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Chapter 2: Problem 57

Solve. 25 is what percent of \(50 ?\)

Short Answer

Expert verified
25 is 50% of 50.

Step by step solution

01

Understand the Problem

We need to find what percentage 25 is of 50. This can be rephrased as finding the ratio of 25 to 50 and then converting that ratio to a percentage.
02

Set Up the Ratio

To find the ratio of 25 to 50, write the fraction \(\frac{25}{50}\). This represents the part (25) over the whole (50).
03

Simplify the Fraction

Simplify \(\frac{25}{50}\) by dividing both the numerator (25) and the denominator (50) by their greatest common divisor (25). So, \(\frac{25}{50} = \frac{1}{2}\).
04

Convert the Fraction to a Percentage

To convert a fraction to a percentage, multiply it by 100. So, \(\frac{1}{2} \times 100 = 50\).
05

State the Final Answer

Therefore, 25 is 50% of 50.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ratio
A ratio is a way to compare two quantities by using division. In this exercise, we want to compare the number 25 to 50.
We do this by writing them as a fraction: \(\frac{25}{50}\).
Here, 25 is the part, and 50 is the whole. Using a ratio helps us see how one number relates to another.
Ratios are a simple but powerful tool to represent relative sizes. They can be written in three ways: 25:50, \(\frac{25}{50}\), or '25 to 50'.
Each format tells us the same information in a slightly different way.
Fraction Simplification
Simplifying fractions means reducing them to their simplest form. We simplify by dividing both the numerator (top number) and denominator (bottom number) by their greatest common divisor (GCD).
For the fraction \(\frac{25}{50}\), the GCD of 25 and 50 is 25. So, we divide both 25 and 50 by 25 to get \(\frac{1}{2}\).
The fraction \(\frac{25}{50}\) simplifies to \(\frac{1}{2}\), which is much easier to work with. Simplifying fractions helps us better understand the relationship between numbers.
Conversion to Percentage
Converting a fraction to a percentage involves multiplying the fraction by 100. A percentage is just a number out of 100.
For example, to convert \(\frac{1}{2}\) to a percentage, we multiply it by 100: \(\frac{1}{2} \times 100 = 50\).
This tells us that \(\frac{1}{2}\) is the same as 50 out of 100, or 50%.
Percentages are useful because they give us a quick way to understand proportions and comparisons. They are used in many aspects of everyday life, from discounts in stores to statistics in reports. Understanding how to convert fractions to percentages is a helpful skill.

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Most popular questions from this chapter

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