Problem 60 - Prealgebra

Question

Twenty-six is \(25 \%\) of what number?

Step-by-Step Solution

Answer

The number is 104.

Step 1: Identify the question

The problem asks us to find the whole number for which 26 is 25%. This can be expressed in mathematical terms as: \(26 = 0.25 \times X\), where \(X\) is the number we need to find.

Step 2: Set up the equation

Based on the problem, the equation is: \[ 26 = 0.25 \times X \]We need to solve for \(X\), which represents the whole number in this context.

Step 3: Isolate the variable

To find \(X\), divide both sides of the equation by 0.25:\[ X = \frac{26}{0.25} \]

Step 4: Simplify the equation

Calculate \( \frac{26}{0.25} \): - To divide by a fraction, you can multiply by its reciprocal. So, \( \frac{26}{0.25} = 26 \times \frac{1}{0.25} \) - Since \( \frac{1}{0.25} = 4 \), we get \( 26 \times 4 = 104 \).Therefore, \( X = 104 \).

Key Concepts

Understanding Prealgebra

Prealgebra lays the foundation for all math you will learn later. It's like learning the basics of a new language before diving into more complex grammar.
You learn how to manipulate numbers and understand the relationships between them. It prepares you to deal with different types of numbers such as whole numbers, fractions, and decimals. In this exercise, we're dealing with a percent, which can be changed into a decimal (like 25% becomes 0.25) to make problems easier to solve using prealgebra concepts.
Prealgebra helps simplify numbers in equations, making comparisons or finding unknowns straightforward. When you encounter a problem asking for a percentage of a number, prealgebra skills allow you to convert these into an easier-to-solve mathematical equation.

Solving Equations

Solving equations is all about finding the unknown values. Shifting numbers around to find the 'X' is essentially what solving equations is about.
Think of an equation as a balanced scale. When you do something to one side, you have to do the same thing to the other side to keep it balanced.

• The equation in our case is: \[ 26 = 0.25 \times X \]
• To find out what 'X' is, we need to make 'X' stand alone on one side of the equation.
• Doing that requires us to get rid of other numbers or factors next to 'X'.

In this exercise, since 'X' is multiplied by 0.25, we do the opposite operation, which is division by 0.25, to isolate 'X'. This is how you solve equations by maintaining balance and systematically working to reveal what the unknowns are.

Mathematical Expressions

Mathematical expressions are combinations of numbers, variables, and operations. They are a way to represent ideas and calculations in math.
In our problem, the mathematical expression is \[ 26 = 0.25 \times X \]. This encompasses understanding percentages, multiplication, and how to rearrange expressions to reveal the unknowns.
Expressions and equations communicate two sides of a math idea, similar to a sentence in language. You can manipulate these expressions just like rearranging sentence parts.

• Change 25% into a decimal when forming your equation.
• Understand that solving it means doing inverse operations.
• For example, if you multiply, you'll divide to simplify and solve.

Learning to handle these expressions is key to cracking codes in more advanced math topics you'll encounter.