What expression is equivalent to 2.8k-8.4

Closest Equivalent Expression

Given the equation:

We need to determine which of the given options (A, B, C, or D) is equivalent to this expression.

Let's rewrite each option for clarity:

Option A:

Simplify:

Option B:

Simplify:

Option C:

Option D:

It is clear that Option B is the equivalent expression. The detailed simplification of Option B shows:

Thus, the expression equivalent to $2.8k - 8.4$ is 0.7(4k - 12).

Understanding the Concept of Simplification of Expressions

In mathematics, the simplification of expressions is the process of reducing a complicated mathematical expression into its simplest form. This can involve several steps, such as combining like terms, applying the distributive property, and reducing fractions. Simplification helps to make expressions easier to work with and can reveal underlying structures or patterns.

Combining Like Terms

Like terms are terms that have the same variables raised to the same powers. For example, in the expression:

we can combine the like terms to get:

Applying the Distributive Property

The distributive property allows us to multiply a single term by each term inside a parenthesis. For example, in the expression:

we apply the distributive property to get:

Reducing Fractions

Simplifying fractions involves dividing the numerator and the denominator by their greatest common divisor (GCD). For instance, the fraction:

can be simplified by dividing both the numerator and the denominator by 3:

Example of a Complex Simplification

Consider a more complex expression:

First, simplify the fraction:

Next, simplify the distributive property part:

Combining all parts together:

Lastly, combine like terms:

Our simplified expression is now:

Simplifying expressions properly makes them more manageable and allows for easier computation and analysis in further mathematical operations.

Understanding the Distributive Property

The distributive property is a fundamental principle in algebra that describes how multiplication interacts with addition or subtraction. It can be stated as follows:

For any numbers $a$, $b$, and $c$:

Practical Application

The distributive property is particularly useful when you need to simplify expressions or solve equations. Here is an example:

Using the distributive property, you can break it down:

Which simplifies to:

Why It Matters

• Efficiency: It helps in solving complex problems more efficiently.
• Foundation for Advanced Mathematics: This property is foundational for more advanced topics like factoring polynomials.
• Mental Math: Enhances mental math skills by simplifying calculations.

Another Example with Variables

Consider an example with variables:

The distributive property ensures that multiplication distributes over addition, maintaining the equality.

Conclusion

The distributive property is a powerful tool in algebra that simplifies expressions and enhances problem-solving skills. Understanding and applying this property is essential for success in mathematics.