Why 2 + 3 × 4 is 14, not 20

Type 2 + 3 × 4 into this calculator and you get 14. Type the same keys into an old pocket calculator and you may well get 20. Both machines are doing exactly what they were built to do. They just follow different rules.

The rule most of us learned at school

In written maths, multiplication and division are done before addition and subtraction. That convention is called operator precedence, and in Australian classrooms it is often taught as BODMAS: Brackets, Orders, Division and Multiplication, Addition and Subtraction.

So 2 + 3 × 4 means “two, plus three lots of four”. Work out 3 × 4 = 12 first, then add the 2. The answer is 14.

Why some calculators say 20

Many basic calculators use immediate execution: every time you press an operator, they finish the sum so far. Press 2 + 3 and then ×, and the calculator quietly turns that into 5 before multiplying by 4. The result is 20.

Immediate execution is simple to build and easy to follow one key at a time, which is why it survived in cheap hardware. It just doesn’t match how the same expression reads on paper.

Which one does stepbystepcalculator.com use?

We follow standard precedence, the same as a scientific calculator, a spreadsheet, or a maths textbook. Multiplication and division happen first, working left to right, then addition and subtraction, also left to right.

A few more examples:

10 − 4 ÷ 2 is 8, because 4 ÷ 2 = 2 comes first.
2 × 3 + 4 × 5 is 26: 6 plus 20.
12 ÷ 3 × 2 is 8. Division and multiplication share a rank, so they run left to right.

When you want the other order

Our basic calculator doesn’t have bracket keys yet. If you want (2 + 3) × 4, press 2 + 3 = first. The 5 lands in your step history, and you can carry on with × 4 = to get 20. Because every step is kept, you can always see how you got there.

Sources

Order of operations (Wikipedia): the precedence rules, BODMAS and the left-to-right convention.
Calculator input methods (Wikipedia): immediate execution and how it differs from formula entry.