Evaluate The Following Expression:$\[ 8 \div [5 \times (16 - 13) - 13] \\]\[$\square\$\]

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Introduction

In this article, we will evaluate the given mathematical expression: 8 ÷ [5 × (16 - 13) - 13]. This expression involves various mathematical operations such as division, multiplication, subtraction, and parentheses. To evaluate this expression, we need to follow the order of operations (PEMDAS) and perform the operations in the correct order.

Understanding the Order of Operations

The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
  3. Multiplication and Division: Evaluate any 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, let's evaluate the given expression step by step:

8÷[5×(16−13)−13]{ 8 \div [5 \times (16 - 13) - 13] }

Step 1: Evaluate the expression inside the parentheses

First, we need to evaluate the expression inside the parentheses: (16 - 13).

16−13=3{ 16 - 13 = 3 }

So, the expression becomes:

8÷[5×3−13]{ 8 \div [5 \times 3 - 13] }

Step 2: Multiply 5 and 3

Next, we need to multiply 5 and 3:

5×3=15{ 5 \times 3 = 15 }

So, the expression becomes:

8÷[15−13]{ 8 \div [15 - 13] }

Step 3: Subtract 13 from 15

Now, we need to subtract 13 from 15:

15−13=2{ 15 - 13 = 2 }

So, the expression becomes:

8÷2{ 8 \div 2 }

Step 4: Divide 8 by 2

Finally, we need to divide 8 by 2:

8÷2=4{ 8 \div 2 = 4 }

Therefore, the final answer is 4.

Conclusion

In this article, we evaluated the given mathematical expression: 8 ÷ [5 × (16 - 13) - 13]. We followed the order of operations (PEMDAS) and performed the operations in the correct order. The final answer is 4.

Frequently Asked Questions

  • What is the order of operations? The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
  • How do I evaluate an expression with multiple operations? To evaluate an expression with multiple operations, follow the order of operations (PEMDAS) and perform the operations in the correct order.
  • What is the final answer to the expression 8 ÷ [5 × (16 - 13) - 13]? The final answer to the expression 8 ÷ [5 × (16 - 13) - 13] is 4.

Further Reading

  • Order of Operations (PEMDAS)
  • Evaluating Expressions with Multiple Operations
  • Basic Arithmetic Operations (Addition, Subtraction, Multiplication, Division)

Introduction

Evaluating mathematical expressions can be a challenging task, especially when dealing with complex expressions that involve multiple operations. In this article, we will provide a Q&A guide to help you evaluate mathematical expressions with confidence.

Q&A Guide

Q1: What is the order of operations?

A1: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q2: How do I evaluate an expression with multiple operations?

A2: To evaluate an expression with multiple operations, follow the order of operations (PEMDAS) and perform the operations in the correct order. This means that you should:

  • Evaluate expressions inside parentheses first
  • Evaluate any exponential expressions next
  • Evaluate any multiplication and division operations from left to right
  • Finally, evaluate any addition and subtraction operations from left to right

Q3: What is the difference between multiplication and division?

A3: Multiplication and division are both arithmetic operations that involve numbers. However, the key difference between the two is that multiplication involves combining numbers to get a product, while division involves splitting a number into equal parts.

Q4: How do I evaluate an expression with fractions?

A4: To evaluate an expression with fractions, you need to follow the order of operations (PEMDAS) and perform the operations in the correct order. This means that you should:

  • Evaluate any expressions inside parentheses first
  • Evaluate any exponential expressions next
  • Evaluate any multiplication and division operations from left to right
  • Finally, evaluate any addition and subtraction operations from left to right

Q5: What is the difference between a numerator and a denominator?

A5: A numerator is the number on top of a fraction, while a denominator is the number on the bottom of a fraction. The numerator represents the number of equal parts, while the denominator represents the total number of parts.

Q6: How do I simplify a fraction?

A6: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator. Then, divide both numbers by the GCD to get the simplified fraction.

Q7: What is the difference between a decimal and a fraction?

A7: A decimal is a way of representing a number as a sum of powers of 10, while a fraction is a way of representing a number as a ratio of two integers. For example, the decimal 0.5 is equivalent to the fraction 1/2.

Q8: How do I convert a decimal to a fraction?

A8: To convert a decimal to a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator. Then, divide both numbers by the GCD to get the fraction.

Q9: What is the difference between a percentage and a fraction?

A9: A percentage is a way of representing a number as a proportion of 100, while a fraction is a way of representing a number as a ratio of two integers. For example, the percentage 25% is equivalent to the fraction 1/4.

Q10: How do I convert a percentage to a fraction?

A10: To convert a percentage to a fraction, you need to divide the percentage by 100 and simplify the resulting fraction.

Conclusion

Evaluating mathematical expressions can be a challenging task, but with practice and patience, you can become proficient in evaluating expressions with confidence. Remember to follow the order of operations (PEMDAS) and perform the operations in the correct order. If you have any further questions or need additional help, don't hesitate to ask.

Frequently Asked Questions

  • What is the order of operations? The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
  • How do I evaluate an expression with multiple operations? To evaluate an expression with multiple operations, follow the order of operations (PEMDAS) and perform the operations in the correct order.
  • What is the difference between multiplication and division? Multiplication and division are both arithmetic operations that involve numbers. However, the key difference between the two is that multiplication involves combining numbers to get a product, while division involves splitting a number into equal parts.

Further Reading

  • Order of Operations (PEMDAS)
  • Evaluating Expressions with Multiple Operations
  • Basic Arithmetic Operations (Addition, Subtraction, Multiplication, Division)
  • Fractions and Decimals
  • Percentages and Fractions