Integers

Integer Order of Operations

Apply order of operations (PEMDAS) to integer expressions: multiplication and division before addition and subtraction, even with negative numbers.

Example

Use PEMDAS with signed numbers. The order of operations works the same with negatives, but each step must also track the sign, since a stray minus changes the result. Handling grouping and higher-priority operations first, while carefully applying the rules for signs, keeps a multi-step signed expression from collapsing into a wrong answer.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

−2+3×(−4)-2 + 3 \times ( -4 )
Choose the operation that must happen first.1multiply3 x (-4) = -122add-2 + (-12) = -143result-14-2 + 3 x (-4)In -2 + 3 x (-4), the multiplication part waits inside the first step box.

Step 2 — Multiply first

Multiply before adding: 3 x -4 = -12.

−2+(-12)-2 + ( \hl{-12} )
Multiply before adding: 3 x (-4) = -12.1multiply3 x (-4) = -122add-2 + (-12) = -143result-14-2 + 3 x (-4)After multiplying, the expression becomes -2 + (-12).

Step 3 — Add

Then add signed numbers: -2 + (-12) = -14.

−2+(−12)=-14-2 + ( -12 )= \hl{-14}
Now combine the signed numbers: -2 + (-12) = -14.1multiply3 x (-4) = -122add-2 + (-12) = -143result-14-2 + 3 x (-4)Both numbers are negative, so the final sum is -14.

Step 4 — Result

Read the final result.

−14-14
The expression equals -14.1multiply3 x (-4) = -122add-2 + (-12) = -143result-14-2 + 3 x (-4)The order was multiply first, then add the signed result.
integer-order-of-operations Order of operations (PEMDAS) with integers: 1. Parentheses 2. Exponents 3. Multiplication and Division (left to right) 4. Addition and Subtraction (left to right) Negative signs follow the same rules.