Order of Operations - Arithmetic Step by Step

Evaluate 2 × (3 + (8 − 5)) by working from the inside out. First do the innermost parentheses (8 − 5 = 3), then the outer parentheses (3 + 3 = 6), then multiply (2 × 6 = 12).

innermost-first When parentheses are nested, start with the innermost group. Replace that group with its value, then work outward one group at a time. After all parentheses are resolved, apply the remaining PEMDAS rules.

Example

Evaluate 2 x (3 + (8 - 5)) by working from the inside out.

highlighted = computed this step

Step 1 — Set up

Write the expression to solve.

2 \times ( 3 + ( 8 - 5 ) )

Step 2 — Innermost parentheses

Innermost parentheses first: 8 - 5 = 3.

2 \times ( 3 + \hl{3} )

Step 3 — Outer parentheses

Now do the outer parentheses: 3 + 3 = 6.

2 \times \hl{6}

Step 4 — Multiply

Multiply after parentheses: 2 x 6 = 12.

\hl{12}

Step 5 — Result

Read the final answer.

12