Problem 22 - Algebra 1: Concepts and Skills

Question

Solve the percent problem. 52 is 12.5% of what number?

Step-by-Step Solution

Answer

The number is 416

Step 1: Convert Percentage to Decimal

Convert the percent to a decimal by dividing the percent by 100. Therefore, 12.5% becomes \( \frac{12.5}{100} = 0.125 \)

Step 2: Write the Equation

The problem can be written as an equation: 0.125 * X = 52, where X is the number we are looking for.

Step 3: Solve for X

To isolate X, divide both sides of the equation by 0.125. \( \frac{52}{0.125} = X \)

Key Concepts

Understanding Percent

Percentages are a way to express a number as a fraction of 100. The symbol for percent is %.
Think of it as "per 100."
For example, 12.5% means 12.5 out of every 100.

• The concept of percent is widely used to describe proportions.
• A key use is in finding parts of a whole.

Understanding percent is crucial in many fields like finance, statistics, and everyday problem-solving.

Decimal Conversion

Converting a percentage into a decimal is a straightforward process.
You simply divide the percentage by 100.
This is because percentages are out of 100, and dividing by 100 scales it appropriately.

• To convert 12.5% to a decimal, divide 12.5 by 100 to get 0.125.
• This conversion helps in performing arithmetic operations easily, like multiplication and division.

By converting percentages to decimals, you simplify the problem-solving process. Understanding this conversion is essential for working with percentages in mathematical equations.

Equation Solving

Equation solving involves finding the value of an unknown variable that makes an equation true.
In the problem, we express it as the equation: 0.125 * X = 52.

• To solve for X, you need to isolate the variable.
• This means performing operations to both sides of the equation without changing its equality.
• In this instance, divide both sides by 0.125 to find X.

This process demonstrates an important algebraic skill.
It allows you to manipulate equations and find unknown values essential in both academic and real-world problems.

Division in Algebra

Division is a fundamental operation in algebra, often used to solve equations.
To isolate a variable, division can help move coefficients.
Let's apply this in the context of our problem: dividing 52 by 0.125.

• Division helps to remove or neutralize coefficients attached to the variable X.
• In this case, dividing 52 by 0.125 gives the result, X = 416.
• Thus, 52 is 12.5% of 416.

Mastery of division in algebraic equations is crucial and helps solve a wide range of mathematical problems efficiently.