Evaluate The Following Expression:$\[ 4 \times 45 / 2 + 8 - 1 / 3 \\]

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Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves performing the operations in the correct order to obtain the final result. In this article, we will evaluate the given expression: 4 × 45 / 2 + 8 - 1 / 3. We will follow the order of operations (PEMDAS) to simplify the expression and obtain the final result.

Understanding the Order of Operations

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. PEMDAS is a popular acronym that stands for:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Evaluating the Expression

Now that we understand the order of operations, let's evaluate the given expression:

4 × 45 / 2 + 8 - 1 / 3

Step 1: Multiply 4 and 45

The first operation is multiplication. We multiply 4 and 45:

4 × 45 = 180

Step 2: Divide 180 by 2

Next, we divide 180 by 2:

180 / 2 = 90

Step 3: Add 8

Now, we add 8 to 90:

90 + 8 = 98

Step 4: Divide 1 by 3

Next, we divide 1 by 3:

1 / 3 = 0.33

Step 5: Subtract 0.33 from 98

Finally, we subtract 0.33 from 98:

98 - 0.33 = 97.67

Conclusion

In this article, we evaluated the given expression: 4 × 45 / 2 + 8 - 1 / 3. We followed the order of operations (PEMDAS) to simplify the expression and obtain the final result. The final result is 97.67.

Tips and Tricks

  • Always follow the order of operations (PEMDAS) when evaluating mathematical expressions.
  • Use parentheses to group operations and avoid confusion.
  • Exponential expressions should be evaluated before multiplication and division operations.
  • Multiplication and division operations should be evaluated from left to right.
  • Addition and subtraction operations should be evaluated from left to right.

Frequently Asked Questions

  • Q: What is the order of operations? A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. PEMDAS is a popular acronym that stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
  • Q: How do I evaluate an expression with multiple operations? A: To evaluate an expression with multiple operations, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Related Topics

  • Evaluating Expressions with Exponents
  • Evaluating Expressions with Fractions
  • Order of Operations (PEMDAS)

References

  • "Order of Operations" by Math Open Reference
  • "Evaluating Expressions" by Khan Academy
  • "PEMDAS" by Math Is Fun

Introduction

Evaluating expressions is a fundamental concept in mathematics that involves simplifying a mathematical expression by performing the operations in the correct order. In our previous article, we evaluated the expression: 4 × 45 / 2 + 8 - 1 / 3. In this article, we will answer some frequently asked questions about evaluating expressions.

Q&A Guide

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. PEMDAS is a popular acronym that stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different effects on the result. Multiplication involves adding a number a certain number of times, while division involves finding the result of a number divided by another number.

Q: How do I evaluate an expression with fractions?

A: To evaluate an expression with fractions, follow the same order of operations as before. First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are both operations that involve numbers, but they have different effects on the result. Addition involves finding the result of two or more numbers added together, while subtraction involves finding the result of one number subtracted from another.

Q: How do I evaluate an expression with decimals?

A: To evaluate an expression with decimals, follow the same order of operations as before. First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change, while a constant is a value that remains the same.

Q: How do I evaluate an expression with variables?

A: To evaluate an expression with variables, follow the same order of operations as before. First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Tips and Tricks

  • Always follow the order of operations (PEMDAS) when evaluating mathematical expressions.
  • Use parentheses to group operations and avoid confusion.
  • Exponential expressions should be evaluated before multiplication and division operations.
  • Multiplication and division operations should be evaluated from left to right.
  • Addition and subtraction operations should be evaluated from left to right.

Frequently Asked Questions

  • Q: What is the order of operations? A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. PEMDAS is a popular acronym that stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
  • Q: How do I evaluate an expression with multiple operations? A: To evaluate an expression with multiple operations, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Related Topics

  • Evaluating Expressions with Exponents
  • Evaluating Expressions with Fractions
  • Order of Operations (PEMDAS)

References

  • "Order of Operations" by Math Open Reference
  • "Evaluating Expressions" by Khan Academy
  • "PEMDAS" by Math Is Fun