By Jillian Holden • Updated Aug 30, 2022
Parentheses are essential tools in arithmetic that dictate the order in which operations are performed. By placing them correctly, you can ensure that an equation evaluates to the intended value.
Begin by transcribing the expression on a clean sheet of paper. For example, consider the equation 1 + 2×3 − 4 = −3. Writing numbers in large, legible type reduces the risk of transcription errors.
PEMDAS—Parentheses, Exponents, Multiplication, Division, Addition, Subtraction—is the standard hierarchy for evaluating expressions. Use it as a roadmap to decide where parentheses will have the greatest impact.
Try grouping the first two terms: (1 + 2)×3 − 4. Evaluate the parentheses first: 1 + 2 = 3. Continue left to right: 3×3 = 9, then 9 − 4 = 5. Since 5 does not match the target of –3, this placement is incorrect.
Place parentheses around both the first two terms and the last two terms: (1 + 2) × (3 − 4). Evaluate each set first: 1 + 2 = 3 and 3 − 4 = −1. Then multiply the results: 3 × (−1) = −3, which matches the target.
Once you find a placement that yields the target value, write the expression again and recompute it to confirm accuracy. Double‑checking eliminates mistakes caused by misreading or mis‑applying the order of operations.
Review the equation first to gauge where parentheses will change the outcome. Test different groupings until the expression equals the desired result. Double‑check your work for confidence.
