1 + 2 * 3 =

If the answer is 7, then the calculator follows the standard order of operations, if the answer is 9 then it doesn’t. If no answer appears, then you are probably standing at IKEA trying to use one of the dummy calculators.

Why it works

A calculator that does not follow the standard order of operations will apply the operators (plus, times, minus, etc.) as they come. In the above example, such a calculator would first add 1 and 2 (which is 3) and then multiply the result by 3 (which is 9).

A calculator that does follow the standard order of operations will first evaluate the “priority” of all operators in a calculation and then calculate the result evaluating the higher-priority operators first. In the above example the [*] operator has a higher priority than the [+] operator. Therefore the calculator evaluates 2 * 3 first (which is 6) and then adds 1 to the result (which is 7).

The standard order of operations

The standard order of operations is a rule which states, that binary operators with a higher priority are evaluated before binary operators with a lower priority. The priorities are as follows:

1. Exponents
2. Multiplication/Division
3. Addition/Subtraction

For more information on the order of operations see this Wikipedia article.