Evaluate The Expression:$\[ B = -34 \times 15 + 34 \times 25 \\]

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Introduction

In mathematics, evaluating expressions is a fundamental concept that involves simplifying mathematical statements to obtain a final value. This process requires a thorough understanding of mathematical operations, including multiplication, addition, and subtraction. In this article, we will evaluate the expression B=−34×15+34×25B = -34 \times 15 + 34 \times 25 and provide a step-by-step solution to obtain the final value of BB.

Understanding the Expression

The given expression is B=−34×15+34×25B = -34 \times 15 + 34 \times 25. To evaluate this expression, we need to follow the order of operations (PEMDAS):

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

Step 1: Multiply -34 by 15

To evaluate the expression, we start by multiplying -34 by 15.

−34×15=−510{ -34 \times 15 = -510 }

Step 2: Multiply 34 by 25

Next, we multiply 34 by 25.

34×25=850{ 34 \times 25 = 850 }

Step 3: Add -510 and 850

Now, we add -510 and 850 to obtain the final value of BB.

B=−510+850{ B = -510 + 850 }

Step 4: Simplify the Expression

To simplify the expression, we combine the two terms.

B=340{ B = 340 }

Conclusion

In this article, we evaluated the expression B=−34×15+34×25B = -34 \times 15 + 34 \times 25 and obtained the final value of BB. By following the order of operations and simplifying the expression, we arrived at the solution B=340B = 340. This example demonstrates the importance of understanding mathematical operations and following the correct order of operations to evaluate expressions.

Real-World Applications

Evaluating expressions is a crucial skill in various fields, including science, engineering, and finance. In science, expressions are used to model real-world phenomena, such as population growth and chemical reactions. In engineering, expressions are used to design and optimize systems, such as electrical circuits and mechanical systems. In finance, expressions are used to calculate investment returns and risk management.

Tips and Tricks

When evaluating expressions, it's essential to follow the order of operations and simplify the expression step-by-step. Here are some tips and tricks to help you evaluate expressions:

  • Use parentheses to group terms and avoid confusion.
  • Evaluate exponents and roots before multiplication and division.
  • Multiply and divide from left to right.
  • Add and subtract from left to right.
  • Simplify the expression by combining like terms.

Common Mistakes

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

  • Failing to follow the order of operations.
  • Not simplifying the expression step-by-step.
  • Not using parentheses to group terms.
  • Not evaluating exponents and roots before multiplication and division.

Final Thoughts

Evaluating expressions is a fundamental concept in mathematics that requires a thorough understanding of mathematical operations. By following the order of operations and simplifying the expression step-by-step, you can arrive at the correct solution. Remember to use parentheses to group terms, evaluate exponents and roots before multiplication and division, and simplify the expression by combining like terms. With practice and patience, you can become proficient in evaluating expressions and apply this skill to real-world problems.

Additional Resources

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

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

Conclusion

In conclusion, evaluating expressions is a crucial skill in mathematics that requires a thorough understanding of mathematical operations. By following the order of operations and simplifying the expression step-by-step, you can arrive at the correct solution. Remember to use parentheses to group terms, evaluate exponents and roots before multiplication and division, and simplify the expression by combining like terms. With practice and patience, you can become proficient in evaluating expressions and apply this skill to real-world problems.

Introduction

Evaluating expressions is a fundamental concept in mathematics that requires a thorough understanding of mathematical operations. In our previous article, we evaluated the expression B=−34×15+34×25B = -34 \times 15 + 34 \times 25 and obtained the final value of BB. In this article, we will provide a Q&A guide to help you understand and evaluate expressions.

Q: What is an expression in mathematics?

A: An expression in mathematics is a mathematical statement that contains variables, constants, and mathematical operations. It is a way to represent a mathematical relationship between variables and constants.

Q: What are the basic mathematical operations?

A: The basic mathematical operations are:

  • Addition (+)
  • Subtraction (-)
  • Multiplication (*)
  • Division (/ or *)
  • Exponents (^)
  • Roots (square root, cube root, etc.)

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which mathematical operations to perform first when evaluating an expression. The order of operations is:

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

Q: How do I evaluate an expression with parentheses?

A: To evaluate an expression with parentheses, follow these steps:

  1. Evaluate the expression inside the parentheses first.
  2. Replace the parentheses with the value you obtained.
  3. Evaluate the remaining expression.

Q: How do I evaluate an expression with exponents?

A: To evaluate an expression with exponents, follow these steps:

  1. Evaluate the base of the exponent first.
  2. Raise the base to the power of the exponent.
  3. Evaluate the remaining expression.

Q: How do I evaluate an expression with multiplication and division?

A: To evaluate an expression with multiplication and division, follow these steps:

  1. Evaluate the multiplication and division operations from left to right.
  2. Multiply and divide the numbers in the order they appear.
  3. Evaluate the remaining expression.

Q: How do I evaluate an expression with addition and subtraction?

A: To evaluate an expression with addition and subtraction, follow these steps:

  1. Evaluate the addition and subtraction operations from left to right.
  2. Add and subtract the numbers in the order they appear.
  3. Evaluate the remaining expression.

Q: What is the difference between an expression and an equation?

A: An expression is a mathematical statement that contains variables, constants, and mathematical operations. An equation is a mathematical statement that contains an expression on one side and a value on the other side.

Q: How do I solve an equation?

A: To solve an equation, follow these steps:

  1. Evaluate the expression on the left side of the equation.
  2. Set the expression equal to the value on the right side of the equation.
  3. Solve for the variable.

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

A: Some common mistakes to avoid when evaluating expressions include:

  • Failing to follow the order of operations.
  • Not simplifying the expression step-by-step.
  • Not using parentheses to group terms.
  • Not evaluating exponents and roots before multiplication and division.

Conclusion

Evaluating expressions is a fundamental concept in mathematics that requires a thorough understanding of mathematical operations. By following the order of operations and simplifying the expression step-by-step, you can arrive at the correct solution. Remember to use parentheses to group terms, evaluate exponents and roots before multiplication and division, and simplify the expression by combining like terms. With practice and patience, you can become proficient in evaluating expressions and apply this skill to real-world problems.

Additional Resources

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

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

Final Thoughts

Evaluating expressions is a crucial skill in mathematics that requires a thorough understanding of mathematical operations. By following the order of operations and simplifying the expression step-by-step, you can arrive at the correct solution. Remember to use parentheses to group terms, evaluate exponents and roots before multiplication and division, and simplify the expression by combining like terms. With practice and patience, you can become proficient in evaluating expressions and apply this skill to real-world problems.