2 + 3 × 4 on a calculator: 14 or 20?

14 is the right answer under the order of operations. A basic calculator that applies each operation as you press the keys will show 20, while a scientific calculator will show 14. It is one of the easiest ways to see that calculators do not all work the same way.

14Order of operations
20Basic calculator, key by key

See it worked out

Order of operations

Multiplication before addition.

= 14

Written out: 2 + 3 × 4

2 + 3 × 4Multiply/divide, left to right
=2 + 12Add/subtract, left to right
=14

Keys pressed one at a time

A basic calculator finishes 2 + 3 before it sees the ×.

= 20

Written out: (2 + 3) × 4

(2 + 3) × 4Parentheses first: add/subtract, left to right
=5 × 4Multiply/divide, left to right
=20

Two kinds of calculator

Many basic four-function calculators use immediate execution: as soon as you press the next operator key, they finish the previous operation. So 2 + 3 becomes 5 the moment you press ×, and 5 × 4 gives 20.

Scientific and graphing calculators, and many software calculators, use algebraic logic instead. They hold the addition back until the multiplication is done, and give 14.

How to check yours

Press 2 + 3 × 4 =. If you see 14, your calculator follows the order of operations. If you see 20, it works through the keys in sequence. On a calculator like that, do the multiplication first and add afterwards, or use brackets if it has them.

Why it matters

Checking homework, invoices or recipe scaling on a basic calculator can give a wrong total without any warning. Working the × and ÷ first, or grouping your own key presses, avoids the surprise.

Answers people give

AnswerHow you get there
14Order of operations: 3 × 4 = 12, then 2 + 12.
20Keys in sequence: 2 + 3 = 5, then 5 × 4.

Try your own expression

Type anything, including brackets, fractions and exponents, and get the steps.

Questions

Which is correct, 14 or 20?

14 is correct by the order of operations. A calculator that shows 20 is answering a different question: what you get by applying each key press as it arrives.

Do phone calculators follow the order of operations?

Many do, at least in their scientific mode, but it varies by app. Test yours with 2 + 3 × 4 and see whether it shows 14.

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