Math as a Language
To use algebra in the real world, you must be able to translate human words into mathematical symbols. The equals sign (\(=\)) is the verb "is."
The Keyword Dictionary
- Addition (+): Sum, plus, increased by, more than.
- Subtraction (-): Difference, minus, decreased by, less than.
- Multiplication (\(\times\)): Product, times, twice (2x), of.
- Division (\(\div\)): Quotient, divided by, ratio.
- Equals (=): Is, results in, same as.
Worked Examples
Example 1: Basic Translation
Sentence: The sum of a number and seven is fifteen.
- "Sum of a number (\(x\)) and seven" \(\to x + 7\).
- "is" \(\to =\).
- "fifteen" \(\to 15\).
- Equation: \(x + 7 = 15\)
Example 2: The "Less Than" Trap
Sentence: Four less than three times a number is eight.
- "Three times a number" \(\to 3x\).
- "Four less than" means you subtract 4 from that result \(\to 3x - 4\). (Note: It is not \(4 - 3x\)).
- Equation: \(3x - 4 = 8\)
Example 3: Parentheses in Words
Sentence: Two times the sum of a number and five is twenty.
- "the sum of a number and five" \(\to (x + 5)\).
- "Two times" that sum \(\to 2(x + 5)\).
- Equation: \(2(x + 5) = 20\)
The Bridge to Quantum Mechanics
Physicists start with a physical "sentence" or intuition. For example: "The total energy of the electron is the sum of its movement and its pull from the nucleus." Translating that sentence into the equation \(E = T + V\) is the first step in formulating the Schrödinger Equation. If you can't translate your physical intuition into an equation, you can't calculate anything. Math is just the sentence written in a more precise alphabet.