Lesson 9

Working with Signed Numbers

  • Let’s work with signed numbers.

9.1: Sorting Expressions

Sort these into two groups, so that the expressions in each group all have the same value.

  • \(3-5\)
  • \(5+3\)
  • \(4 \boldcdot 2\)
  • \(\text- \frac13 \boldcdot 6\)
  • \(5 - \text-3\)
  • \(\text-4 \boldcdot \text-2\)
  • \(3 + \text-5\)
  • \(\frac13 \boldcdot \text-6\)

9.2: Expanded Form

For each expression given in factored form, write two equivalent expressions in expanded form. If you get stuck, draw a diagram to represent the product. Some blank diagrams are provided—draw additional diagrams as needed.

  1. \((30 + 3)(30 - 2)\)
  2. \((20 - 1)(20 -1)\)
  3. \((100 + 5)(100 - m)\)
  4. \((40 - a)(40 + b)\)
  5. \(y(11-y)\)
  6. \(\text-7(3a-1)\)
  7. \(\frac14 (\text-8a + 12a)\)
  8. \(\text-x(3x-5)\)

9.3: Factoring and Expanding

In each row, write the equivalent expression. If you get stuck, use a diagram to organize your work. The first row is provided as an example. Diagrams are provided for the first three rows.

on left, 2 squares, width = -3. length = 5 and -2y. areas = -15 and 6y. in middle. width = c. length = c and -5. on right, width = 4. areas = 8a and -4b. 
factored expanded
\(\text-3(5-2y)\) \(\text-15+6y\)
\(c(c-5)\)  
  \(8a-4b\)
\(\text-3(2w-7z)\)  
\(\text-(3y-2x)\)  
  \(12x-14x^2\)
\(n(3-10)\)  
  \(5y-7y\)
\(\text-5x(y-2z)\)  
  \(wt-tv-5tz\)
\(\text-a(2b-4c+a)\)  

Summary