The Universal Calculation Engine
The Universal Calculation Engine

Why we use letters when numbers repeat

Part of: Math as a Language

A useful rule about math notation: what stays true when the numbers change.

The rule

For math notation, the rule is the part that still works when you try new examples. Math as a Language puts it in context with practice.

Why it works

Example: multiplying both sides of a true equation by the same nonzero number gives another true equation, because every term was scaled by the same factor. The same “do it to both sides” logic carries over to math notation.

Small numbers

Try 2 + 3 = 5. Multiply both sides by 4: 8 + 12 = 20. Still true. That is the same idea as “do the same thing to both sides” when you solve.

Test it

The rule
A quick test

Try values

Core lesson

Related: Math as a Language. Use the calculator with your own numbers when the example is not close to your case.

Use the calculator

FAQ

Where is the main lesson?

Math as a Language has the full topic, examples, and practice links.

Which calculator first?

After your setup is on paper, open Fraction for a quick numeric pass.