Parentheses are super important in math! They tell you what to do first in a calculation. Using them right helps you get the correct answers, especially with fractions or when numbers are negative.

Why Parentheses Are Essential

In math, we have a special order for doing things like adding or dividing. You might know it as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Parentheses () make sure you do what’s inside them first. If you forget them, your calculator might do things in the wrong order, and your answer will be wrong!

Key Times to Use Parentheses

Here are the most important times to use parentheses to make sure your calculations are correct:

1. When You Have Math on Top or Bottom of a Fraction

If you have a plus (+) or minus (-) on the top (numerator) or bottom (denominator) of a fraction, put parentheses around that whole part. This tells the calculator to finish that part first.

  • Example 1: Sum on Top You want to calculate $\frac{10 + 5}{2}$.
    • Correct way to type: (10 + 5) / 2
    • What happens without parentheses: 10 + 5 / 2 (Calculator does 5 divided by 2 first, then adds 10. WRONG!)
  • Example 2: Multiply on Bottom You want to calculate $\frac{20}{4 \times 5}$.
    • Correct way to type: 20 / (4 * 5)
    • What happens without parentheses: 20 / 4 * 5 (Calculator does 20 divided by 4 first, then multiplies by 5. WRONG!)

2. When You Need to Group Operations Before Multiplying or Dividing

If you have a set of additions or subtractions that need to happen before you multiply or divide, use parentheses around them.

  • Example: You want to calculate $(5 + 3) \times (6 - 2)$.
    • Correct way to type: (5 + 3) * (6 - 2)
    • What happens without parentheses: 5 + 3 * 6 - 2 (Calculator does 3 times 6 first, then adds 5 and subtracts 2. WRONG!)

3. When a Whole Math Problem is Inside a Function

If you’re using a math button like sin() or log(), and the input to that button is a calculation itself, put that calculation in parentheses.

  • Example: You want to calculate $\sin(30^\circ + 15^\circ)$.
    • Correct way to type: sin(30 + 15)
    • What happens without parentheses: sin 30 + 15 (Calculator does sin(30) first, then adds 15. WRONG!)

Interactive: Parentheses Power!

Look at the math problem below. Type the expression into the box exactly as you would to get the correct answer on a calculator. Then, click “Check My Input” to see if you got it right and how incorrect input can change the result!

Rule of Thumb: When in Doubt, Use Parentheses!

It never hurts to add extra parentheses if you’re unsure. The calculator will simply process them, and it’s much better to have too many than too few. Over-parenthesizing won’t give you a wrong answer, but under-parenthesizing definitely will!

Common Mistakes to Avoid

Watch out for these common mistakes:

  • Forgetting parentheses on the top or bottom of fractions: This is a very common source of errors.
  • Not grouping operations that need to happen first: Like (5 + 3) * (6 - 2).
  • Thinking your calculator “knows” what you mean: Always be clear!
  • Confusing multiplication with implied parentheses: 2(3+4) might not work on all calculators, but 2 * (3+4) always will.

Related Concepts & Skills

Practice Problems

Test your skills with parentheses in these problems:

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