### Introduction

In many situations, we must take multiple steps to solve a problem: if we want to make it to first base in a game of kickball, we must first kick the ball, then run to first base; if we want to bake a cake, we must first mix the ingredients, then place the cake in the oven; when we go shopping, we must first choose the items we want to buy, then pay for them.

In each of these cases, the order is important: it wouldn't work to run to first base before we kick the ball; we can't place our cake in the oven before we mix the ingredients; we can't purchase items we haven't added to our cart.

When multiple steps are involved in mathematics, the order is important. For example, multiplying before we add will give us a different answer than adding before we multiply. For this reason, we use a specific order, the order of operations, to solve multi-step math problems.

**What is the order of operations?**

Considering addition, subtraction, multiplication and division, operations are evaluated in the following order:

- Evaluate operations within parentheses
- Evaluate multiplication and division from left to right
- Evaluate addition and subtraction from left to right

**How is the order of operations used in computer science?**

Many computer programming languages, including Python and JavaScript, evaluate expressions according to the order of operations. In video game development, multi-step expressions are often used to describe the interactions or physics that influence the movement of various game objects.

### Examples

**The order of operations (no parentheses)**

**Q:** Evaluate: 3 + 4 × 5

**A:** *The order of operations dictates that multiplication must be evaluated before addition:
3 + 4 × 5 = 3 + 20 = 23*

**The order of operations (no parentheses)**

**Q:** Evaluate: 6 ÷ 3 × 2

**A:** *The order of operations dictates that multiplication and division are evaluated from left to right:
6 ÷ 3 × 2 = 2 × 2 = 4*

**The order of operations (with parentheses)**

**Q:** Evaluate: (3 + 4) × 5

**A:** *The inclusion of parentheses changes the order in which the operations must be evaluated:
(3 + 4) × 5 = 7 × 5 = 35.*

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