# Evaluate Numerical Expressions with ( ), { } and [ ] – Part 1

## Overview

Math problems can be written with more than one operation. To solve these more

difficult problems, we follow a sequence called the **order of operations**.

Consider the numerical expression

There are two possible solutions to this problem:

How do I know which part of the problem to solve first?

The **order of operations** will guide you.

**ORDER OF OPERATIONS:**

**Step One:** Calculate operations in grouping symbols first. Grouping symbols include **parentheses**, **brackets** or **braces**. If an expression has more than one grouping symbol, calculate the operations in parentheses first, brackets second, and braces third.

**Step Two: **Solve** exponents**, including square roots. It’s okay if you aren’t familiar

with these terms yet. We will learn more about them in an upcoming chapter.

**Step Three:** **Multiply** and **Divide**. If both multiplication and division appear in an

expression, complete the operations from left to right.

**Step Four:** **Add** and **Subtract**. If both addition and subtraction appear in an

expression, complete the operations from left to right.

**PEMDAS**

You can use the acronym PEMDAS to help you remember the order of operations.

**P** – Parentheses, Brackets, Braces

**E** – Exponents

**MD** – Multiplication/Division

**AS** – Addition/Subtraction

Let’s look at another example.

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Solve

Show your work.

17

First, calculate

Which part of the expression should be calculated first? Explain your answer.

**A.** **B.** **C.** **D.**

**D.** 6 – 3

Parentheses should be solved before brackets or braces.

Add parentheses to the equation without changing it’s value.

First, calculate 7 + 8 = 15. Then, multiply by 3.

Solve

Show your work.

22

First, calculate (8 – 3) = 5. Then add 5 + 6. The multiply

Which numerical expression has the same value as **A.** **B.** **C.** **D.**

**B.**

Both expressions are equal to 29.

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