Order of Operations with Grouping Symbols

Pre-Algebra · Order of operations

Order of Operations with Grouping Symbols

Problem

(8 + 4) \div (7 - 4)

Answer

4

Two sets of parentheses mean two groups. Finish both, then combine them.

Step-by-step solution

Simplify the first group.
$8 + 4 = 12$
Why: Parentheses come first.
Simplify the second group.
$7 - 4 = 3$
Why: The second set of parentheses is its own group.
Divide the two results.
$12 \div 3 = 4$
Why: After the groups become single numbers, the only operation left is division.

Common mistakes

Dividing before both groups are simplified: 8 + 4 / 7 - 4.
Subtracting the groups instead of dividing them.
Swapping the groups: (7 - 4) / (8 + 4) gives 1/4, not 4.

Practice problems

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

$(15 - 3) \div (2 + 2)$

Show answer

$3$
$(6 + 6) \div (9 - 6)$

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$4$
$2 \times (5 + 3) - (4 + 2)$

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$10$
$(20 - 5) \div (1 + 4)$

Show answer

$3$
$(7 + 8) \div (6 - 3)$

Show answer

$5$