6
   
3. Is the solution positive or negative?
   a. 2 · x = 6
   b. -2 · x = 6.1
   c. 2.9 · x = -6.04
   d. -2.473 · x = -6.859
   
4. Find the solution mentally
   a. 3 ·(-4) = a
   b. b · (-3) = -12
   c. (-12) · c = 12
   d. d · 24 = -12
   
5. In order to make a specific shade of green paint, a painter mixes 1 1/2 quarts of blue paint, 2 cups of green paint, and 1/2 gallon of white paint. How much of each color is needed to make 100 cups of this shade of green paint?
   

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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