AlgebraStructure & Method · Book 1All Chapters

Variables and Equations

1-2Grouping Symbols

Overview

Parentheses, brackets, and fraction bars tell us which operations to perform first. Follow the order of operations.

Key ideas

  • Order: parentheses → exponents → ×/÷ (left-to-right) → +/− (left-to-right).
  • A fraction bar groups its numerator and its denominator.
  • Work from the innermost grouping outward.

Worked examples

Example 1

Problem. Simplify 2(3 + 4) − 5.

Solution. 2(7) − 5 = 14 − 5 = 9

Example 2

Problem. Simplify (12 − 4) ÷ (1 + 3).

Solution. 8 ÷ 4 = 2

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Simplify 3 + 4 · 2.

  2. 2.

    Simplify 5(2 + 3) − 4·2.

  3. 3.

    Simplify (20 − 8) / (2 + 2).

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Simplify 2[3 + 4(5 − 2)] − 6.

  2. 2.

    Simplify (18 − 2·3)² ÷ (4 + 2·3).