Simplify The Expression: $ \frac{1}{6} - \left( \frac{-5}{8} \right) $
Introduction
When dealing with mathematical expressions, simplifying them is an essential step to understand and work with the given problem. In this article, we will focus on simplifying the expression $ \frac{1}{6} - \left( \frac{-5}{8} \right) $. This involves understanding the concept of negative numbers, fractions, and the order of operations. By the end of this article, you will be able to simplify the given expression and understand the underlying mathematical concepts.
Understanding the Expression
The given expression is $ \frac1}{6} - \left( \frac{-5}{8} \right) $. To simplify this expression, we need to understand the concept of negative numbers and fractions. A negative number is a number that is less than zero, and a fraction is a way of representing a part of a whole. In this expression, we have two fractions{6} $ and $ \frac{-5}{8} $. The first fraction is a positive fraction, while the second fraction is a negative fraction.
Simplifying the Expression
To simplify the expression, we need to follow the order of operations (PEMDAS):
- Parentheses: Evaluate the expression inside the parentheses.
- Exponents: Evaluate any exponents (none in this case).
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.
In this case, we need to evaluate the expression inside the parentheses first. The expression inside the parentheses is $ \frac{-5}{8} $. This is a negative fraction, which means that it is less than zero.
Evaluating the Expression Inside the Parentheses
To evaluate the expression inside the parentheses, we need to understand the concept of negative fractions. A negative fraction is a fraction that is less than zero. In this case, the fraction $ \frac{-5}{8} $ is a negative fraction because the numerator is negative.
Simplifying the Negative Fraction
To simplify the negative fraction, we need to understand that a negative fraction is equal to the negative of the fraction. In other words, $ \frac{-5}{8} = -\frac{5}{8} $. This means that the expression inside the parentheses is equal to $ -\frac{5}{8} $.
Evaluating the Expression
Now that we have evaluated the expression inside the parentheses, we can evaluate the entire expression. The expression is $ \frac{1}{6} - \left( \frac{-5}{8} \right) $. We can rewrite this expression as $ \frac{1}{6} - \left( -\frac{5}{8} \right) $.
Simplifying the Expression
To simplify the expression, we need to understand the concept of subtracting a negative number. When we subtract a negative number, we are essentially adding a positive number. In this case, we are subtracting a negative fraction, which means that we are adding a positive fraction.
Evaluating the Expression
To evaluate the expression, we need to find a common denominator for the two fractions. The common denominator is 24. We can rewrite the fractions as:
$ \frac{1}{6} = \frac{4}{24} $
$ -\frac{5}{8} = -\frac{15}{24} $
Simplifying the Expression
Now that we have found a common denominator, we can simplify the expression. We can rewrite the expression as:
$ \frac{4}{24} - \left( -\frac{15}{24} \right) $
Evaluating the Expression
To evaluate the expression, we need to subtract the two fractions. When we subtract a negative fraction, we are essentially adding a positive fraction. In this case, we are subtracting a negative fraction, which means that we are adding a positive fraction.
Simplifying the Expression
To simplify the expression, we need to understand the concept of adding fractions with a common denominator. When we add fractions with a common denominator, we can add the numerators and keep the denominator the same. In this case, we can add the numerators and keep the denominator the same.
Evaluating the Expression
To evaluate the expression, we need to add the numerators and keep the denominator the same. The numerator is 4 + 15 = 19. The denominator is 24.
Simplifying the Expression
Now that we have evaluated the expression, we can simplify it. The expression is $ \frac{19}{24} $.
Conclusion
In this article, we simplified the expression $ \frac{1}{6} - \left( \frac{-5}{8} \right) $. We used the order of operations (PEMDAS) to evaluate the expression inside the parentheses and then simplified the expression by finding a common denominator and adding the fractions. The simplified expression is $ \frac{19}{24} $. This article demonstrated the importance of understanding the concept of negative numbers, fractions, and the order of operations in simplifying mathematical expressions.
Frequently Asked Questions
- Q: What is the simplified expression of $ \frac1}{6} - \left( \frac{-5}{8} \right) $? A{24} $.
