Order of Operations with Nested Parentheses

Pre-Algebra · Order of operations

Order of Operations with Nested Parentheses

Problem

2 + 3 \times (4 + 5) - 6 \div 2

Answer

26

The parentheses act like a box: solve what is inside first, then treat the box as one number.

Step-by-step solution

Work inside the parentheses first.
$4 + 5 = 9$
Why: Parentheses come before every other operation.
Replace the parentheses with 9.
$2 + 3 \times 9 - 6 \div 2$
Why: The group is now a single number.
Multiply and divide from left to right.
$2 + 27 - 3$
Why: Multiplication and division rank the same.
Add and subtract from left to right.
$2 + 27 - 3 = 29 - 3 = 26$
Why: Addition and subtraction rank the same, so work left to right.

Common mistakes

Adding 2 + 3 before handling the parentheses.
Doing 6 / 2 before 3 x 9. Work left to right.
Multiplying 3 x 4 but forgetting the + 5 inside the brackets.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

$3 + 2 \times (5 + 1)$

Show answer

$15$
$(9 - 4) \times 2 + 3$

Show answer

$13$
$20 - 2 \times (6 - 2)$

Show answer

$12$
$5 + 2 \times (10 - 7)$

Show answer

$11$
$(6 + 2) \times 3 - 4$

Show answer

$20$