THE COMPOUND // FIELD NOTES // WEEK 02
Evaluation, distribution, and first word problems
Method
Paper first, every step
Clean evaluation and clean distribution. Every case this year gets built from these moves.
What you have to be able to do
- Evaluate an expression and combine like terms
- Distribute through parentheses and manage the signs
- Clear decimals and solve consecutive integer problems
The procedures
Evaluate, then combineField Book Lesson 3
- Substitute the given values in parentheses before touching anything.
- Like terms carry identical variable parts. Combine their coefficients only.
Distribute with signsField Book Lesson 4
- Multiply every inside term by the outside factor.
- A minus in front of parentheses changes every sign inside.
Fractional part word problemsField Book Lesson 5
- Translate the sentence directly: of means times, is means equals.
- Watch the order on less than and subtracted from: they reverse.
Decimal and consecutive integer equationsField Book Lesson 6
- Multiply through by 10, 100, or 1000 to clear every decimal, then solve.
- Consecutive integers are N, N + 1, N + 2. Consecutive evens or odds step by 2.
Worked: clearing decimals
- Solve 0.2x + 1.4 = 3.
- Multiply every term by 10: 2x + 14 = 30.
- 2x = 16, so x = 8.
Terms on the record
| Term | Meaning |
|---|
| like terms | terms whose variable parts are identical |
| distributive property | a(b + c) = ab + ac |
| consecutive integers | integers that follow one another, written N, N + 1, N + 2 |