Simplify The Following Expression:${ 5 \cdot 2 + 5 \cdot 3 + 5 \cdot 4 + 5 \cdot 7 + 2\left[2 \cdot 3 + \frac{1}{2}(2 \cdot 4)\right] }$

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Introduction

Mathematical expressions can be complex and challenging to simplify. In this article, we will focus on simplifying a given mathematical expression step by step. The expression involves multiplication, addition, and fractions, making it a great example for demonstrating various mathematical operations.

The Given Expression

The given expression is:

5⋅2+5⋅3+5⋅4+5⋅7+2[2⋅3+12(2⋅4)]{ 5 \cdot 2 + 5 \cdot 3 + 5 \cdot 4 + 5 \cdot 7 + 2\left[2 \cdot 3 + \frac{1}{2}(2 \cdot 4)\right] }

Step 1: Simplify the Terms Inside the Brackets

To simplify the expression, we will start by simplifying the terms inside the brackets. The expression inside the brackets is:

2⋅3+12(2⋅4){ 2 \cdot 3 + \frac{1}{2}(2 \cdot 4) }

We can simplify this expression by following the order of operations (PEMDAS):

  1. Multiply 2 and 3: 2 * 3 = 6
  2. Multiply 2 and 4: 2 * 4 = 8
  3. Divide 8 by 2: 8 / 2 = 4
  4. Add 6 and 4: 6 + 4 = 10

So, the simplified expression inside the brackets is:

10{ 10 }

Step 2: Simplify the Terms Outside the Brackets

Now that we have simplified the expression inside the brackets, we can focus on simplifying the terms outside the brackets. The expression outside the brackets is:

5⋅2+5⋅3+5⋅4+5⋅7+2⋅10{ 5 \cdot 2 + 5 \cdot 3 + 5 \cdot 4 + 5 \cdot 7 + 2 \cdot 10 }

We can simplify this expression by multiplying 5 by each of the numbers:

  1. Multiply 5 and 2: 5 * 2 = 10
  2. Multiply 5 and 3: 5 * 3 = 15
  3. Multiply 5 and 4: 5 * 4 = 20
  4. Multiply 5 and 7: 5 * 7 = 35
  5. Multiply 2 and 10: 2 * 10 = 20

So, the simplified expression outside the brackets is:

10+15+20+35+20{ 10 + 15 + 20 + 35 + 20 }

Step 3: Add the Terms

Now that we have simplified the expression outside the brackets, we can add the terms:

  1. Add 10 and 15: 10 + 15 = 25
  2. Add 25 and 20: 25 + 20 = 45
  3. Add 45 and 35: 45 + 35 = 80
  4. Add 80 and 20: 80 + 20 = 100

So, the final simplified expression is:

100{ 100 }

Conclusion

In this article, we simplified a given mathematical expression step by step. We started by simplifying the terms inside the brackets, then simplified the terms outside the brackets, and finally added the terms to get the final simplified expression. This example demonstrates the importance of following the order of operations and simplifying expressions step by step.

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. The acronym PEMDAS is commonly used to remember the order of operations:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction

Q: How do I simplify a mathematical expression?

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

  1. Simplify the terms inside any parentheses or brackets.
  2. Simplify any exponents.
  3. Perform any multiplication and division operations from left to right.
  4. Perform any addition and subtraction operations from left to right.

Q: What is the final simplified expression?

A: The final simplified expression is 100.

Further Reading

If you want to learn more about simplifying mathematical expressions, check out the following resources:

  • Khan Academy: Simplifying Expressions
  • Mathway: Simplifying Expressions
  • Wolfram Alpha: Simplifying Expressions

References

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Introduction

In our previous article, we simplified a given mathematical expression step by step. In this article, we will answer some frequently asked questions related to simplifying mathematical expressions.

Q&A

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. The acronym PEMDAS is commonly used to remember the order of operations:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction

Q: How do I simplify a mathematical expression?

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

  1. Simplify the terms inside any parentheses or brackets.
  2. Simplify any exponents.
  3. Perform any multiplication and division operations from left to right.
  4. Perform any addition and subtraction operations from left to right.

Q: What is the difference between simplifying and solving an equation?

A: Simplifying an equation involves reducing the equation to its simplest form, while solving an equation involves finding the value of the variable that makes the equation true.

Q: Can I simplify an expression with variables?

A: Yes, you can simplify an expression with variables. However, you must follow the order of operations and simplify the expression step by step.

Q: How do I handle negative numbers when simplifying an expression?

A: When simplifying an expression with negative numbers, follow the same order of operations as with positive numbers. Remember that the negative sign can be treated as a multiplication by -1.

Q: Can I simplify an expression with fractions?

A: Yes, you can simplify an expression with fractions. To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.

Q: What is the final simplified expression?

A: The final simplified expression is 100.

Tips and Tricks

Tip 1: Use the Order of Operations

When simplifying an expression, always follow the order of operations (PEMDAS). This will ensure that you simplify the expression correctly.

Tip 2: Simplify Inside the Brackets First

When simplifying an expression with parentheses or brackets, simplify the terms inside the brackets first.

Tip 3: Use Exponents Wisely

When simplifying an expression with exponents, remember that exponents can be treated as repeated multiplication.

Tip 4: Check Your Work

When simplifying an expression, always check your work to ensure that you have simplified the expression correctly.

Common Mistakes

Mistake 1: Not Following the Order of Operations

One common mistake when simplifying an expression is not following the order of operations (PEMDAS).

Mistake 2: Not Simplifying Inside the Brackets First

Another common mistake is not simplifying the terms inside the brackets first.

Mistake 3: Not Using Exponents Wisely

Not using exponents wisely can lead to incorrect simplification of an expression.

Mistake 4: Not Checking Your Work

Not checking your work can lead to incorrect simplification of an expression.

Conclusion

In this article, we answered some frequently asked questions related to simplifying mathematical expressions. We also provided some tips and tricks to help you simplify expressions correctly. Remember to always follow the order of operations and simplify inside the brackets first.

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. The acronym PEMDAS is commonly used to remember the order of operations:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction

Q: How do I simplify a mathematical expression?

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

  1. Simplify the terms inside any parentheses or brackets.
  2. Simplify any exponents.
  3. Perform any multiplication and division operations from left to right.
  4. Perform any addition and subtraction operations from left to right.

Q: What is the difference between simplifying and solving an equation?

A: Simplifying an equation involves reducing the equation to its simplest form, while solving an equation involves finding the value of the variable that makes the equation true.

Further Reading

If you want to learn more about simplifying mathematical expressions, check out the following resources:

  • Khan Academy: Simplifying Expressions
  • Mathway: Simplifying Expressions
  • Wolfram Alpha: Simplifying Expressions

References