Which Expression Is Equivalent To 2a+1/10a-5?
The expression equivalent to 2a+1/10a-5 is 2/10a+1/10a-5. Which Expression Is Equivalent To 2a+1/10a-5? This question often arises in algebraic equations involving fractions. By simplifying the terms, we can see that the answer is a straightforward 2/10a+1/10a-5. Understanding how to manipulate expressions like this is crucial in solving complex math problems. Knowing how to combine like terms and simplify fractions is essential for success in higher-level mathematics. Let’s break down the steps involved in finding the equivalent expression for 2a+1/10a-5.
Contents
| Equivalent expressions are 2a+1/10a-5. |
| Simplify the expression to get the equivalent form. |
| Combine like terms in the expression. |
| Express the given expression in a simpler form. |
| Find the equivalent expression for 2a+1/10a-5. |
- Use distributive property to simplify the expression.
- Divide each term by a common factor.
- Combine the terms by adding or subtracting.
- Express the given expression in a more compact form.
- Identify the equivalent form of 2a+1/10a-5.
What is the simplified form of 2a+1/10a-5?
When dealing with algebraic expressions, it is essential to simplify them to their most reduced form. In the case of the expression 2a+1/10a-5, we can simplify it by finding a common denominator for the fractions and combining like terms.
- Step 1: Find a common denominator for the fractions. Since the denominators are already different, we need to find the least common multiple of 10a and 1.
- Step 2: Combine the fractions by adding or subtracting the numerators while keeping the common denominator.
| Original Expression | 2a + 1/10a – 5 |
|---|---|
| Common Denominator | 10a |
| Simplified Form | (2a*10a + 1)/10a – 5 |
How can we further simplify the expression 2a+1/10a-5?
After combining the fractions and finding a common denominator, we can simplify the expression 2a+1/10a-5 even further by multiplying out the terms and simplifying any remaining factors.
- Step 1: Distribute the numerator across the terms within the parentheses.
- Step 2: Combine like terms and simplify the expression as much as possible.
| Simplified Form | (2a*10a + 1)/10a – 5 |
|---|---|
| Multiplying Out | (20a^2 + 1)/10a – 5 |
What is the final simplified form of the expression 2a+1/10a-5?
After following the steps to simplify the expression and multiplying out the terms, the final simplified form of 2a+1/10a-5 is (20a^2 + 1)/10a – 5.
Can the expression 2a+1/10a-5 be written in a different form?
Expressions in algebra can often be rearranged or written in different forms while maintaining their equivalence. The expression 2a+1/10a-5 can be rewritten as (20a^2 + 1)/10a – 5 to emphasize the combined terms and fractions.
Why is simplifying algebraic expressions like 2a+1/10a-5 important?
Simplifying algebraic expressions is crucial for clarity and efficiency in mathematical calculations. By reducing complex expressions like 2a+1/10a-5 to their simplest form, it becomes easier to manipulate them in equations and solve for variables.
What are the key steps to simplifying an expression like 2a+1/10a-5?
When simplifying algebraic expressions, it is essential to follow a systematic approach to ensure accuracy and consistency. Key steps include finding a common denominator, combining fractions, distributing terms, and simplifying factors.
How does the expression 2a+1/10a-5 demonstrate algebraic operations?
The expression 2a+1/10a-5 showcases various algebraic operations such as addition, subtraction, multiplication, and division. By understanding how these operations interact within the expression, one can effectively simplify and manipulate it.
What role does the variable ‘a’ play in the expression 2a+1/10a-5?
The variable ‘a’ in the expression 2a+1/10a-5 represents an unknown quantity that can take on different values. It serves as a placeholder for a numerical value that can be substituted into the expression to evaluate its outcome.
How can the expression 2a+1/10a-5 be applied in real-world scenarios?
Algebraic expressions like 2a+1/10a-5 can be applied in various real-world situations, such as calculating rates of change, analyzing financial data, or solving engineering problems. By understanding how to simplify and work with such expressions, individuals can tackle practical problems more effectively.