Which Expression Is Equivalent To 1.2y 4.5-3.4y-6.3

Which Expression is Equivalent to 1.2y + 4.5 - 3.4y - 6.3? A Comprehensive Guide to Simplifying Algebraic Expressions

This article delves into the simplification of the algebraic expression 1.2y + 4.5 - 3.4y - 6.3, explaining the process step-by-step and providing a deeper understanding of algebraic manipulation. We'll cover the fundamental principles involved, explore common mistakes to avoid, and offer practice problems to solidify your understanding. This guide is perfect for students learning algebra or anyone looking to refresh their knowledge of simplifying expressions.

Understanding Algebraic Expressions

Before we tackle the simplification of our specific expression, let's review the basics of algebraic expressions. An algebraic expression is a mathematical phrase that combines numbers, variables, and operations (like addition, subtraction, multiplication, and division). Variables are usually represented by letters, such as x or y, and they represent unknown values.

Key Terms:

• Terms: Individual parts of an expression separated by addition or subtraction signs. In the expression 1.2y + 4.5 - 3.4y - 6.3, there are four terms: 1.2y, 4.5, -3.4y, and -6.3.
• Like Terms: Terms that have the same variable raised to the same power. For example, 1.2y and -3.4y are like terms because they both contain the variable y raised to the power of 1. Constant terms (numbers without variables) are also considered like terms. 4.5 and -6.3 are like terms.
• Coefficients: The numerical factor of a term. In the term 1.2y, the coefficient is 1.2. In the term -3.4y, the coefficient is -3.4.
• Constants: Numerical terms without variables. In our expression, 4.5 and -6.3 are constants.

Simplifying the Expression: 1.2y + 4.5 - 3.4y - 6.3

The goal of simplifying an algebraic expression is to combine like terms to create a more concise and manageable expression. Let's break down the process for our given expression: 1.2y + 4.5 - 3.4y - 6.3

Step 1: Identify Like Terms

We have two sets of like terms:

• Terms with y: 1.2y and -3.4y
• Constant terms: 4.5 and -6.3

Step 2: Combine Like Terms

To combine like terms, we add or subtract their coefficients.

• Combining terms with y: 1.2y - 3.4y = (1.2 - 3.4)y = -2.2y
• Combining constant terms: 4.5 - 6.3 = -1.8

Step 3: Write the Simplified Expression

After combining like terms, our simplified expression is:

-2.2y - 1.8

Therefore, the expression equivalent to 1.2y + 4.5 - 3.4y - 6.3 is -2.2y - 1.8.

Common Mistakes to Avoid

Several common errors can occur when simplifying algebraic expressions. Let's examine some of them:

• Incorrectly combining unlike terms: A frequent mistake is attempting to combine terms that are not like terms. Remember, you can only combine terms with the same variable raised to the same power. For example, you cannot combine 2x and 3y.
• Errors in arithmetic: Careless mistakes in addition, subtraction, multiplication, or division can lead to incorrect results. Double-check your calculations to ensure accuracy.
• Forgetting to include negative signs: Pay close attention to the signs of the coefficients. Neglecting negative signs is a common source of errors.
• Incorrect application of the order of operations (PEMDAS/BODMAS): Remember the order of operations: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Practice Problems

Let's test your understanding with some practice problems:

1. Simplify: 5x + 2 - 3x - 7
2. Simplify: 2.5a - 1.5b + 4.5a + 3b
3. Simplify: -4m + 6n + 2m - 5n + 8

Solutions:

1. 2x - 5
2. 7a + 1.5b
3. -2m + n + 8

Advanced Concepts and Further Exploration

While simplifying expressions like 1.2y + 4.5 - 3.4y - 6.3 forms the foundation of algebra, there are many more advanced concepts to explore. These include:

• Expanding expressions: Removing parentheses by applying the distributive property. For example, expanding 2(x + 3) results in 2x + 6.
• Factoring expressions: The reverse of expanding, where you rewrite an expression as a product of simpler expressions.
• Solving equations: Using algebraic manipulation to find the value of the variable that makes an equation true.
• Working with polynomials: Expressions with multiple terms involving variables raised to different powers.

Mastering the simplification of algebraic expressions is crucial for success in higher-level mathematics. By understanding the fundamental principles and practicing regularly, you can build a strong foundation for tackling more complex algebraic problems. Remember to always double-check your work and be mindful of common mistakes. With consistent practice and attention to detail, you'll become proficient in simplifying algebraic expressions and confidently navigate the world of algebra.