- Q: How do I simplify a negative fraction? A: A negative fraction is equal to the negative of the fraction. In other words, $ \frac{-5}{8} = -\frac{5}{8} $.
- Q: How do I evaluate an expression with a negative fraction? A: To evaluate an expression with a negative fraction, you need to understand the concept of subtracting a negative number. When you subtract a negative number, you are essentially adding a positive number.
Final Thoughts
Simplifying mathematical expressions is an essential step in understanding and working with mathematical problems. In this article, we simplified the expression $ \frac{1}{6} - \left( \frac{-5}{8} \right) $ by using the order of operations (PEMDAS) and understanding the concept of negative numbers, fractions, and the order of operations. By following the steps outlined in this article, you can simplify any mathematical expression and understand the underlying mathematical concepts.
Introduction
Simplifying mathematical expressions is an essential step in understanding and working with mathematical problems. In our previous article, we simplified the expression $ \frac{1}{6} - \left( \frac{-5}{8} \right) $ by using the order of operations (PEMDAS) and understanding the concept of negative numbers, fractions, and the order of operations. In this article, we will answer some frequently asked questions about simplifying mathematical expressions.
Q&A
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. PEMDAS stands for:
- Parentheses: Evaluate the expressions inside the parentheses first.
- Exponents: Evaluate any exponents (none in this case).
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.
Q: How do I simplify a negative fraction?
A: A negative fraction is equal to the negative of the fraction. In other words, $ \frac{-5}{8} = -\frac{5}{8} $. To simplify a negative fraction, you can rewrite it as a positive fraction with a negative sign in front of it.
Q: How do I evaluate an expression with a negative fraction?
A: To evaluate an expression with a negative fraction, you need to understand the concept of subtracting a negative number. When you subtract a negative number, you are essentially adding a positive number. For example, $ \frac{1}{6} - \left( \frac{-5}{8} \right) $ can be rewritten as $ \frac{1}{6} + \frac{5}{8} $.
Q: What is the difference between a positive fraction and a negative fraction?
A: A positive fraction is a fraction that is greater than zero, while a negative fraction is a fraction that is less than zero. For example, $ \frac{1}{6} $ is a positive fraction, while $ \frac{-5}{8} $ is a negative fraction.
Q: How do I add fractions with a common denominator?
A: To add fractions with a common denominator, you can add the numerators and keep the denominator the same. For example, $ \frac{1}{6} + \frac{5}{6} = \frac{6}{6} = 1 $.
Q: How do I subtract fractions with a common denominator?
A: To subtract fractions with a common denominator, you can subtract the numerators and keep the denominator the same. For example, $ \frac{1}{6} - \frac{5}{6} = \frac{-4}{6} = -\frac{2}{3} $.
Q: What is the difference between a fraction and a decimal?
A: A fraction is a way of representing a part of a whole, while a decimal is a way of representing a fraction as a decimal number. For example, $ \frac{1}{2} $ is a fraction, while 0.5 is a decimal.
Q: How do I convert a fraction to a decimal?
A: To convert a fraction to a decimal, you can divide the numerator by the denominator. For example, $ \frac{1}{2} = 0.5 $.
Q: How do I convert a decimal to a fraction?
A: To convert a decimal to a fraction, you can write the decimal as a fraction with a denominator of 1 and then simplify the fraction. For example, 0.5 can be written as $ \frac{1}{2} $.
Conclusion
Simplifying mathematical expressions is an essential step in understanding and working with mathematical problems. In this article, we answered some frequently asked questions about simplifying mathematical expressions, including the order of operations (PEMDAS), simplifying negative fractions, evaluating expressions with negative fractions, and converting fractions to decimals. By following the steps outlined in this article, you can simplify any mathematical expression and understand the underlying mathematical concepts.
Final Thoughts
Simplifying mathematical expressions is a crucial skill that is used in many areas of mathematics, science, and engineering. By understanding the concepts of fractions, decimals, and the order of operations (PEMDAS), you can simplify any mathematical expression and solve problems with confidence. Remember to always follow the order of operations (PEMDAS) and to simplify fractions and decimals as needed. With practice and patience, you can become proficient in simplifying mathematical expressions and solving problems with ease.