Simplify The Expression:${ \frac{-42}{1} + 5(2) - 3 }$

Introduction

Mathematical expressions are a fundamental part of mathematics, and simplifying them is an essential skill that every student and professional should possess. In this article, we will focus on simplifying a specific expression, $\frac{-42}{1} + 5(2) - 3$, and provide a step-by-step guide on how to solve it.

Understanding the Expression

Before we dive into simplifying the expression, let's first understand what it means. The expression $\frac{-42}{1} + 5(2) - 3$ consists of three main components:

1. Fraction: $\frac{-42}{1}$, which represents a division operation.
2. Multiplication: $5(2)$, which represents a multiplication operation.
3. Subtraction: $-3$, which represents a subtraction operation.

Step 1: Simplify the Fraction

The first step in simplifying the expression is to simplify the fraction $\frac{-42}{1}$. Since the denominator is 1, we can simply remove it, and the fraction becomes $-42$.

Step 2: Simplify the Multiplication

Next, we need to simplify the multiplication operation $5(2)$. To do this, we simply multiply 5 by 2, which gives us 10.

Step 3: Combine the Terms

Now that we have simplified the fraction and the multiplication operation, we can combine the terms. The expression now becomes $-42 + 10 - 3$.

Step 4: Simplify the Expression

To simplify the expression, we need to perform the addition and subtraction operations. First, we add 10 and -3, which gives us 7. Then, we add -42 to 7, which gives us -35.

Conclusion

In conclusion, the simplified expression is $-35$. By following the steps outlined in this article, we have successfully simplified the expression $\frac{-42}{1} + 5(2) - 3$.

Tips and Tricks

Here are some tips and tricks to help you simplify mathematical expressions:

• Follow the order of operations: When simplifying an expression, always follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
• Simplify fractions: When simplifying a fraction, always simplify the numerator and denominator separately.
• Combine like terms: When combining terms, always combine like terms (terms with the same variable and exponent).

Real-World Applications

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

• Science and engineering: Simplifying mathematical expressions is essential in science and engineering, where complex equations need to be solved to model real-world phenomena.
• Finance: Simplifying mathematical expressions is also essential in finance, where complex financial models need to be solved to make informed investment decisions.
• Computer programming: Simplifying mathematical expressions is also essential in computer programming, where complex algorithms need to be implemented to solve real-world problems.

Final Thoughts

In conclusion, simplifying mathematical expressions is an essential skill that every student and professional should possess. By following the steps outlined in this article, you can simplify even the most complex expressions. Remember to always follow the order of operations, simplify fractions, and combine like terms to simplify mathematical expressions.

Frequently Asked Questions

Here are some frequently asked questions about simplifying mathematical expressions:

• Q: What is the order of operations? A: The order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
• Q: How do I simplify fractions? A: To simplify a fraction, always simplify the numerator and denominator separately.
• Q: How do I combine like terms? A: To combine like terms, always combine terms with the same variable and exponent.

References

Here are some references for further reading on simplifying mathematical expressions:

• "Algebra" by Michael Artin: This book provides a comprehensive introduction to algebra, including simplifying mathematical expressions.
• "Calculus" by Michael Spivak: This book provides a comprehensive introduction to calculus, including simplifying mathematical expressions.
• "Mathematics for Computer Science" by Eric Lehman: This book provides a comprehensive introduction to mathematics for computer science, including simplifying mathematical expressions.
  

Introduction

In our previous article, we discussed how to simplify a mathematical expression, $\frac{-42}{1} + 5(2) - 3$. We provided a step-by-step guide on how to solve it, and also discussed some tips and tricks to help you simplify mathematical expressions. In this article, we will provide a Q&A guide to help you understand and simplify mathematical expressions.

Q&A Guide

Q: What is the order of operations?

A: The order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. This means that you should perform operations in the following order:

1. Evaluate expressions inside parentheses.
2. Evaluate any exponential expressions.
3. Perform any multiplication and division operations from left to right.
4. Perform any addition and subtraction operations from left to right.

