Order of Operations

Order of Operations

Nested Parentheses

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).

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×(3+(8−5))2 \times ( 3 + ( 8 - 5 ) )
Work inside out: start with the innermost parentheses.2x(3+(8-5))inner parentheses8 - 5 = 3outer parenthesesnot yetmultiply lastnot yetcurrent expression: 2 x (3 + (8 - 5))

Step 2 — Innermost parentheses

Innermost parentheses first: 8 - 5 = 3.

2×(3+3)2 \times ( 3 + \hl{3} )
Inner parentheses: 8 - 5 = 3.2x(3+3)inner parentheses8 - 5 = 3outer parenthesesnot yetmultiply lastnot yetcurrent expression: 2 x (3 + 3)

Step 3 — Outer parentheses

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

2×62 \times \hl{6}
Outer parentheses: 3 + 3 = 6.2x6inner parentheses8 - 5 = 3outer parentheses3 + 3 = 6multiply lastnot yetcurrent expression: 2 x 6

Step 4 — Multiply

Multiply after parentheses: 2 x 6 = 12.

12\hl{12}
Multiply last: 2 x 6 = 12.12inner parentheses8 - 5 = 3outer parentheses3 + 3 = 6multiply last2 x 6 = 12current expression: 12

Step 5 — Result

Read the final answer.

1212
Final answer: 12.12inner parentheses8 - 5 = 3outer parentheses3 + 3 = 6multiply last2 x 6 = 12answer = 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.