Simplify The Following Expression:${ 10 + 6 + 3 - 8 \times 2 + 7 - 14 + 20 \div 5 + 2^3 }$

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Introduction

Mathematical expressions can be complex and challenging to simplify, especially when they involve multiple operations and different types of numbers. In this article, we will simplify the given mathematical expression step by step, using the order of operations and basic arithmetic rules.

The Given Expression

The given expression is:

10+6+3−8×2+7−14+20÷5+23{ 10 + 6 + 3 - 8 \times 2 + 7 - 14 + 20 \div 5 + 2^3 }

Step 1: Evaluate Exponents

The first step in simplifying the expression is to evaluate any exponents. In this case, we have a single exponent, 2^3, which means 2 to the power of 3.

23=2×2×2=8{ 2^3 = 2 \times 2 \times 2 = 8 }

Step 2: Evaluate Multiplication and Division

Next, we need to evaluate any multiplication and division operations. In this case, we have two multiplication operations and one division operation.

8×2=16{ 8 \times 2 = 16 } 20÷5=4{ 20 \div 5 = 4 }

Step 3: Replace the Results of Exponents, Multiplication, and Division

Now that we have evaluated the exponents, multiplication, and division operations, we can replace the results in the original expression.

10+6+3−16+7−14+4+8{ 10 + 6 + 3 - 16 + 7 - 14 + 4 + 8 }

Step 4: Evaluate Addition and Subtraction

Finally, we can evaluate the addition and subtraction operations from left to right.

10+6+3=19{ 10 + 6 + 3 = 19 } 19−16=3{ 19 - 16 = 3 } 3+7=10{ 3 + 7 = 10 } 10−14=−4{ 10 - 14 = -4 } −4+4=0{ -4 + 4 = 0 } 0+8=8{ 0 + 8 = 8 }

Conclusion

By following the order of operations and basic arithmetic rules, we have simplified the given mathematical expression.

10+6+3−8×2+7−14+20÷5+23=8{ 10 + 6 + 3 - 8 \times 2 + 7 - 14 + 20 \div 5 + 2^3 = 8 }

Tips and Tricks

When simplifying mathematical expressions, it's essential to follow the order of operations:

  1. Evaluate exponents
  2. Evaluate multiplication and division operations from left to right
  3. Evaluate addition and subtraction operations from left to right

By following these steps, you can simplify even the most complex mathematical expressions.

Common Mistakes

When simplifying mathematical expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

  • Not following the order of operations
  • Not evaluating exponents, multiplication, and division operations correctly
  • Not replacing the results of exponents, multiplication, and division operations in the original expression

Real-World Applications

Simplifying mathematical expressions is a crucial skill in many real-world applications, including:

  • Science and engineering: Simplifying mathematical expressions is essential in scientific and engineering calculations.
  • Finance: Simplifying mathematical expressions is necessary in financial calculations, such as calculating interest rates and investment returns.
  • Computer programming: Simplifying mathematical expressions is a critical skill in computer programming, where mathematical expressions are used to solve complex problems.

Final Thoughts

Simplifying mathematical expressions may seem like a daunting task, but by following the order of operations and basic arithmetic rules, you can simplify even the most complex expressions. Remember to evaluate exponents, multiplication, and division operations correctly, and replace the results in the original expression. With practice and patience, you'll become a master of simplifying mathematical expressions.

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Introduction

In our previous article, we simplified the given mathematical expression step by step, using the order of operations and basic arithmetic rules. In this article, we will answer some frequently asked questions (FAQs) related to simplifying mathematical expressions.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when there are multiple operations in an expression. The order of operations is:

  1. Evaluate exponents
  2. Evaluate multiplication and division operations from left to right
  3. Evaluate addition and subtraction operations from left to right

Q: Why is it important to follow the order of operations?

A: Following the order of operations is essential to ensure that mathematical expressions are evaluated correctly. If we don't follow the order of operations, we may get incorrect results.

Q: What are some common mistakes to avoid when simplifying mathematical expressions?

A: Some common mistakes to avoid when simplifying mathematical expressions include:

  • Not following the order of operations
  • Not evaluating exponents, multiplication, and division operations correctly
  • Not replacing the results of exponents, multiplication, and division operations in the original expression

Q: How do I simplify a mathematical expression with multiple operations?

A: To simplify a mathematical expression with multiple operations, follow these steps:

  1. Evaluate any exponents
  2. Evaluate any multiplication and division operations from left to right
  3. Evaluate any addition and subtraction operations from left to right

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are two basic arithmetic operations. Addition involves combining two or more numbers to get a total, while subtraction involves finding the difference between two numbers.

Q: How do I simplify a mathematical expression with fractions?

A: To simplify a mathematical expression with fractions, follow these steps:

  1. Simplify any fractions in the expression
  2. Evaluate any exponents
  3. Evaluate any multiplication and division operations from left to right
  4. Evaluate any addition and subtraction operations from left to right

Q: What is the difference between multiplication and division?

A: Multiplication and division are two basic arithmetic operations. Multiplication involves finding the product of two or more numbers, while division involves finding the quotient of two numbers.

Q: How do I simplify a mathematical expression with decimals?

A: To simplify a mathematical expression with decimals, follow these steps:

  1. Simplify any decimals in the expression
  2. Evaluate any exponents
  3. Evaluate any multiplication and division operations from left to right
  4. Evaluate any addition and subtraction operations from left to right

Q: What are some real-world applications of simplifying mathematical expressions?

A: Simplifying mathematical expressions has many real-world applications, including:

  • Science and engineering: Simplifying mathematical expressions is essential in scientific and engineering calculations.
  • Finance: Simplifying mathematical expressions is necessary in financial calculations, such as calculating interest rates and investment returns.
  • Computer programming: Simplifying mathematical expressions is a critical skill in computer programming, where mathematical expressions are used to solve complex problems.

Conclusion

Simplifying mathematical expressions is a crucial skill in many real-world applications. By following the order of operations and basic arithmetic rules, you can simplify even the most complex expressions. Remember to evaluate exponents, multiplication, and division operations correctly, and replace the results in the original expression. With practice and patience, you'll become a master of simplifying mathematical expressions.