Week 8: Word problems, distributing into equations, and negative and zero exponents

Field Book

28 to 31

Due

Test 6 due

Method

Paper first, every step

Words become equations this week: sums, differences, and products get letters, and the word is turns into an equals sign. The exponent story also finishes its edges: what a zero exponent means, and what a negative one does.

What you have to be able to do

Translate a sentence into an equation and solve it
Solve equations that need a distribution first
Evaluate zero and negative exponents

The procedures

Translating words

Name the unknown with a letter before anything else.
Sum means add, difference means subtract, product means multiply, is means equals.
Twice a number is 2n; seven more than it is n + 7.

Distribute, then solve

If the variable is locked in a group, distribute to free it.
Then it is the multi-step routine from last week.
Check against the original sentence, not just the equation.

Zero and negative exponents

Any nonzero base to the zero power is one. Exactly one.
A negative exponent means the reciprocal of the positive power.
4⁻² is one over 4².

Worked

WORKED

Seven more than twice a number is 31. Find the number.
Let n be the number: 2n + 7 = 31.
Subtract 7, divide by 2.
ANSWER: n = 12

WORKED

Evaluate 5⁰ + 2⁻³.
5⁰ is 1.
2⁻³ is 18.
ANSWER: 98

Terms

Term	Meaning
negative exponent	flip to the reciprocal and make the exponent positive
zero exponent	any nonzero base raised to the zero is one
sum	the answer to an addition

Check yourself

1. Solve: 3(x + 4) = 27

2. Evaluate 10⁰

3. Evaluate 4⁻²

reveal answers

x = 5 · 1 · 116

This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.