Master the art of evaluating expressions

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Master the art of evaluating expressions

Table of Contents

  1. Introduction
  2. Understanding PEMDAS
  3. Evaluating Expressions with Parentheses and Brackets
  4. Example 1: Evaluating an Expression with Parentheses and Multiplication
  5. Example 2: Evaluating an Expression with Parentheses and Division
  6. Example 3: Evaluating an Expression with Brackets and Parentheses
  7. Practice Problems: Evaluating Expressions
  8. Conclusion

Introduction

In this lesson, we will be learning how to evaluate expressions using the PEMDAS acronym. PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. By following the order of operations, we can find the correct answers to mathematical expressions. Throughout this article, we will go step by step, solving various examples and practice problems to solidify our understanding of evaluating expressions.

Understanding PEMDAS

Before we dive into solving expressions, let's first understand the key components of PEMDAS. Each letter of PEMDAS represents a specific operation that we need to follow in order to evaluate an expression correctly.

  1. Parentheses: Perform operations within parentheses first.
  2. Exponents: Evaluate any exponents or powers.
  3. Multiplication and Division: Multiply or divide from left to right.
  4. Addition and Subtraction: Perform addition or subtraction from left to right.

By following this order, we ensure that we arrive at the correct solution for any given expression.

Evaluating Expressions with Parentheses and Brackets

Now that we have a good understanding of PEMDAS, let's put it into practice by evaluating expressions that involve parentheses and brackets.

Example 1: Evaluating an Expression with Parentheses and Multiplication

Let's start with an example: 3.6 × (9.8 × 2) - 3.

To solve this, we must first perform the multiplication within the parentheses: 9.8 × 2 = 19.6.

Next, we subtract 3 from 19.6, resulting in 16.6.

Lastly, we multiply 3.6 by 16.6, giving us an answer of 59.76.

Therefore, the solution to the expression is 59.76.

Example 2: Evaluating an Expression with Parentheses and Division

Consider the expression: 5.8 + 5 × (5.8 - 3.2) ÷ 2.

First, we need to solve the expression within the parentheses: 5.8 - 3.2 = 2.6.

Next, we multiply 5 by 2.6, resulting in 13.

Then, we divide 13 by 2, giving us 6.5.

Finally, we add 5.8 to 6.5, resulting in an answer of 12.3.

So, the solution to the expression is 12.3.

Example 3: Evaluating an Expression with Brackets and Parentheses

Let's try a more complex expression: 2 × [6.2 - 3 + (24 ÷ 12)].

First, we evaluate the expression within the brackets: 24 ÷ 12 = 2.

Next, we add 6.2 and 3, resulting in 9.2.

Then, we multiply 2 by 9.2, giving us 18.4.

So, the solution to the expression is 18.4.

Practice Problems: Evaluating Expressions

Now it's time for some practice problems to test our understanding of evaluating expressions. Try these on your own before checking the solutions.

  1. 36 ÷ 18 + (9.6 + 4.12 × 2)
  2. 2.1 + 0.8 ÷ 2 + [9.8 ÷ 2 + (4.2 ÷ 3)]

Solution to Problem 1:

Start by calculating 4.12 × 2 = 8.24.

Then, within the parentheses, add 9.6 and 8.24, resulting in 17.84.

Next, divide 36 by 18 to get 2.

Finally, add 2 and 17.84, giving us 19.84 as the solution.

Solution to Problem 2:

First, divide 0.8 by 2, resulting in 0.4.

Next, within the brackets, add 9.8 ÷ 2 and 4.2 ÷ 3. This gives us (4.9 + 1.4).

Then, add 4.9 and 1.4, resulting in 6.3.

Lastly, add 2.1 and 6.3 to get the final answer of 8.4.

Conclusion

By understanding and applying the PEMDAS order of operations, we can effectively evaluate expressions with parentheses and brackets. Remember to follow the order of operations: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. Practice solving a variety of expressions to further strengthen your skills in evaluating expressions accurately and efficiently. Keep practicing, and soon you'll become a master at evaluating mathematical expressions!

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