5 Essential Steps Order Of Operations Cheat Sheet

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Mastering the order of operations is a crucial math skill that can make all the difference in solving mathematical expressions correctly. Whether you're a student, a teacher, or simply someone who wants to brush up on their math skills, having a solid understanding of the order of operations is essential. In this article, we'll break down the 5 essential steps of the order of operations, provide you with a handy cheat sheet, and offer some practical examples to help you apply this knowledge in real-life scenarios.

The order of operations is a set of rules that dictates the order in which mathematical operations should be performed when there are multiple operations in an expression. This concept is often represented by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Step 1: Parentheses

The first step in the order of operations is to evaluate any expressions inside parentheses. This means that any calculations within parentheses should be performed before moving on to the next step. By doing so, you can ensure that any calculations that need to be performed in a specific order are done correctly.

Step 2: Exponents

Once you've evaluated any expressions inside parentheses, the next step is to evaluate any exponents. Exponents are shorthand for repeated multiplication, and they should be evaluated from left to right. For example, in the expression 2^3^2, the exponent 3 should be evaluated first, followed by the exponent 2.

Step 3: Multiplication and Division

After evaluating any exponents, the next step is to perform any multiplication and division operations from left to right. This means that any multiplication operations should be performed before moving on to any division operations. For example, in the expression 6 ÷ 2 × 3, the division operation should be performed first, followed by the multiplication operation.

Multiplication and Division Examples

• 6 ÷ 2 × 3 =?
  • Divide 6 by 2: 6 ÷ 2 = 3
  • Multiply 3 by 3: 3 × 3 = 9
• 12 × 3 ÷ 4 =?
  • Multiply 12 by 3: 12 × 3 = 36
  • Divide 36 by 4: 36 ÷ 4 = 9

Step 4: Addition and Subtraction

Finally, the last step in the order of operations is to perform any addition and subtraction operations from left to right. This means that any addition operations should be performed before moving on to any subtraction operations. For example, in the expression 3 + 4 - 2, the addition operation should be performed first, followed by the subtraction operation.

Addition and Subtraction Examples

• 3 + 4 - 2 =?
  • Add 3 and 4: 3 + 4 = 7
  • Subtract 2 from 7: 7 - 2 = 5
• 10 - 3 + 2 =?
  • Subtract 3 from 10: 10 - 3 = 7
  • Add 2 to 7: 7 + 2 = 9

Step 5: Putting it all Together

Now that we've broken down each step of the order of operations, let's put it all together with a few examples.

Example 1

• Expression: 2 × 3 + 12 ÷ 4 - 5
  • Multiply 2 and 3: 2 × 3 = 6
  • Divide 12 by 4: 12 ÷ 4 = 3
  • Add 6 and 3: 6 + 3 = 9
  • Subtract 5 from 9: 9 - 5 = 4

Example 2

• Expression: 10 - 3 + 2 × 4
  • Subtract 3 from 10: 10 - 3 = 7
  • Multiply 2 by 4: 2 × 4 = 8
  • Add 7 and 8: 7 + 8 = 15

By following these 5 essential steps, you can ensure that you're performing mathematical operations in the correct order. Remember to always evaluate expressions inside parentheses first, followed by exponents, multiplication and division, and finally addition and subtraction.

We hope this article has provided you with a helpful guide to the order of operations. With practice and patience, you'll become a pro at solving mathematical expressions in no time!