Why does my calculator give a different answer for 1 + 2 × 3?

· Avinash Kumar

Voice Calculator runs on iPhone. The app is available in English, Japanese, German, French, Spanish, Portuguese and Chinese.

It depends on the calculator. A scientific calculator follows the order of operations (PEMDAS), so 1 + 2 × 3 = 7. A basic calculator works through each step as you enter it, so it adds 1 + 2 first and shows 9. Neither is broken; they follow different rules.

Which rule does math class use?

Homework follows the order of operations: parentheses, exponents, multiplication and division (left to right), then addition and subtraction (left to right). So 8 − 2 × 3 = 2, not 18.

The 5-second test

Enter 1 + 2 × 3 = on any calculator.

Result What it does
7 Follows the order of operations
9 Calculates left to right, step by step

How to check homework answers without getting caught out

  1. Run the test above first.
  2. On a left-to-right calculator, do the multiplications and divisions yourself first, then add the results.
  3. Read each number back before you press equals. Most wrong “checks” are a typo, not a math mistake.

Checking out loud

I build Voice Calculator. It has both modes: Basic works left to right (1 + 2 × 3 = 9) and Scientific follows the order of operations (1 + 2 × 3 = 7). A student can say the problem aloud and see each number on the tape before the answer appears, then tap Read to hear the whole line back. It checks arithmetic only; it doesn’t show steps or explain the method.

Related: why a voice calculator should show what it heard, calculator help for dyscalculia and the Voice Calculator guides.

Questions people ask

Is 1 + 2 × 3 equal to 7 or 9?
By the order of operations (PEMDAS) it's 7: multiply first, then add. A basic calculator that works left to right shows 9.
How do I know which kind my calculator is?
Type 1 + 2 × 3 =. If it shows 7 it follows the order of operations; if it shows 9 it calculates each step as you go.
Does Voice Calculator follow PEMDAS?
In Scientific mode, yes. Basic mode works left to right, like a desk adding machine.

Voice Calculator

A calculator you talk to: say the numbers, check each one on the tape, hear the total.

Download on the App Store

Keep reading

Also available in: Deutsch · Español (Latinoamérica) · Français · 日本語