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
- Run the test above first.
- On a left-to-right calculator, do the multiplications and divisions yourself first, then add the results.
- 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.
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