~ 5.11 ~

Dividing Rational Numbers


Learning Targets

  • I can divide rational numbers.

Notes

Any division problem is actually a multiplication problem:

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.

Activities

11.2 Multiplication and Division

  1. Find the missing values in the equations

      • -3 • 4 = ?

      • -3 • ? = 12

      • 3 • ? = 12

      • ? • - 4 = 12

      • ? • 4 = -12

  2. Rewrite the unknown factor problems as division problems.

  3. Complete the sentences. Be prepared to explain your reasoning.

      • The sign of a positive number divided by a positive number is always:

      • The sign of a positive number divided by a negative number is always:

      • The sign of a negative number divided by a positive number is always:

      • 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.

      • Where is each person 10 seconds before they meet up?

      • When is each person at the position -10 feet from the meeting place?

11.3 Drilling Down

What do you remember about proportional relationships?

  • We can write equations about proportional relationships and they look like y = kx.

  • A graph representing a proportional relationship is a line through (0,0) and (1, k).


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, in your workbook or Geogebra: https://www.geogebra.org/m/rp3yp8tc

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

Summary

Assignment

Check Google Classroom!