Evaluate The Expression:$\[ -1 \times 4 \times 5 \\]

by ADMIN 53 views

Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves performing the operations in the correct order to obtain a result. In this article, we will evaluate the expression −1×4×5-1 \times 4 \times 5 and explore the concepts of order of operations and mathematical notation.

Understanding the Expression

The given expression is −1×4×5-1 \times 4 \times 5. This expression consists of three numbers: −1-1, 44, and 55. The operation between these numbers is multiplication, denoted by the symbol ×\times. To evaluate this expression, we need to follow the order of operations, which dictates that multiplication should be performed before addition or subtraction.

Order of Operations

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: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

In the given expression, there are no parentheses, exponents, or division operations. Therefore, we will follow the order of operations by performing the multiplication operations first.

Evaluating the Expression

To evaluate the expression −1×4×5-1 \times 4 \times 5, we will follow the order of operations:

  1. Multiply −1-1 and 44: −1×4=−4-1 \times 4 = -4
  2. Multiply −4-4 and 55: −4×5=−20-4 \times 5 = -20

Therefore, the final result of the expression −1×4×5-1 \times 4 \times 5 is −20-20.

Conclusion

In this article, we evaluated the expression −1×4×5-1 \times 4 \times 5 and explored the concepts of order of operations and mathematical notation. We followed the order of operations to perform the multiplication operations and obtained a final result of −20-20. This example illustrates the importance of following the order of operations when evaluating mathematical expressions.

Frequently Asked Questions

  • What is the order of operations? 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.
  • How do I evaluate an expression with multiple operations? To evaluate an expression with multiple operations, follow the order of operations:
    1. Evaluate expressions inside parentheses first.
    2. Evaluate any exponential expressions next.
    3. Evaluate multiplication and division operations from left to right.
    4. Finally, evaluate any addition and subtraction operations from left to right.
  • What is the result of the expression −1×4×5-1 \times 4 \times 5? The result of the expression −1×4×5-1 \times 4 \times 5 is −20-20.

Further Reading

  • Order of Operations: A Comprehensive Guide
  • Evaluating Mathematical Expressions: A Step-by-Step Guide
  • Mathematical Notation: A Guide to Understanding and Using Mathematical Symbols

References

  • "Mathematics for Dummies" by Mary Jane Sterling
  • "Algebra and Trigonometry" by James Stewart
  • "Mathematics: A Very Short Introduction" by Timothy Gowers

Introduction

Evaluating mathematical expressions is a fundamental concept in mathematics that involves performing operations to obtain a result. In our previous article, we evaluated the expression −1×4×5-1 \times 4 \times 5 and explored the concepts of order of operations and mathematical notation. In this article, we will provide a Q&A guide to help you understand and evaluate mathematical expressions.

Q&A Guide

General 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.
  • Q: How do I evaluate an expression with multiple operations? A: To evaluate an expression with multiple operations, follow the order of operations:
    1. Evaluate expressions inside parentheses first.
    2. Evaluate any exponential expressions next.
    3. Evaluate multiplication and division operations from left to right.
    4. Finally, evaluate any addition and subtraction operations from left to right.
  • Q: What is the result of the expression −1×4×5-1 \times 4 \times 5? A: The result of the expression −1×4×5-1 \times 4 \times 5 is −20-20.

Multiplication and Division Questions

  • Q: What is the result of the expression 2×3×42 \times 3 \times 4? A: To evaluate this expression, follow the order of operations:
    1. Multiply 22 and 33: 2×3=62 \times 3 = 6
    2. Multiply 66 and 44: 6×4=246 \times 4 = 24 Therefore, the result of the expression 2×3×42 \times 3 \times 4 is 2424.
  • Q: What is the result of the expression 6÷2×36 \div 2 \times 3? A: To evaluate this expression, follow the order of operations:
    1. Divide 66 by 22: 6÷2=36 \div 2 = 3
    2. Multiply 33 and 33: 3×3=93 \times 3 = 9 Therefore, the result of the expression 6÷2×36 \div 2 \times 3 is 99.

Addition and Subtraction Questions

  • Q: What is the result of the expression 2+3−42 + 3 - 4? A: To evaluate this expression, follow the order of operations:
    1. Add 22 and 33: 2+3=52 + 3 = 5
    2. Subtract 44 from 55: 5−4=15 - 4 = 1 Therefore, the result of the expression 2+3−42 + 3 - 4 is 11.
  • Q: What is the result of the expression 5−2+35 - 2 + 3? A: To evaluate this expression, follow the order of operations:
    1. Subtract 22 from 55: 5−2=35 - 2 = 3
    2. Add 33 to 33: 3+3=63 + 3 = 6 Therefore, the result of the expression 5−2+35 - 2 + 3 is 66.

Exponential Questions

  • Q: What is the result of the expression 232^3? A: To evaluate this expression, follow the order of operations:
    1. Raise 22 to the power of 33: 23=82^3 = 8 Therefore, the result of the expression 232^3 is 88.
  • Q: What is the result of the expression 32+43^2 + 4? A: To evaluate this expression, follow the order of operations:
    1. Raise 33 to the power of 22: 32=93^2 = 9
    2. Add 44 to 99: 9+4=139 + 4 = 13 Therefore, the result of the expression 32+43^2 + 4 is 1313.

Conclusion

In this article, we provided a Q&A guide to help you understand and evaluate mathematical expressions. We covered general questions, multiplication and division questions, addition and subtraction questions, and exponential questions. By following the order of operations and understanding the concepts of mathematical notation, you can evaluate mathematical expressions with confidence.

Frequently Asked Questions

  • What is the order of operations? 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.
  • How do I evaluate an expression with multiple operations? To evaluate an expression with multiple operations, follow the order of operations:
    1. Evaluate expressions inside parentheses first.
    2. Evaluate any exponential expressions next.
    3. Evaluate multiplication and division operations from left to right.
    4. Finally, evaluate any addition and subtraction operations from left to right.

Further Reading

  • Order of Operations: A Comprehensive Guide
  • Evaluating Mathematical Expressions: A Step-by-Step Guide
  • Mathematical Notation: A Guide to Understanding and Using Mathematical Symbols

References

  • "Mathematics for Dummies" by Mary Jane Sterling
  • "Algebra and Trigonometry" by James Stewart
  • "Mathematics: A Very Short Introduction" by Timothy Gowers