Simplifying Mathematical Expressions: Understanding 2 - 2x/3y 31/y

When dealing with mathematical expressions, clarity and accuracy are essential. In this article, we will explore the simplification of the given expression, 2 - 2x/3y 31/y. We will break down the process, discuss common pitfalls, and ensure the expression is simplified to its most understandable form. Let's dive in!

Understanding the Expression

The expression at hand is 2 - 2x/3y 31/y. Upon initial inspection, it appears that the terms have different denominators, making it challenging to combine them directly. However, there are two possible interpretations for the expression: 2 - (2x/3y) (31/y) or 2 - (2x/3y) 3(1/y). We will consider both interpretations and provide a detailed analysis of each.

Interpretation 1: 2 - 2x/3y 31/y

In this interpretation, the expression is 2 - (2x/3y) (31/y). Let's break it down step-by-step. First, we can rewrite the expression with a common denominator of 3y for the second and third terms:

2 - (2x/3y) (3 * 3/y)

Next, we simplify the expression:

Add the numbers without x or y in them:

Subtract 2x/3y from 2.

Add 3 * 3/y to the result.

2 - 2x/3y (3 * 3/y) 2 - 2x/3y 9/y

Now, let's combine the terms with the common denominator 3y: The term 2 can be rewritten as 6y/3y to have the same denominator. The term 9/y can be rewritten as 27/3y to have the same denominator. Thus, the expression becomes:

6y/3y - 2x/3y 27/3y (6y - 2x 27)/3y

Interpretation 2: 2 - 2x/3y 31/y

In this interpretation, the expression is 2 - (2x/3y) 3(1/y). Let's break it down step-by-step. First, we can rewrite the expression with a common denominator of 3y for the second and third terms: 2 - (2x/3y) 3 * (y/y)

Next, we simplify the expression:

Add the numbers without x.

Subtract 2x/3y from 2.

Add 3 * (y/y) to the result.

2 - (2x/3y) 3 * (y/y) 2 - 2x/3y 3

Now, combine the terms without x or y in them:

2 3 - 2x/3y 5 - 2x/3y

Finally, we can rewrite the expression with a common denominator of 3y for the term 5 and the term 2x/3y: The term 5 can be rewritten as 15y/3y to have the same denominator. The term 2x/3y remains the same. Thus, the expression becomes:

15y/3y - 2x/3y (15y - 2x)/3y

Conclusion

Both interpretations of the expression lead to different results. However, it is crucial to understand the context in which the expression is used to determine the appropriate interpretation. In either case, the simplified form of the expression is:

If the expression is 2 - 2x/3y 31/y, it simplifies to (15y - 2x)/3y.

If the expression is 2 - 2x/3y 3(1/y), it simplifies to (15y - 2x)/3y.

Understanding these steps and recognizing the importance of common denominators is key to accurately simplifying mathematical expressions. This knowledge can be applied to a wide range of algebraic problems and enhance one's problem-solving skills in mathematics.

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math expression algebra simplifying expressions

Author Bio

Author: [Your Name]
Mathematics Educator, dedicated to simplifying complex mathematical concepts for students of all ages. With a passion for teaching and a background in mathematics, [Your Name] helps individuals build a strong foundation in algebra and other areas of math.

References

Algebra I For Dummies (2020) by Mary Jane Sterling. Elementary and Intermediate Algebra (2021) by Jerome E. Kaufmann and Karen L. Schwitters.

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