Q: How do I simplify fractions?

A: To simplify a fraction, you should simplify the numerator and denominator separately. For example, if you have the fraction $\frac{12}{4}$, you can simplify it by dividing both the numerator and denominator by 4, which gives you $\frac{3}{1}$.

Q: How do I combine like terms?

A: To combine like terms, you should combine terms with the same variable and exponent. For example, if you have the expression $2x + 3x$, you can combine the like terms by adding the coefficients, which gives you $5x$.

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change, while a constant is a value that does not change. For example, in the expression $2x + 3$, the variable is $x$ and the constants are 2 and 3.

Q: How do I evaluate expressions with exponents?

A: To evaluate expressions with exponents, you should follow the order of operations. For example, if you have the expression $2^3 + 4$, you should first evaluate the exponent, which gives you $8 + 4$, and then add the two numbers together.

Q: What is the difference between a function and an expression?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). An expression, on the other hand, is a combination of variables, constants, and mathematical operations that can be evaluated to produce a value.

Q: How do I simplify expressions with absolute values?

A: To simplify expressions with absolute values, you should follow the definition of absolute value. For example, if you have the expression $|x|$, you can simplify it by considering two cases: $x \geq 0$ and $x < 0$. If $x \geq 0$, then $|x| = x$. If $x < 0$, then $|x| = -x$.

Q: What is the difference between a rational expression and a rational number?

A: A rational expression is a fraction that contains variables and/or constants in the numerator and/or denominator. A rational number, on the other hand, is a fraction that contains only integers in the numerator and denominator.

Q: How do I simplify expressions with radicals?

A: To simplify expressions with radicals, you should follow the rules of radicals. For example, if you have the expression $\sqrt{16}$, you can simplify it by finding the largest perfect square that divides 16, which is 4. Then, you can simplify the expression by taking the square root of 4, which gives you 2.

Tips and Tricks

Here are some additional tips and tricks to help you simplify mathematical expressions:

• Use the order of operations: Always follow the order of operations (PEMDAS) when simplifying mathematical expressions.
• Simplify fractions: Always simplify fractions by dividing both the numerator and denominator by their greatest common divisor.
• Combine like terms: Always combine like terms by adding or subtracting the coefficients.
• Evaluate expressions with exponents: Always evaluate expressions with exponents by following the order of operations.
• Simplify expressions with absolute values: Always simplify expressions with absolute values by considering two cases: $x \geq 0$ and $x < 0$.

Real-World Applications

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

• Science and engineering: Simplifying mathematical expressions is essential in science and engineering, where complex equations need to be solved to model real-world phenomena.
• Finance: Simplifying mathematical expressions is also essential in finance, where complex financial models need to be solved to make informed investment decisions.
• Computer programming: Simplifying mathematical expressions is also essential in computer programming, where complex algorithms need to be implemented to solve real-world problems.

Final Thoughts

In conclusion, simplifying mathematical expressions is an essential skill that every student and professional should possess. By following the order of operations, simplifying fractions, combining like terms, and evaluating expressions with exponents, you can simplify even the most complex expressions. Remember to always use the order of operations, simplify fractions, combine like terms, and evaluate expressions with exponents to simplify mathematical expressions.

Frequently Asked Questions

Here are some frequently asked questions about simplifying mathematical expressions:

• Q: What is the order of operations? A: The order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
• Q: How do I simplify fractions? A: To simplify a fraction, you should simplify the numerator and denominator separately.
• Q: How do I combine like terms? A: To combine like terms, you should combine terms with the same variable and exponent.

References

Here are some references for further reading on simplifying mathematical expressions:

• "Algebra" by Michael Artin: This book provides a comprehensive introduction to algebra, including simplifying mathematical expressions.
• "Calculus" by Michael Spivak: This book provides a comprehensive introduction to calculus, including simplifying mathematical expressions.
• "Mathematics for Computer Science" by Eric Lehman: This book provides a comprehensive introduction to mathematics for computer science, including simplifying mathematical expressions.