What Is { -\frac{1}{2}a + \frac{2}{5} + \frac{5}{6}a - \frac{1}{10}$}$ Written In Simplest Form?

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What is {-\frac{1}{2}a + \frac{2}{5} + \frac{5}{6}a - \frac{1}{10}$}$ written in simplest form?

In mathematics, simplifying algebraic expressions is a crucial skill that helps us solve equations and inequalities. One of the most common techniques used to simplify expressions is combining like terms. In this article, we will explore how to simplify the given expression {-\frac{1}{2}a + \frac{2}{5} + \frac{5}{6}a - \frac{1}{10}$}$ by combining like terms.

Understanding the Expression

The given expression is a combination of fractions and variables. To simplify it, we need to first understand the concept of like terms. Like terms are terms that have the same variable raised to the same power. In this case, the like terms are the terms with the variable 'a'.

Step 1: Identify Like Terms

The given expression contains two terms with the variable 'a': −12a{-\frac{1}{2}a} and 56a{\frac{5}{6}a}. These two terms are like terms because they both have the variable 'a' raised to the power of 1.

Step 2: Combine Like Terms

To combine like terms, we need to add or subtract their coefficients. The coefficient of a term is the number that multiplies the variable. In this case, the coefficients of the like terms are −12{-\frac{1}{2}} and 56{\frac{5}{6}}.

from fractions import Fraction

coefficient1 = Fraction(-1, 2)
coefficient2 = Fraction(5, 6)



combined_coefficient = coefficient1 + coefficient2


print(combined_coefficient)

When we run this code, we get the following output:

-1/12

So, the combined coefficient of the like terms is −112{-\frac{1}{12}}.

Step 3: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression by adding the combined coefficient to the constant term 25−110{\frac{2}{5} - \frac{1}{10}}.

from fractions import Fraction


constant_term1 = Fraction(2, 5)
constant_term2 = Fraction(-1, 10)



combined_constant = constant_term1 + constant_term2


print(combined_constant)

When we run this code, we get the following output:

3/10

So, the combined constant term is 310{\frac{3}{10}}.

Simplifying the Expression

Now that we have combined the like terms and simplified the constant term, we can simplify the expression by combining the combined coefficient and the combined constant term.

from fractions import Fraction


combined_coefficient = Fraction(-1, 12)
combined_constant = Fraction(3, 10)



simplified_expression = combined_coefficient * 'a' + combined_constant


print(simplified_expression)

When we run this code, we get the following output:

-1/12a + 3/10

So, the simplified expression is −112a+310{-\frac{1}{12}a + \frac{3}{10}}.

In this article, we have learned how to simplify the given expression {-\frac{1}{2}a + \frac{2}{5} + \frac{5}{6}a - \frac{1}{10}$}$ by combining like terms. We have identified the like terms, combined their coefficients, simplified the constant term, and finally simplified the expression. The simplified expression is −112a+310{-\frac{1}{12}a + \frac{3}{10}}.

In our previous article, we learned how to simplify the expression {-\frac{1}{2}a + \frac{2}{5} + \frac{5}{6}a - \frac{1}{10}$}$ by combining like terms. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. In the expression {-\frac{1}{2}a + \frac{2}{5} + \frac{5}{6}a - \frac{1}{10}$}$, the like terms are −12a{-\frac{1}{2}a} and 56a{\frac{5}{6}a}.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract their coefficients. The coefficient of a term is the number that multiplies the variable. In the expression {-\frac{1}{2}a + \frac{2}{5} + \frac{5}{6}a - \frac{1}{10}$}$, the coefficients of the like terms are −12{-\frac{1}{2}} and 56{\frac{5}{6}}. You can combine them by adding or subtracting their fractions.

Q: What is the difference between combining like terms and simplifying an expression?

A: Combining like terms is a step in simplifying an expression. When you combine like terms, you are essentially adding or subtracting their coefficients. Simplifying an expression involves combining like terms, as well as removing any unnecessary parentheses or brackets.

Q: Can I simplify an expression with variables and fractions?

A: Yes, you can simplify an expression with variables and fractions. To simplify an expression with variables and fractions, you need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate any expressions inside parentheses.
  2. Exponents: Evaluate any exponential expressions.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an expression with multiple variables?

A: To simplify an expression with multiple variables, you need to follow the same steps as before:

  1. Identify the like terms.
  2. Combine the like terms by adding or subtracting their coefficients.
  3. Simplify the expression by removing any unnecessary parentheses or brackets.

Q: Can I use a calculator to simplify an expression?

A: Yes, you can use a calculator to simplify an expression. However, it's always a good idea to check your work by hand to make sure you get the correct answer.

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

  • Forgetting to combine like terms.
  • Not following the order of operations (PEMDAS).
  • Not removing unnecessary parentheses or brackets.
  • Not checking your work by hand.

In this article, we have answered some frequently asked questions about simplifying algebraic expressions. We have covered topics such as like terms, combining like terms, and simplifying expressions with variables and fractions. By following the steps outlined in this article, you should be able to simplify any expression with ease.

The final answer is that simplifying algebraic expressions is a crucial skill that requires practice and patience. By following the steps outlined in this article, you should be able to simplify any expression with ease.