Smart Math guide · Problem Solving

Work Backward

When the final result is known and operations are reversible, undo them in reverse order.

All levelsWorked example includedSelf-check included
← Smart MathRelated calculators
The method

How to use it

  1. List the forward operations.
  2. Reverse their order.
  3. Replace each with its inverse.
Worked example

See it in action

A number is doubled then 7 added to get 25: 25−7=18, then ÷2=9.

Check your thinking

How to verify it

Forward check: 9×2+7=25.

Keep learning

More Problem Solving guides

Problem Solving

Use Understand–Plan–Solve–Check

A repeatable problem-solving cycle reduces rushed mistakes and makes reasoning visible.

Read guide →
Problem Solving

Draw a Diagram

A labeled sketch can reveal relationships that are hidden in words.

Read guide →
Problem Solving

Make a Table

Tables organize repeated cases, patterns, and input-output relationships.

Read guide →
Problem Solving

Let Units Guide the Formula

Units can show which operations make sense and expose mismatched formulas.

Read guide →
CalculatorWiser

Calculators, math tools, reference tables, games, guides and a growing math library.

All calculators · Math Blog
Latest from the Math BlogWho invented mathematics?Euclid: life, ideas, and mathematical legacyWhy zero changed mathematicsMaya mathematics and calendars
Policies & trustPrivacy PolicyCookie PolicyAdvertising & Affiliate DisclosureTerms of UseDisclaimerEditorial PolicyAccessibilityPrivacy Choices