Evaluate The Expression When M = 12 M=12 M = 12 And N = 24 N=24 N = 24 :${ M+\frac{n}{6} }$ { 16 \}

Mar 13, 2025 by ADMIN 102 views

Evaluate the Expression: A Step-by-Step Guide

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Introduction

In mathematics, evaluating expressions is a crucial skill that helps us solve problems and understand complex concepts. In this article, we will focus on evaluating the expression $m+\frac{n}{6}$ when $m=12$ and $n=24$ . We will break down the problem step by step, using simple language and clear explanations.

Understanding the Expression

The given expression is $m+\frac{n}{6}$ . To evaluate this expression, we need to substitute the values of $m$ and $n$ into the equation. In this case, $m=12$ and $n=24$ . Our goal is to find the value of the expression when these values are substituted.

Substituting Values

To substitute the values of $m$ and $n$ , we will replace $m$ with $12$ and $n$ with $24$ in the expression. This gives us:

${ 12+\frac{24}{6} }$

Simplifying the Expression

Now that we have substituted the values, we can simplify the expression. To do this, we need to follow the order of operations (PEMDAS):

Divide $24$ by $6$ : $\frac{24}{6}=4$
Add $12$ and $4$ : $12+4=16$

Conclusion

Therefore, when $m=12$ and $n=24$ , the value of the expression $m+\frac{n}{6}$ is $16$ .

Why is Evaluating Expressions Important?

Evaluating expressions is an essential skill in mathematics because it helps us solve problems and understand complex concepts. By breaking down expressions into smaller parts and following the order of operations, we can find the value of the expression and make sense of the problem.

Real-World Applications

Evaluating expressions has many real-world applications. For example, in finance, we use expressions to calculate interest rates and investment returns. In science, we use expressions to model complex phenomena and make predictions. In engineering, we use expressions to design and optimize systems.

Tips for Evaluating Expressions

Here are some tips for evaluating expressions:

Follow the order of operations: PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) is a helpful acronym to remember the order of operations.
Substitute values carefully: Make sure to replace variables with their correct values and simplify the expression accordingly.
Simplify the expression step by step: Break down the expression into smaller parts and simplify each part before moving on to the next one.

Common Mistakes to Avoid

Here are some common mistakes to avoid when evaluating expressions:

Not following the order of operations: Failing to follow the order of operations can lead to incorrect results.
Substituting values incorrectly: Substituting values incorrectly can lead to incorrect results.
Not simplifying the expression step by step: Failing to simplify the expression step by step can lead to incorrect results.

Conclusion

Evaluating expressions is a crucial skill in mathematics that helps us solve problems and understand complex concepts. By following the order of operations, substituting values carefully, and simplifying the expression step by step, we can find the value of the expression and make sense of the problem. Remember to avoid common mistakes and practice regularly to become proficient in evaluating expressions.

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Introduction

In our previous article, we discussed how to evaluate the expression $m+\frac{n}{6}$ when $m=12$ and $n=24$ . We broke down the problem step by step, using simple language and clear explanations. In this article, we will answer some frequently asked questions about evaluating expressions.

Q&A

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 we have multiple operations in an expression. The acronym PEMDAS is a helpful way to remember the order of operations:

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: How do I substitute values into an expression?

A: To substitute values into an expression, simply replace the variables with their correct values. For example, if we have the expression $x+y$ and we want to substitute $x=3$ and $y=4$ , we would replace $x$ with $3$ and $y$ with $4$ to get $3+4$ .

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

A: A variable is a symbol that represents a value that can change. For example, $x$ is a variable because its value can change depending on the context. A constant, on the other hand, is a value that does not change. For example, $5$ is a constant because its value is always $5$ .

Q: How do I simplify an expression?

A: To simplify an expression, we need to follow the order of operations and combine like terms. For example, if we have the expression $2x+3x$ , we can combine the like terms to get $5x$ .

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

A: An expression is a group of numbers, variables, and operators that is used to represent a value. For example, $2x+3$ is an expression. An equation, on the other hand, is a statement that says two expressions are equal. For example, $2x+3=5$ is an equation.

Q: How do I evaluate an expression with fractions?

A: To evaluate an expression with fractions, we need to follow the order of operations and simplify the fractions. For example, if we have the expression $\frac{1}{2}x+\frac{1}{3}x$ , we can combine the fractions to get $\frac{5}{6}x$ .

Common Mistakes to Avoid

Here are some common mistakes to avoid when evaluating expressions:

Not following the order of operations: Failing to follow the order of operations can lead to incorrect results.
Substituting values incorrectly: Substituting values incorrectly can lead to incorrect results.
Not simplifying the expression step by step: Failing to simplify the expression step by step can lead to incorrect results.

Conclusion

Additional Resources

If you want to learn more about evaluating expressions, here are some additional resources:

Math textbooks: Check out your math textbook for more information on evaluating expressions.
Online resources: Websites like Khan Academy, Mathway, and Wolfram Alpha offer interactive lessons and exercises on evaluating expressions.
Practice problems: Try solving practice problems to reinforce your understanding of evaluating expressions.

Final Tips

Here are some final tips for evaluating expressions:

Practice regularly: Practice evaluating expressions regularly to become proficient.
Use online resources: Use online resources like Khan Academy, Mathway, and Wolfram Alpha to get help with evaluating expressions.
Ask for help: Don't be afraid to ask for help if you're struggling with evaluating expressions.