Simplifying Algebraic Expressions: 2x^2y^3/4xy^5
In this article, we will explore how to simplify the algebraic expression 2x^2y^3/4xy^5.
Understanding the Expression
Before we start simplifying, let's break down the given expression:
2x^2y^3/4xy^5
This expression is a fraction, with a numerator (2x^2y^3) and a denominator (4xy^5). To simplify this expression, we need to follow the rules of algebraic fractions.
Simplifying the Expression
To simplify the expression, we can start by canceling out any common factors between the numerator and the denominator.
Canceling out common factors
In the numerator, we have 2x^2y^3. In the denominator, we have 4xy^5. Let's see if we can cancel out any common factors:
- 2x^2y^3 = 2 × x × x × y × y × y
- 4xy^5 = 4 × x × y × y × y × y × y
We can see that both the numerator and the denominator have a common factor of xy^3. Let's cancel it out:
(2x^2y^3) / (4xy^5) = (2x^2y^3) / (4x(y^3)y^2)
Now, we can cancel out the common factor of xy^3:
= 2x / (4y^2)
Simplifying further
We can simplify the expression further by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD is 2.
= (2x / 2) / (4y^2 / 2)
= x / (2y^2)
Therefore, the simplified expression is:
x / (2y^2)
Conclusion
In this article, we learned how to simplify the algebraic expression 2x^2y^3/4xy^5 by canceling out common factors and dividing by the greatest common divisor. The final simplified expression is x / (2y^2).
