Calculate The Following Expression:${ 6 \times 2 - 9 + 8 \div 2 + 8 - 9 + \sqrt{25} }$

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Introduction

In this article, we will delve into the world of mathematics and calculate the given expression step by step. The expression is a combination of arithmetic operations, including multiplication, division, addition, and subtraction, as well as a square root operation. We will break down the expression into manageable parts and solve each part individually to arrive at the final result.

Expression Breakdown

The given expression is:

6×2−9+8÷2+8−9+25{ 6 \times 2 - 9 + 8 \div 2 + 8 - 9 + \sqrt{25} }

To calculate this expression, we need to follow the order of operations (PEMDAS):

  1. Parentheses: None
  2. Exponents: None
  3. Multiplication and Division: From left to right
  4. Addition and Subtraction: From left to right

Step 1: Multiply 6 and 2

The first operation is to multiply 6 and 2.

6×2=12{ 6 \times 2 = 12 }

Step 2: Divide 8 by 2

The next operation is to divide 8 by 2.

8÷2=4{ 8 \div 2 = 4 }

Step 3: Calculate the Square Root of 25

The square root of 25 is a whole number.

25=5{ \sqrt{25} = 5 }

Step 4: Add and Subtract from Left to Right

Now that we have the results of the multiplication, division, and square root operations, we can add and subtract from left to right.

12−9=3{ 12 - 9 = 3 }

3+4=7{ 3 + 4 = 7 }

7+8=15{ 7 + 8 = 15 }

15−9=6{ 15 - 9 = 6 }

6+5=11{ 6 + 5 = 11 }

Conclusion

The final result of the given expression is:

11{ 11 }

In this article, we have broken down the given expression into manageable parts and solved each part individually to arrive at the final result. We have followed the order of operations (PEMDAS) and performed the arithmetic operations step by step.

Frequently Asked Questions

Q: What is the order of operations (PEMDAS)?

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

  • Parentheses: Evaluate expressions inside parentheses first
  • Exponents: Evaluate any exponential expressions next
  • Multiplication and Division: Evaluate multiplication and division operations from left to right
  • Addition and Subtraction: 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 arithmetic operations that involve numbers. However, multiplication involves combining numbers to get a product, while division involves splitting a number into equal parts.

Q: What is the square root of 25?

A: The square root of 25 is a whole number, which is 5.

Final Thoughts

In conclusion, calculating the given expression involves breaking it down into manageable parts and solving each part individually. We have followed the order of operations (PEMDAS) and performed the arithmetic operations step by step to arrive at the final result. This article has provided a step-by-step guide to calculating the given expression and has also answered some frequently asked questions related to the topic.

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Introduction

In our previous article, we calculated the given expression step by step and arrived at the final result. However, we also received several questions from readers regarding the calculation process and mathematical operations. In this article, we will address some of the frequently asked questions related to calculating mathematical expressions.

Q&A Session

Q: What is the order of operations (PEMDAS)?

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

  • Parentheses: Evaluate expressions inside parentheses first
  • Exponents: Evaluate any exponential expressions next
  • Multiplication and Division: Evaluate multiplication and division operations from left to right
  • Addition and Subtraction: 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 arithmetic operations that involve numbers. However, multiplication involves combining numbers to get a product, while division involves splitting a number into equal parts.

Q: What is the square root of 25?

A: The square root of 25 is a whole number, which is 5.

Q: How do I calculate expressions with multiple operations?

A: To calculate expressions with multiple operations, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses, then evaluate any exponential expressions, followed by multiplication and division operations from left to right, and finally, evaluate any addition and subtraction operations from left to right.

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

A: A fraction is a way of expressing a part of a whole, while a decimal is a way of expressing a number as a sum of powers of 10. For example, the fraction 1/2 is equal to the decimal 0.5.

Q: How do I calculate expressions with negative numbers?

A: To calculate expressions with negative numbers, follow the same order of operations as before. However, when multiplying or dividing negative numbers, remember that two negative numbers multiplied or divided together result in a positive number, while a negative number multiplied or divided by a positive number results in a negative number.

Q: What is the difference between an exponent and a power?

A: An exponent is a small number that is raised to a power, while a power is the result of raising a number to a certain exponent. For example, 2^3 is equal to 2 to the power of 3, which is 8.

Q: How do I calculate expressions with variables?

A: To calculate expressions with variables, follow the same order of operations as before. However, when working with variables, remember that the variable can take on different values, so the expression may have different results depending on the value of the variable.

Conclusion

In this article, we have addressed some of the frequently asked questions related to calculating mathematical expressions. We have covered topics such as the order of operations, multiplication and division, square roots, fractions and decimals, negative numbers, exponents and powers, and variables. By following the order of operations and understanding the different mathematical operations, you can calculate complex expressions with ease.

Final Thoughts

Calculating mathematical expressions is an essential skill that is used in many areas of life, from science and engineering to finance and economics. By understanding the different mathematical operations and following the order of operations, you can solve complex problems and make informed decisions. Remember to always follow the order of operations and to be careful when working with negative numbers, fractions, and decimals.

Additional Resources

For more information on calculating mathematical expressions, check out the following resources:

  • Khan Academy: Math
  • Mathway: Math Problem Solver
  • Wolfram Alpha: Math and Science Calculator

By following these resources and practicing your math skills, you can become proficient in calculating mathematical expressions and solving complex problems.