Step-by-Step Order of Operations (and Why 8 ÷ 2(2 + 2) Is 16)

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Opens on Chapter 3’s example: the viral puzzle 8 ÷ 2(2 + 2).

Calculation digits, + − × ÷ (or * /), ^ or ², brackets; a fraction as (top)/(bottom)

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Enter your numbers, then press Work it out.

How it works

Innermost brackets first, then powers (a power belongs only to what sits right before it), then multiplication and division as they come from left to right, then addition and subtraction from left to right. A number written against a bracket, as in 2(2 + 2), is an ordinary multiplication and takes its turn with the other × and ÷. The fraction bar groups its top and its bottom, so (12 + 8)/4 needs its brackets when typed on one line. The panel underneath shows what two common misreadings give: working strictly left to right like a basic calculator, and taking PEMDAS letter by letter (× always before ÷, + always before −).

From the book, Chapter 3. 8 ÷ 2(2 + 2) is 16 in the agreed order; reading 2(2 + 2) as one block gives 1. The receipt is $16 ($19.38 left to right); 2 × 3² is 18, not 36; 20 − 6 + 4 is 18, not 10; two pizzas shared four ways is $5 each, not $14; 2(3 + 4(5 − 2)) is 30; =A1+B1/2 gives 13 where 8 was meant. Every chapter and its calculator →

Numbers can be typed as 1,450, $38, 0.40, 12%, 1/6 or 2 3/8. The algebra is done with exact fractions, so 1/3 stays 1/3; decimals are rounded half up, the way the book rounds. Everything stays in your browser: no sign-up, nothing stored or sent.