5 Order Operations Tips

Introduction to Order of Operations

The order of operations is a fundamental concept in mathematics that dictates the order in which mathematical operations should be performed when there are multiple operations in an expression. This concept is crucial in ensuring that mathematical expressions are evaluated consistently and accurately. In this article, we will explore five essential tips for working with the order of operations, helping you to better understand and apply this concept in your mathematical endeavors.

Tip 1: Remember the Acronym PEMDAS

The acronym PEMDAS is a helpful tool for remembering the order of operations. It stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. By following this order, you can ensure that mathematical expressions are evaluated correctly. For example, in the expression 2 + 3 × 4, using PEMDAS, we would first perform the multiplication (3 × 4 = 12) and then the addition (2 + 12 = 14).

Tip 2: Evaluate Expressions Inside Parentheses First

When working with expressions that contain parentheses, it is essential to evaluate the operations inside the parentheses first. This rule applies even if there are exponents or multiplication and division operations outside the parentheses. For instance, in the expression (2 + 3) × 4, we would first evaluate the expression inside the parentheses (2 + 3 = 5) and then perform the multiplication (5 × 4 = 20).

Tip 3: Exponents Come Next

After evaluating expressions inside parentheses, the next step is to evaluate any exponents (such as squaring or cubing). For example, in the expression 2 × 3^2, we would first evaluate the exponent (3^2 = 9) and then perform the multiplication (2 × 9 = 18). It is crucial to remember that exponents have higher precedence than multiplication and division.

Tip 4: Multiply and Divide from Left to Right

When an expression contains both multiplication and division operations, we evaluate these operations from left to right. This means that we perform the operation that appears first from the left. For example, in the expression 12 ÷ 3 × 4, we would first perform the division (12 ÷ 3 = 4) and then the multiplication (4 × 4 = 16).

Tip 5: Finally, Add and Subtract from Left to Right

The final step in the order of operations is to evaluate any addition and subtraction operations from left to right. This ensures that these operations are performed in the correct order. For instance, in the expression 10 + 5 - 3, we would first perform the addition (10 + 5 = 15) and then the subtraction (15 - 3 = 12).

📝 Note: It's essential to follow the order of operations to avoid confusion and ensure accuracy in mathematical calculations.

To further illustrate the application of these tips, consider the following example:

Expression	Evaluation
2 + 3 × 4	2 + 12 = 14
(2 + 3) × 4	5 × 4 = 20
2 × 3^2	2 × 9 = 18
12 ÷ 3 × 4	4 × 4 = 16
10 + 5 - 3	15 - 3 = 12

In conclusion, understanding and applying the order of operations is vital for accurate mathematical calculations. By following the PEMDAS acronym, evaluating expressions inside parentheses first, considering exponents, and performing multiplication, division, addition, and subtraction operations in the correct order, you can ensure that your mathematical expressions are evaluated correctly. Remembering these tips will help you become more proficient in mathematics and improve your overall problem-solving skills.