Evaluate The Expression $\frac{1}{2} M + \frac{3}{4}$ When $m = \frac{1}{4}$.

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Introduction

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In mathematics, evaluating expressions with variables is a fundamental concept that helps us solve problems and make predictions. In this article, we will focus on evaluating the expression $\frac{1}{2} m + \frac{3}{4}$ when $m = \frac{1}{4}$. We will break down the problem into smaller steps and use simple language to explain each concept.

Understanding the Problem

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The problem requires us to evaluate the expression $\frac{1}{2} m + \frac{3}{4}$ when $m = \frac{1}{4}$. This means we need to substitute the value of $m$ into the expression and simplify it to get the final answer.

Substituting the Value of $m$

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To substitute the value of $m$, we need to replace $m$ with $\frac{1}{4}$ in the expression $\frac{1}{2} m + \frac{3}{4}$. This gives us:

$$\frac{1}{2} \left(\frac{1}{4}\right) + \frac{3}{4}$$

Simplifying the Expression

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

1. Multiply $\frac{1}{2}$ and $\frac{1}{4}$:

$$\frac{1}{2} \left(\frac{1}{4}\right) = \frac{1}{8}$$

2. Add $\frac{1}{8}$ and $\frac{3}{4}$:

$$\frac{1}{8} + \frac{3}{4}$$

Finding a Common Denominator

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To add $\frac{1}{8}$ and $\frac{3}{4}$, we need to find a common denominator. The least common multiple (LCM) of 8 and 4 is 8. Therefore, we can rewrite $\frac{3}{4}$ as:

$$\frac{3}{4} = \frac{6}{8}$$

Adding the Fractions

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Now that we have a common denominator, we can add the fractions:

$$\frac{1}{8} + \frac{6}{8} = \frac{7}{8}$$

Conclusion

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In conclusion, we have evaluated the expression $\frac{1}{2} m + \frac{3}{4}$ when $m = \frac{1}{4}$. We substituted the value of $m$, simplified the expression, and found the final answer to be $\frac{7}{8}$.

Tips and Tricks

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• When evaluating expressions with variables, always follow the order of operations (PEMDAS).
• Make sure to substitute the value of the variable into the expression.
• Simplify the expression by combining like terms and finding a common denominator.
• Use simple language to explain each concept and break down the problem into smaller steps.

Frequently Asked Questions

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• Q: What is the value of $m$ in the expression $\frac{1}{2} m + \frac{3}{4}$? A: The value of $m$ is $\frac{1}{4}$.
• Q: How do I simplify the expression $\frac{1}{2} m + \frac{3}{4}$ when $m = \frac{1}{4}$? A: To simplify the expression, follow the order of operations (PEMDAS) and substitute the value of $m$ into the expression.

Further Reading

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• For more information on evaluating expressions with variables, check out our article on Solving Linear Equations.
• For more practice problems, try our Math Practice Exercises.

References

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• Khan Academy
• Mathway
  

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Introduction

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In our previous article, we discussed how to evaluate the expression $\frac{1}{2} m + \frac{3}{4}$ when $m = \frac{1}{4}$. In this article, we will provide a Q&A guide to help you better understand the concept of evaluating expressions with variables.

Q&A Guide

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Q: What is the value of $m$ in the expression $\frac{1}{2} m + \frac{3}{4}$?

A: The value of $m$ is $\frac{1}{4}$.

Q: How do I simplify the expression $\frac{1}{2} m + \frac{3}{4}$ when $m = \frac{1}{4}$?

A: To simplify the expression, follow the order of operations (PEMDAS) and substitute the value of $m$ into the expression.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

• 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 find a common denominator when adding fractions?

A: To find a common denominator, you need to find the least common multiple (LCM) of the denominators of the fractions. For example, if you have two fractions with denominators 4 and 6, the LCM is 12. You can then rewrite each fraction with the common denominator of 12.

Q: What is the final answer to the expression $\frac{1}{2} m + \frac{3}{4}$ when $m = \frac{1}{4}$?

A: The final answer is $\frac{7}{8}$.

Tips and Tricks

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• When evaluating expressions with variables, always follow the order of operations (PEMDAS).
• Make sure to substitute the value of the variable into the expression.
• Simplify the expression by combining like terms and finding a common denominator.
• Use simple language to explain each concept and break down the problem into smaller steps.

Common Mistakes

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• Not following the order of operations (PEMDAS) when evaluating expressions with variables.
• Not substituting the value of the variable into the expression.
• Not simplifying the expression by combining like terms and finding a common denominator.

Further Reading

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• For more information on evaluating expressions with variables, check out our article on Solving Linear Equations.
• For more practice problems, try our Math Practice Exercises.

References

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• Khan Academy
• Mathway

Additional Resources

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• Math Open Reference
• Purplemath

Conclusion

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Evaluating expressions with variables is a fundamental concept in mathematics. By following the order of operations (PEMDAS) and simplifying the expression, you can solve problems and make predictions. Remember to substitute the value of the variable into the expression and use simple language to explain each concept. With practice and patience, you will become proficient in evaluating expressions with variables.