Why Does 1 + 2 x 3 Equal 7? Calculator Order of Operations Explained

Type 1 + 2 x 3 into a scientific calculator and the screen reads 7. Type the exact same keys into a cheap four-function calculator and the screen can read 9 instead. Neither calculator is broken. Both are following a real rule, and the rule itself is the reason the two answers do not match. That rule is called order of operations, and once you know it, both answers make complete sense.

What Does Order of Operations Mean, and Why Does 1 + 2 x 3 Equal 7?

Order of operations is the fixed sequence math uses to decide which part of an expression to solve first. It exists because 1 + 2 x 3 contains two operations, addition and multiplication, and without a fixed order, different people would get different answers from the exact same expression.

The rule says multiplication happens before addition, regardless of which operation appears first when reading left to right. In 1 + 2 x 3, the multiplication 2 x 3 gets solved before the addition, not after.

Working the expression correctly: 2 x 3 = 6 first, then 1 + 6 = 7. That is the standard, universally accepted answer for 1 + 2 x 3 in every math classroom and on every scientific or graphing calculator.

A calculator that instead reads keys strictly left to right, with no concept of operator priority, produces a different result: 1 + 2 = 3 first, then 3 x 3 = 9. Nine is not a random glitch. It is the correct answer to a different, simpler rule, one that ignores operation priority entirely.

What Is PEMDAS or BODMAS?

PEMDAS and BODMAS are two names for the same order of operations rule, taught under different labels in different countries. PEMDAS stands for Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. BODMAS stands for Brackets, Orders, Division and Multiplication, Addition and Subtraction.

Both acronyms describe the identical four-level priority list. Parentheses or brackets get solved first, no matter where they sit in the expression. Exponents, also called orders (things like squares and cubes), come next. Multiplication and division share the third level and get solved left to right against each other. Addition and subtraction share the fourth level and also get solved left to right against each other.

A common misreading of the acronym treats multiplication as always outranking division, and addition as always outranking subtraction, purely because of letter order. That reading is wrong. Multiplication and division are equal-priority operations solved left to right in the order they appear, and the same is true for addition and subtraction.

Take 12 / 3 x 2 as an example. Reading left to right at equal priority: 12 / 3 = 4 first, then 4 x 2 = 8. Solving the multiplication first instead would wrongly give 12 / 6 = 2, a different and incorrect result.

Why Would a Calculator Show 9 Instead of 7?

A calculator shows 9 for 1 + 2 x 3 because it lacks operator priority logic and processes each key the instant it gets pressed. This design is common on very basic four-function calculators, the kind built for simple running totals rather than full arithmetic.

A scientific calculator stores the whole expression before calculating, checks which operations rank higher, and solves those parts first. That is why a scientific or graphing calculator, and most calculator apps on a phone, correctly return 7 for 1 + 2 x 3.

A basic four-function calculator instead performs each operation the moment the next operator key gets pressed. Pressing 1, then +, then 2 immediately computes 1 + 2 = 3 and stores that running total. Pressing x next multiplies that running total by whatever comes after, so 3 x 3 becomes the final answer of 9.

Neither device is malfunctioning. The four-function calculator is correctly executing its own simpler rule, immediate left-to-right evaluation, which was a common design choice on cheap calculators built mainly for quick totals rather than full multi-step arithmetic.

Checking a device’s manual is the only reliable way to confirm which type a specific model uses, since the outside of the calculator rarely states this design choice directly.

How Do Parentheses Force the Correct Order?

Parentheses override the default order and tell any calculator, of either type, to solve the enclosed part first. Wrapping 1 + 2 in parentheses forces that addition to happen before the multiplication, changing the outcome entirely: (1 + 2) x 3 = 3 x 3 = 9.

Notice that 9 becomes the correct, intended answer once parentheses request it deliberately, rather than being an accidental left-to-right error. The difference between a mistaken 9 and a deliberate 9 is entirely about intent, and parentheses are how that intent gets communicated to the machine.

Wrapping 2 x 3 in parentheses instead, as in 1 + (2 x 3), changes nothing about the outcome, because multiplication was already going to happen first under standard order of operations. The parentheses simply confirm what the rule already does.

A basic four-function calculator without a parentheses key cannot force this order directly. The workaround is solving the parenthetical part first by hand or in a separate step, then feeding that result back into the remaining calculation.

A calculator with a parentheses key removes that extra step entirely, letting a single continuous keypress sequence produce the intended answer no matter which priority level a particular sub-expression needs.

What Do More Worked Examples Look Like?

Working through several examples side by side shows how quickly a left-to-right calculator and a standard-order calculator can disagree. Each row below shows the same keypresses evaluated both ways.

Consider 10 – 2 x 3. Standard order solves the multiplication first: 2 x 3 = 6, then 10 – 6 = 4. A strict left-to-right calculator instead computes 10 – 2 = 8 first, then 8 x 3 = 24, a very different result from the correct answer of 4.

Wrapping the subtraction in parentheses, as in (10 – 2) x 3, deliberately forces that order and correctly produces 24, the same number the left-to-right calculator gave by accident. This example shows exactly how a wrong-looking answer and a correct, parentheses-forced answer can share the same final number for entirely different reasons.

Consider a slightly longer expression: 2 + 3 x 4 – 1. Standard order solves 3 x 4 = 12 first, giving 2 + 12 – 1, then addition and subtraction proceed left to right: 2 + 12 = 14, then 14 – 1 = 13. A strict left-to-right calculator instead computes 2 + 3 = 5, then 5 x 4 = 20, then 20 – 1 = 19.

Exponents follow the same priority pattern as multiplication and division, ranking above addition and subtraction. Consider 2 + 3^2, read as 2 plus 3 squared. Standard order solves the exponent first: 3^2 = 9, then 2 + 9 = 11. A left-to-right calculator without exponent priority instead computes 2 + 3 = 5, then squares that running total, 5^2 = 25.

How Can You Tell Which Type of Calculator You Have?

Test your calculator with 1 + 2 x 3 and read the result. Standard scientific calculators, most phone calculator apps, and any calculator with a dedicated parentheses key almost always return 7 for this expression, since they respect order of operations by design.

A result of 9 signals a basic four-function calculator, evaluating strictly left to right without regard for operator priority. Neither type is defective. Each is executing its own built-in rule correctly and consistently.

A quick second check helps confirm the pattern: try 2 + 3 x 4. Standard order gives 2 + 12 = 14. Strict left to right gives 5 x 4 = 20. Getting matching results on both test expressions confirms which rule a specific device follows before it matters for a real calculation.

Checking a device’s manual remains the most reliable source for this detail, since exact behavior varies by brand and model, and some calculators offer a settings menu that changes how expressions get evaluated.

Reaching for parentheses removes the guesswork entirely. Any calculator that supports a parentheses key, entered directly in the keypress sequence, produces the intended order regardless of which default rule the device otherwise follows. Practicing this kind of multi-step expression is easier with real numbers in front of you, and our Math Calculators hub is a good place to try different combinations and watch how the order changes the result. No single dedicated order-of-operations tool exists on this site yet, so the hub works as a general practice ground rather than a purpose-built solver.

FAQs About Calculator Order of Operations

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This article is for general math education only. Exact calculator behavior varies by brand and model, so check your device’s manual for specifics. Reviewed for accuracy by Prof. Dr. Khalil Mudassar, PhD. Last updated September 23, 2026.