Evaluate The Expression:$\[ -\frac{1}{2} - \frac{2}{5} = \\]

Feb 26, 2025 by ADMIN 61 views

$Evaluate the Expression: $-\frac{1}{2} - \frac{2}{5}$$

Introduction

In mathematics, evaluating expressions is a fundamental concept that involves simplifying mathematical expressions by performing operations such as addition, subtraction, multiplication, and division. In this article, we will evaluate the expression $-\frac{1}{2} - \frac{2}{5}$ and provide a step-by-step solution to simplify it.

Understanding the Expression

The given expression is $-\frac{1}{2} - \frac{2}{5}$ . This expression consists of two fractions, $-\frac{1}{2}$ and $-\frac{2}{5}$ , which are being subtracted from each other. To evaluate this expression, we need to find a common denominator for the two fractions.

Finding a Common Denominator

To find a common denominator, we need to identify the least common multiple (LCM) of the denominators of the two fractions. The denominators are 2 and 5. The LCM of 2 and 5 is 10.

Simplifying the Expression

Now that we have found the common denominator, we can rewrite the fractions with the common denominator.

-\frac{1}{2} - \frac{2}{5} = -\frac{5}{10} - \frac{4}{10}

Combining the Fractions

Now that the fractions have the same denominator, we can combine them by adding or subtracting the numerators.

-\frac{5}{10} - \frac{4}{10} = -\frac{9}{10}

Conclusion

In conclusion, the expression $-\frac{1}{2} - \frac{2}{5}$ can be simplified to $-\frac{9}{10}$ by finding a common denominator and combining the fractions.

Importance of Evaluating Expressions

Evaluating expressions is an essential skill in mathematics that helps us simplify complex mathematical expressions. It is used in various mathematical operations, such as solving equations, graphing functions, and calculating probabilities. By mastering the skill of evaluating expressions, we can solve a wide range of mathematical problems and make informed decisions in various fields.

Real-World Applications

Evaluating expressions has numerous real-world applications in fields such as science, engineering, economics, and finance. For example, in physics, evaluating expressions is used to calculate the trajectory of objects, while in engineering, it is used to design and optimize systems. In economics, evaluating expressions is used to calculate the cost of goods and services, while in finance, it is used to calculate the value of investments.

Tips for Evaluating Expressions

Here are some tips for evaluating expressions:

Identify the operation: The first step in evaluating an expression is to identify the operation being performed, such as addition, subtraction, multiplication, or division.
Find a common denominator: If the expression contains fractions, find a common denominator to simplify the expression.
Combine the fractions: Once the fractions have a common denominator, combine them by adding or subtracting the numerators.
Simplify the expression: Finally, simplify the expression by canceling out any common factors in the numerator and denominator.

Common Mistakes to Avoid

Here are some common mistakes to avoid when evaluating expressions:

Not identifying the operation: Failing to identify the operation being performed can lead to incorrect results.
Not finding a common denominator: Failing to find a common denominator can make it difficult to simplify the expression.
Not combining the fractions: Failing to combine the fractions can lead to incorrect results.
Not simplifying the expression: Failing to simplify the expression can make it difficult to interpret the results.

Conclusion

In conclusion, evaluating expressions is a fundamental concept in mathematics that involves simplifying mathematical expressions by performing operations such as addition, subtraction, multiplication, and division. By mastering the skill of evaluating expressions, we can solve a wide range of mathematical problems and make informed decisions in various fields. Remember to identify the operation, find a common denominator, combine the fractions, and simplify the expression to avoid common mistakes and get accurate results.

Introduction

Evaluating expressions is a fundamental concept in mathematics that involves simplifying mathematical expressions by performing operations such as addition, subtraction, multiplication, and division. 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 combination of numbers, variables, and mathematical operations that can be simplified to a single value.

Q: What are the basic operations in evaluating expressions?

A: The basic operations in evaluating expressions are addition, subtraction, multiplication, and division.

Q: How do I evaluate an expression with fractions?

A: To evaluate an expression with fractions, you need to find a common denominator and combine the fractions by adding or subtracting the numerators.

Q: What is a common denominator?

A: A common denominator is the least common multiple (LCM) of the denominators of the fractions in an expression.

Q: How do I find a common denominator?

A: To find a common denominator, you need to identify the least common multiple (LCM) of the denominators of the fractions in an expression.

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers.

Q: How do I combine fractions with different denominators?

A: To combine fractions with different denominators, you need to find a common denominator and then add or subtract the numerators.

Q: What is the order of operations in evaluating expressions?

A: The order of operations in evaluating expressions is:

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

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

A: An expression is a combination of numbers, variables, and mathematical operations that can be simplified to a single value. An equation is a statement that two expressions are equal.

Q: How do I simplify an expression?

A: To simplify an expression, you need to combine like terms, eliminate any unnecessary parentheses, and reduce any fractions to their simplest form.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power.

Q: How do I eliminate unnecessary parentheses?

A: To eliminate unnecessary parentheses, you need to simplify the expression inside the parentheses first.

Q: What is the importance of evaluating expressions?

A: Evaluating expressions is an essential skill in mathematics that helps us simplify complex mathematical expressions. It is used in various mathematical operations, such as solving equations, graphing functions, and calculating probabilities.

Q: What are some real-world applications of evaluating expressions?

A: Evaluating expressions has numerous real-world applications in fields such as science, engineering, economics, and finance. For example, in physics, evaluating expressions is used to calculate the trajectory of objects, while in engineering, it is used to design and optimize systems.

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

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

Not identifying the operation being performed
Not finding a common denominator
Not combining the fractions
Not simplifying the expression
Not following the order of operations