THE COMPOUND // FIELD NOTES // WEEK 10
Multiplying fractions, compounds, and difference of squares
Field Book
Lessons 36 to 39
Due
Test 8 due · Quiz 2 · Supplement 10
Method
Paper first, every step
Review 2 runs this week. Factor and cancel before you multiply: the lazy path is the accurate path.
What you have to be able to do
- Multiply rational expressions by factor and cancel
- Analyze a chemical compound by mass parts
- Solve by factoring with the zero product rule and factor a difference of squares
The procedures
Multiply fractionsField Book Lesson 36
- Factor every top and bottom completely.
- Cancel matching factors across the multiplication, then multiply what remains.
Chemical compoundsField Book Lesson 37
- Total the mass parts of the formula.
- Each element's share is its parts over the total, times the sample mass.
Zero product ruleField Book Lesson 38
- Move everything to one side so the equation equals zero.
- Factor. If a product is zero, some factor is zero: set each factor to zero and solve.
Difference of squaresField Book Lesson 39
- Identify the two square roots first.
- A2 - B2 = (A + B)(A - B). A parallelogram's opposite sides stay equal, the proof pattern of the week.
Worked: zero product
- Solve x2 - 9 = 0.
- Factor: (x + 3)(x - 3) = 0.
- x = -3 or x = 3.
Terms on the record
| Term | Meaning |
|---|
| zero product rule | if a product equals zero, at least one factor equals zero |
| difference of squares | A2 - B2, which factors as (A + B)(A - B) |
| mass parts | the relative masses contributed by each element in a compound |