Dividing Rational Numbers

Warmup

Small tool for students to practice integer Division. In this lesson, the min value is the negative of the max value. Read the problem. Decide whether the answer is positive or negative. Find the value of the division to 2 decimal places.

Activity #1

Exercise on Division of Integers.

• Try to solve all the problems. When the answer is correct, the red dot changes into a green dot. Click on to do more.

Activity #2

Application of Division to Solve Problems.

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

• Use the above information to answer the following questions:

(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 below to show the drill’s progress.

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

Activity #3

Division Practice.

• Do the following exercise questions to demonstrate your understanding.

(1.) Find the quotients:

(2.) Find the quotients:

(3.) Find the answers to the following without solving. Express your answer as a decimal where ever you have a fraction..

(4.) Is the solution to the equation positive or negative? Click on the correct answer.

Challenge #1

Complete the sentences below. 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:

Challenge #2

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?

Challenge #3

In order to make a specific shade of green paint, a painter mixes  quarts of blue paint, 2 cups of green paint, and gallon of white paint. How much of each color is needed to make 100 cups of this shade of green paint?