The Universal Calculation Engine
Insights
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

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.

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

Go deeper: Math as a Language. Use the calculators below with your own loan or bill numbers, not only the examples on this page.

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.