Mathematical Expression: Ten Times the Product of Two Numbers q and r Divided by Thrice a Third
When dealing with complex mathematical concepts and expressions, it is essential to understand how to represent and solve them correctly. One such problem is the expression 'ten times the product of two numbers q and r divided by thrice a third.' This article will delve into the detailed steps to write this expression correctly and how to solve it step-by-step.
About the Expression
The phrase 'ten times the product of two numbers q and r divided by thrice a third' can be translated into a mathematical expression. This expression involves both multiplication and division, making it a crucial topic for students and professionals alike.
Writing the Expression
The correct way to write this mathematical expression is: 10qr / (3x). Let's break down each component:
10qr: This part represents 'ten times the product of two numbers q and r'. In algebra, we use variables to represent unknown values, and their product is represented as the multiplication of these variables, with a numerical coefficient (10) accompanying it. 3x: This represents 'thrice a third'. In algebra, 'thrice' means three times, and a 'third' would be represented as 1/x or 1/x.3 in this context. Therefore, thrice a third would be 3*(1/x).When a fraction is written in the denominator, it can be represented with a numerator and a denominator. Therefore, the expression 10qr / (3x) effectively captures the given concept.
Understanding the Expression
The entire expression 10qr / (3x) is a complex fraction, indicating that 10qr is divided by 3x. To solve such an expression, it is crucial to follow the BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) and PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) rules to ensure the correct order of operations.
Solution: Since there is no more information about the variable x, the expression cannot be further simplified. The final expression is: 10qr / (3x).
Practical Applications
Understanding such expressions is crucial in various fields, including mathematics, physics, and engineering. For instance, in physics, this expression might represent a physical quantity like force, energy, or a rate of change, where q and r could be related to physical parameters, and the division by 3x might relate to some kind of scaling or normalization.
In engineering, such expressions are often used in formulas that require precise calculations. Engineers must have a thorough understanding of these expressions to perform calculations accurately and make informed decisions.
Conclusion
In conclusion, the expression 'ten times the product of two numbers q and r divided by thrice a third' can be represented as 10qr / (3x). This expression is a fundamental concept in algebra and demonstrates the importance of correct mathematical writing and understanding. Whether it is in the realm of mathematics, physics, or engineering, the ability to interpret and manipulate such expressions is a crucial skill.
Understanding the intricacies of mathematical expressions enhances our problem-solving abilities and provides a solid foundation for more advanced studies. By mastering the art of interpreting complex expressions, you can tackle a wide range of mathematical and scientific challenges with greater confidence.