In math, numerical expressions are like sentences made up of numbers and operations (like addition, subtraction, multiplication, and division). Sometimes, we use special symbols like parentheses ( ), brackets [ ], or braces { } to tell us which parts of the expression we should calculate first. These symbols help organize our work and make sure everyone solves the problem the same way.

Definition

• Parentheses ( ): Always do the math inside parentheses first.
• Brackets [ ]: These are used to group parts of an expression that might already have parentheses.
• Braces { }: Even though you won't use braces often, they're another way to group things when you already have both parentheses and brackets.

Example 1: Parentheses

Let’s say we have the expression:
5 + (3 × 4)

Without parentheses, you might think to add 5 and 3 first, but because of the parentheses, we do the 3 × 4 first, then add the 5.

• Step 1: Multiply what’s inside the parentheses:
  3 × 4 = 12
• Step 2: Add the 5:
  5 + 12 = 17

So, 5 + (3 × 4) = 17.

Example 2: Brackets

Here’s an expression with both parentheses and brackets:
[5 + (2 × 3)] + 4

First, solve what’s inside the parentheses, then solve what’s inside the brackets.

• Step 1: Solve the parentheses:
  2 × 3 = 6
• Step 2: Solve inside the brackets:
  5 + 6 = 11
• Step 3: Add the 4:
  11 + 4 = 15

So, [5 + (2 × 3)] + 4 = 15.

Why It Matters

Using parentheses, brackets, and braces helps us follow the Order of Operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). They make sure we all solve the expression the same way and avoid mistakes.

Let's practice and evaluate together, solving expressions step by step using parentheses, brackets, and braces!