Evaluate The Expression:$\[ 5 + \frac{1}{5} = \\]\begin{tabular}{|c|c|c|c|c|}\hline 1 Whole & 1 Whole & 1 Whole & 1 Whole & 1 Whole \\\hline\end{tabular}

Introduction

In mathematics, expressions are a fundamental concept that helps us represent and solve problems. Evaluating expressions is a crucial skill that involves simplifying and solving mathematical expressions. In this article, we will evaluate the expression $5 + \frac{1}{5}$ using a step-by-step approach.

Understanding the Expression

The given expression is $5 + \frac{1}{5}$. This expression consists of two parts: a whole number $5$ and a fraction $\frac{1}{5}$. To evaluate this expression, we need to add the whole number and the fraction.

Adding Whole Numbers and Fractions

When adding whole numbers and fractions, we need to follow a specific order of operations. The order of operations is:

1. Add the whole numbers.
2. Add the fractions.

Step 1: Add the Whole Numbers

In this step, we add the whole numbers $5$ and $0$ (since there is no whole number part in the fraction). The result is:

5 + 0 = 5

Step 2: Add the Fractions

In this step, we add the fractions $\frac{1}{5}$ and $0$ (since there is no fraction part in the whole number). To add fractions, we need to have the same denominator. In this case, the denominator is $5$. Since the numerator of the fraction $\frac{1}{5}$ is $1$, we can add it to the whole number $5$ without changing the denominator.

5 + 1/5 = 5 + 1/5

Step 3: Simplify the Expression

In this step, we simplify the expression by combining the whole number and the fraction. To do this, we need to convert the whole number to a fraction with the same denominator as the fraction. In this case, the denominator is $5$. We can convert the whole number $5$ to a fraction with the denominator $5$ by multiplying it by $\frac{5}{5}$.

5 = 5/1 = 25/5

Now, we can add the fractions:

25/5 + 1/5 = 26/5

Conclusion

In conclusion, the expression $5 + \frac{1}{5}$ can be evaluated by following the order of operations and simplifying the expression. The result is $\frac{26}{5}$.

Real-World Applications

Evaluating expressions is a crucial skill that has many real-world applications. For example, in finance, evaluating expressions is used to calculate interest rates and investment returns. In science, evaluating expressions is used to model and solve complex problems.

Common Mistakes to Avoid

When evaluating expressions, there are several common mistakes to avoid. These include:

• Not following the order of operations
• Not simplifying the expression
• Not converting whole numbers to fractions with the same denominator

Tips and Tricks

Here are some tips and tricks to help you evaluate expressions:

• Always follow the order of operations
• Simplify the expression as much as possible
• Convert whole numbers to fractions with the same denominator
• Use a calculator to check your answers

Practice Problems

Here are some practice problems to help you evaluate expressions:

• Evaluate the expression $3 + \frac{2}{3}$
• Evaluate the expression $2 + \frac{1}{2}$
• Evaluate the expression $4 + \frac{3}{4}$

Conclusion

Introduction

In our previous article, we discussed how to evaluate expressions using a step-by-step approach. In this article, we will answer some frequently asked questions about evaluating expressions.

Q: What is an expression?

A: An expression 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 is the order of operations?

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

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

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly. Once you have the LCM, you can convert both fractions to have the same denominator, and then add them.

Q: How do I simplify an expression?

A: To simplify an expression, you need to combine like terms and eliminate any unnecessary operations. Like terms are terms that have the same variable and exponent. You can combine like terms by adding or subtracting their coefficients.

Q: What is a variable?

A: A variable is a letter or symbol that represents a value that can change. Variables are used to represent unknown values or values that can change.

Q: What is a constant?

A: A constant is a value that does not change. Constants are used to represent values that are known or fixed.

Q: How do I evaluate an expression with parentheses?

A: To evaluate an expression with parentheses, you need to follow the order of operations. First, evaluate any expressions inside the parentheses. Then, evaluate any exponential expressions. Finally, evaluate any multiplication and division operations from left to right.

Q: How do I evaluate an expression with exponents?

A: To evaluate an expression with exponents, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Finally, evaluate any multiplication and division operations from left to right.

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

A: To evaluate an expression with multiplication and division, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Finally, evaluate any multiplication and division operations from left to right.

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

A: To evaluate an expression with addition and subtraction, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Finally, evaluate any addition and subtraction operations from left to right.

Conclusion

In conclusion, evaluating expressions is a crucial skill that involves simplifying and solving mathematical expressions. By following the order of operations and simplifying the expression, we can evaluate expressions and solve complex problems. Remember to avoid common mistakes and use tips and tricks to help you evaluate expressions. With practice, you will become proficient in evaluating expressions and solving complex problems.

Practice Problems

Here are some practice problems to help you evaluate expressions:

• Evaluate the expression $2x + 3y$
• Evaluate the expression $x^2 + 4x + 5$
• Evaluate the expression $3x - 2y + 1$

Additional Resources

Here are some additional resources to help you evaluate expressions:

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