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PEMDAS: The Order of Operations Explained

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PEMDAS: The Order of Operations Explained

In the world of mathematics, there’s a specific order in which we solve equations. It’s like a recipe, where each step has its own place. This order is known as the order of operations, and it’s essential to get the right answers. Think of it like following a set of directions to get to a destination, if you don’t follow them in the correct order you might end up lost!

What is PEMDAS?

PEMDAS is an acronym that helps us remember the order of operations. It stands for:

  • **P**arentheses
  • **E**xponents
  • **M**ultiplication and **D**ivision (from left to right)
  • **A**ddition and **S**ubtraction (from left to right)

Why is PEMDAS important?

Imagine you have the equation 2 + 3 x 4. If you solve it from left to right, you’d get 5 x 4 = 20. But that’s not the correct answer. According to PEMDAS, we need to perform multiplication before addition. So, the correct answer is 2 + 12 = 14.

Let’s break it down:

Here’s a step-by-step explanation of PEMDAS:

  1. **Parentheses:** Solve everything inside parentheses first. If there are multiple sets of parentheses, work from the innermost set outwards.
  2. **Exponents:** Next, calculate any exponents. Remember, an exponent tells us how many times to multiply a number by itself.
  3. **Multiplication and Division:** Now, perform multiplication and division from left to right. It doesn’t matter which one comes first in the equation, you work them out as they appear.
  4. **Addition and Subtraction:** Finally, do addition and subtraction from left to right. Again, the order they appear in the equation is what matters.

Examples:

Let’s see how PEMDAS works in practice:

  1. 10 + 5 x 2
    * Multiplication first: 5 x 2 = 10
    * Then addition: 10 + 10 = 20
  2. (3 + 4) x 2
    * Parentheses first: 3 + 4 = 7
    * Then multiplication: 7 x 2 = 14
  3. 8 ÷ 22
    * Exponent first: 22 = 4
    * Then division: 8 ÷ 4 = 2

Remember:

PEMDAS is a helpful acronym to remember the order of operations, but it’s important to remember that it doesn’t always dictate the exact order. For example, if you have a long equation with multiple operations, you might need to break it down into smaller steps to make it easier to solve.

Practice Makes Perfect!

The best way to master PEMDAS is to practice. Try solving different equations and see if you can get the right answers. You can also find online quizzes and games that help you learn and practice the order of operations.

Elementary Math