Which Expression Is Equivalent To \left(-2 \frac{1}{3} D+\frac{4}{5}\right)-\left(1 \frac{5}{6} D+\frac{9}{10}\right ]?A. − 1 2 D − 1 10 -\frac{1}{2} D-\frac{1}{10} − 2 1 D − 10 1 B. − 25 6 D − 1 10 -\frac{25}{6} D-\frac{1}{10} − 6 25 D − 10 1 C. $\frac{25}{6} D \div
Introduction
Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying a specific algebraic expression involving fractions and variables. We will break down the expression step by step, using various mathematical operations to arrive at the final simplified form.
The Expression to Simplify
The given expression is:
This expression involves two terms, each containing a variable and a fraction. Our goal is to simplify this expression by combining like terms and performing the necessary arithmetic operations.
Step 1: Convert Mixed Numbers to Improper Fractions
To simplify the expression, we need to convert the mixed numbers to improper fractions. A mixed number is a combination of a whole number and a fraction. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator.
For the first term, we have:
Similarly, for the second term, we have:
Step 2: Rewrite the Expression with Improper Fractions
Now that we have converted the mixed numbers to improper fractions, we can rewrite the expression as:
Step 3: Distribute the Negative Sign
Q&A: Simplifying Algebraic Expressions
Q: What is the first step in simplifying the given expression? A: The first step is to convert the mixed numbers to improper fractions. This involves multiplying the whole number by the denominator and adding the numerator.
Q: How do I convert a mixed number to an improper fraction? A: To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and add the numerator. For example, to convert 2 1/3 to an improper fraction, you would multiply 2 by 3 and add 1, resulting in 7/3.
Q: What is the next step after converting the mixed numbers to improper fractions? A: After converting the mixed numbers to improper fractions, the next step is to rewrite the expression with the improper fractions. This involves replacing the mixed numbers with their equivalent improper fractions.
Q: How do I distribute the negative sign when subtracting a term? A: When subtracting a term, you need to distribute the negative sign to the terms inside the parentheses. This means that you multiply each term inside the parentheses by -1.
Q: What is the result of distributing the negative sign to the terms inside the parentheses? A: When you distribute the negative sign to the terms inside the parentheses, you get:
Q: How do I combine like terms? A: To combine like terms, you need to identify the terms that have the same variable and coefficient. In this case, the terms with the variable d are -7/3d and -11/6d. You can combine these terms by finding a common denominator and adding them together.
Q: What is the common denominator for the terms -7/3d and -11/6d? A: The common denominator for the terms -7/3d and -11/6d is 6. You can rewrite the first term as -14/6d to make it easier to combine the terms.
Q: How do I combine the terms -14/6d and -11/6d? A: To combine the terms -14/6d and -11/6d, you add their coefficients. This results in:
Q: What is the final simplified form of the expression? A: The final simplified form of the expression is:
Q: How do I simplify the expression further? A: To simplify the expression further, you need to find a common denominator for the fractions. The common denominator for the fractions 1/10 and 4/5 is 10. You can rewrite the second fraction as 8/10 to make it easier to combine the fractions.
Q: How do I combine the fractions 1/10 and 8/10? A: To combine the fractions 1/10 and 8/10, you add their numerators. This results in:
Q: What is the final simplified form of the expression? A: The final simplified form of the expression is:
Q: How do I rewrite the expression in the form of a single fraction? A: To rewrite the expression in the form of a single fraction, you need to find a common denominator for the fractions. The common denominator for the fractions 25/6 and 9/10 is 30. You can rewrite the first fraction as -125/30 and the second fraction as 27/30 to make it easier to combine the fractions.
Q: How do I combine the fractions -125/30 and 27/30? A: To combine the fractions -125/30 and 27/30, you add their numerators. This results in:
Q: What is the final simplified form of the expression? A: The final simplified form of the expression is: