Evaluate The Expression: ${ -\frac{5}{6} - \frac{1}{8} }$
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Introduction
When it comes to simplifying fractions, it's essential to understand the rules and procedures involved. In this article, we will delve into the world of fractions and explore how to evaluate the expression: ${-\frac{5}{6} - \frac{1}{8}}$. We will break down the steps involved in simplifying fractions and provide a comprehensive guide to help you master this essential math skill.
Understanding Fractions
Fractions are a way of representing a part of a whole. They consist of two parts: the numerator (the top number) and the denominator (the bottom number). The numerator represents the number of equal parts we have, while the denominator represents the total number of parts the whole is divided into.
For example, in the fraction ${\frac{1}{2}}$, the numerator is 1 and the denominator is 2. This means we have 1 part out of a total of 2 parts.
Simplifying Fractions
Simplifying fractions involves reducing them to their lowest terms. This means we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by it.
For example, let's simplify the fraction ${\frac{6}{8}}$. To do this, we need to find the GCD of 6 and 8, which is 2. We can then divide both numbers by 2 to get ${\frac{3}{4}}$.
Evaluating the Expression
Now that we have a solid understanding of fractions and simplifying them, let's evaluate the expression: ${-\frac{5}{6} - \frac{1}{8}}$.
To do this, we need to follow the order of operations (PEMDAS):
- Parentheses: None
- Exponents: None
- Multiplication and Division: None
- Addition and Subtraction: Perform the operations from left to right
Step 1: Find a Common Denominator
To add or subtract fractions, we need to have a common denominator. In this case, the denominators are 6 and 8. We can find the least common multiple (LCM) of 6 and 8, which is 24.
Step 2: Convert the Fractions
We can now convert both fractions to have a denominator of 24:
Step 3: Add the Fractions
Now that we have a common denominator, we can add the fractions:
Conclusion
Evaluating the expression $-\frac{5}{6} - \frac{1}{8}}$ involves simplifying fractions and following the order of operations. By finding a common denominator, converting the fractions, and adding them, we can arrive at the final answer{24}}$.
Tips and Tricks
- When simplifying fractions, always find the GCD of the numerator and the denominator.
- When adding or subtracting fractions, find a common denominator and convert both fractions to have that denominator.
- Always follow the order of operations (PEMDAS) when evaluating expressions.
Real-World Applications
Simplifying fractions and evaluating expressions are essential skills in many real-world applications, such as:
- Cooking: When a recipe calls for a fraction of an ingredient, you need to simplify the fraction to know how much to use.
- Building: When building a structure, you need to calculate the area and volume of different shapes, which often involves simplifying fractions.
- Science: In scientific calculations, you often need to simplify fractions to arrive at the correct answer.
Final Thoughts
Evaluating the expression ${-\frac{5}{6} - \frac{1}{8}}$ may seem like a simple task, but it requires a solid understanding of fractions and the order of operations. By following the steps outlined in this article, you can master this essential math skill and apply it to real-world situations. Remember to always simplify fractions and follow the order of operations to arrive at the correct answer.
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Introduction
In our previous article, we explored how to evaluate the expression: ${-\frac{5}{6} - \frac{1}{8}}$. We broke down the steps involved in simplifying fractions and provided a comprehensive guide to help you master this essential math skill. In this article, we will answer some of the most frequently asked questions related to evaluating expressions with fractions.
Q&A
Q: What is the difference between a numerator and a denominator?
A: The numerator is the top number in a fraction, representing the number of equal parts we have. The denominator is the bottom number, representing the total number of parts the whole is divided into.
Q: How do I find the greatest common divisor (GCD) of two numbers?
A: To find the GCD of two numbers, you can use the Euclidean algorithm or simply list the factors of each number and find the greatest common factor.
Q: What is the least common multiple (LCM) of two numbers?
A: The LCM of two numbers is the smallest number that both numbers can divide into evenly. You can find the LCM by listing the multiples of each number and finding the smallest common multiple.
Q: How do I convert a fraction to have a common denominator?
A: To convert a fraction to have a common denominator, you can multiply the numerator and denominator by the same number. For example, to convert $\frac{1}{2}}$ to have a denominator of 4, you can multiply both numbers by 2{2 \times 2} = \frac{2}{4}}$.
Q: What is the order of operations (PEMDAS)?
A: The order of operations is a set of rules that tells you which operations to perform first when evaluating 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 simplify a fraction?
A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by it. For example, to simplify $\frac{6}{8}}$, you can find the GCD of 6 and 8, which is 2, and divide both numbers by 2{4}}$.
Q: What is the difference between adding and subtracting fractions?
A: When adding fractions, you need to have a common denominator. When subtracting fractions, you also need to have a common denominator. However, when subtracting fractions, you need to change the sign of the second fraction.
Q: How do I evaluate an expression with multiple fractions?
A: To evaluate an expression with multiple fractions, you need to follow the order of operations (PEMDAS). First, simplify any fractions that can be simplified. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.
Conclusion
Evaluating expressions with fractions can be a challenging task, but with practice and patience, you can master this essential math skill. By following the steps outlined in this article and answering the frequently asked questions, you can become more confident in your ability to evaluate expressions with fractions.
Tips and Tricks
- Always simplify fractions before evaluating an expression.
- Follow the order of operations (PEMDAS) when evaluating an expression.
- Use a common denominator when adding or subtracting fractions.
- Change the sign of the second fraction when subtracting fractions.
Real-World Applications
Evaluating expressions with fractions is an essential skill in many real-world applications, such as:
- Cooking: When a recipe calls for a fraction of an ingredient, you need to simplify the fraction to know how much to use.
- Building: When building a structure, you need to calculate the area and volume of different shapes, which often involves simplifying fractions.
- Science: In scientific calculations, you often need to simplify fractions to arrive at the correct answer.
Final Thoughts
Evaluating expressions with fractions is a fundamental math skill that requires practice and patience. By following the steps outlined in this article and answering the frequently asked questions, you can become more confident in your ability to evaluate expressions with fractions. Remember to always simplify fractions and follow the order of operations to arrive at the correct answer.