Simplifying Algebraic Expressions: 3/4x + 2/3y - 3/8x + 1/2y
In algebra, simplifying expressions is an essential skill to master. It involves combining like terms to express an equation in its most compact form. In this article, we will explore how to simplify the algebraic expression 3/4x + 2/3y - 3/8x + 1/2y.
Step 1: Identify the Like Terms
The first step in simplifying an algebraic expression is to identify the like terms. Like terms are terms that have the same variable (x or y) and the same coefficient (number multiplied by the variable). In this expression, we have two like terms:
- 3/4x and -3/8x (both have the variable x)
- 2/3y and 1/2y (both have the variable y)
Step 2: Combine the Like Terms
Now that we have identified the like terms, we can combine them by adding or subtracting their coefficients.
- Combine the x terms: 3/4x - 3/8x
- To combine these terms, we need to find a common denominator, which is 8. So, we can rewrite the terms as:
- 6/8x - 3/8x = 3/8x
- To combine these terms, we need to find a common denominator, which is 8. So, we can rewrite the terms as:
- Combine the y terms: 2/3y + 1/2y
- To combine these terms, we need to find a common denominator, which is 6. So, we can rewrite the terms as:
- 4/6y + 3/6y = 7/6y
- To combine these terms, we need to find a common denominator, which is 6. So, we can rewrite the terms as:
Step 3: Write the Simplified Expression
Now that we have combined the like terms, we can write the simplified expression:
3/8x + 7/6y
This is the simplified form of the original expression 3/4x + 2/3y - 3/8x + 1/2y. By following these steps, we have successfully simplified the expression by combining like terms.
