Problem 334 - Intermediate Algebra

Question

In the following exercises, simplify. $$ 100(0.01 p) $$

Step-by-Step Solution

Answer

\( p \)

Step 1 - Understand the Problem

The expression to simplify is given as \( 100(0.01p) \). The task is to simplify the expression.

Step 2 - Identify the Multiplication

Identify that \( 100 \) needs to be multiplied by \( 0.01p \). This can be done by treating \( 0.01p \) as a product where \( 0.01 \) and \( p \) are multiplied together.

Step 3 - Multiply Constants

First, multiply the constants: \( 100 \) and \( 0.01 \). The multiplication yields: \[ 100 \times 0.01 = 1 \]

Step 4 - Simplify the Expression

After multiplying the constants, incorporate the variable \( p \). The expression becomes: \[ 1 \times p = p \]

Key Concepts

Multiplication of Constants

When simplifying algebraic expressions, one of the first steps is to handle the multiplication of constants.
Constants are numbers on their own, without any variables attached.
In our example, we start with the constants 100 and 0.01.

To multiply these two constants, we simply perform the arithmetic calculation:
100 multiplied by 0.01 equals 1, which is shown mathematically as: \( 100 \times 0.01 = 1 \)

Once the constants are multiplied, we can move on to the next part of the expression.

Variable Multiplication

After handling the constants, the next step is to incorporate any variables involved.
Variables are symbols that represent unknown values, typically letters like \( x \), \( y \), or in our case, \( p \).
In our example, we are multiplying 0.01 by \( p \)::
0.01 is already included in our earlier step as part of the constant multiplication. So, we just need to attach \( p \) to our result.

After the constants are handled, we simply multiply the result by the variable:
\( 1 \times p \)

The multiplication of a constant with a variable is straightforward: We keep the variable as it is and place it next to the resulting constant.

Algebraic Simplification

The final step is the algebraic simplification.
Algebraic simplification involves condensing the expression to its simplest form.
In the earlier steps, we found that 100 multiplied by 0.01 gives us 1, and we multiplied that result by the variable \( p \).

This results in the simplified expression: \( 1p \), which is typically written as just \( p \).
Remember, in algebra, when a variable is multiplied by 1, we can omit the 1 for simplicity.
Thus, \( 100(0.01p) \) simplifies neatly to \( p \).

By following steps of multiplying constants, managing variable multiplication, and finally simplifying algebraically, we attain the simplest form of the given expression.