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It may be obvious to you that the sum of two even numbers is always even, for example $2+6=8$, $16+264=280$, and so on. But can you prove it?

In the display below you have to create the proof that the sum of two even numbers is even.

Use your mouse (or finger for touch devices) to drag statements into the correct order. The gauge shows if you are moving in the right direction.


Once you have understand the symbols, notation and language of mathematics, then you have to put it all together in a logical form. The concept of proof is central - and unique - to mathematics. Proof requires clear logical thinking. To help the clarity of your written work, pay attention to how you arrange things on the page. Work down the page rather than across. Use one line for each step. Line up things like "equals" or "implies" symbols as you work down the page so that the flow of the mathematics is as clear as possible.

Software/Applets used on this page

This page uses the RankItems JavaScript applet, written for the site by David Viner, as well as the MathJax system for displaying maths symbols.



a convincing demonstration that some mathematical statement is necessarily true, within the accepted standards of the field. A logical argument, not an empirical one. A proposition must be demonstrated to be true in all cases to which it applies, without a single exception.


Equal to F x s, where F is the force in Newtons and s is the distance travelled and is measured in Joules.

Full Glossary List

This question appears in the following syllabi:

AQA A-Level (UK - Pre-2017)C1ProofProofs
AQA AS Maths 2017Pure MathsProofProof
AQA AS/A2 Maths 2017Pure MathsProofProof
CCEA A-Level (NI)C1ProofProofs
CIE A-Level (UK)P1ProofProofs
A ProofA1 ProofProofs
Edexcel A-Level (UK - Pre-2017)C1ProofProofs
Edexcel AS Maths 2017Pure MathsAlgebraic MethodsProof
Edexcel AS/A2 Maths 2017Pure MathsAlgebraic MethodsProof
Methods (UK)M6ProofProofs
OCR A-Level (UK - Pre-2017)C1ProofProofs
OCR AS Maths 2017Pure MathsProofProof
OCR MEI AS Maths 2017Pure MathsProblem Solving and ProofProof
OCR-MEI A-Level (UK - Pre-2017)C3ProofProofs
Pre-U A-Level (UK)1ProofProofs
Scottish Advanced HighersM2ProofProofs
Scottish (Highers + Advanced)AM2ProofProofs
Universal (all site questions)PProofProofs
WJEC A-Level (Wales)C1ProofProofs