Problem 333 - Intermediate Algebra

Question

In the following exercises, simplify. $$ 10(0.1 d) $$

Step-by-Step Solution

Answer

d

Step 1: Understand the Expression

The given expression is \(10(0.1d)\). It consists of a constant (10) and a product involving a variable \(d\) multiplied by a decimal (0.1).

Step 2: Multiply the Constants

To simplify the expression, start by multiplying the constants: \(10 \times 0.1\).

Step 3: Perform the Multiplication

Multiply 10 and 0.1: \(10 \times 0.1 = 1\).

Step 4: Combine with the Variable

Now, combine your result with the variable \(d\): \(1 \times d = d\).

Step 5: Write the Simplified Expression

The simplified expression is \(d\).

Key Concepts

Multiplication of Constants

When simplifying algebraic expressions, it's essential to multiply the constants first. In the given example, you have the expression \(10(0.1d)\), where 10 and 0.1 are constants. Here's what you need to do:

• Identify the constants: 10 and 0.1.
• Multiply them together, ignoring the variable for now.

Performing this multiplication step independently makes the simplification process more manageable. For instance, here we compute \(10 \times 0.1\), resulting in 1.
Always deal with constants first before incorporating any variables to minimize complexity.

Simplification Steps

Step-by-step simplifications ensure that you grasp each part of the process thoroughly. Following are the steps taken for the expression \(10(0.1d)\):

• Step 1: Understand the Expression – Recognize the structure of the expression, which has a constant multiplied by a variable term.
• Step 2: Multiply the Constants – Perform multiplication of the constants (10 and 0.1).
• Step 3: Perform the Multiplication – Calculate \(10 \times 0.1 = 1\).
• Step 4: Combine with the Variable – Attach the resulting constant to the variable: \(1 \times d = d\).
• Step 5: Write the Simplified Expression – Present the final simplified form: \(d\).

These steps break down the process, making it easier to follow and apply to similar expressions.

Algebraic Expression

An algebraic expression includes numbers, variables, and operations. For example, \(10(0.1d)\) involves:

• Constants: Numbers that stand alone, such as 10 and 0.1.
• Variables: Symbols representing numbers, like the variable \(d\).
• Operations: Mathematical operations such as multiplication.

Understanding these components helps in simplifying the expression efficiently. Start with basic operations like multiplication before combining terms. In the given expression, once constants are multiplied, the resulting constant (1) is combined with the variable \(d\), leading to the simplified form \(d\).

Remember, simplifying an algebraic expression is all about breaking it down into manageable steps ensuring each part is understood.