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Chapter 6: Problem 430

In the following exercises, solve the percent problem. 65 is what percent of 260\(?\)

Short Answer

Expert verified
65 is 25% of 260.

Step by step solution

01

Understand the Problem

To find what percent 65 is of 260, you need to determine the ratio of 65 to 260 and then convert that ratio into a percentage.
02

Set Up the Ratio

Set up the ratio of 65 to 260 as \(\frac{65}{260}\).
03

Simplify the Ratio

Simplify the fraction \(\frac{65}{260}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 65: \(\frac{65 \/ 65}{260 \/ 65} = \frac{1}{4}\).
04

Convert the Fraction to a Percentage

Convert the simplified fraction \(\frac{1}{4}\) to a percentage by multiplying by 100: \(\frac{1}{4} \times 100 = 25\%\).

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Key Concepts

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

ratio
A ratio compares two quantities to show the relative size of one quantity to another. In our exercise, the ratio is \(\frac{65}{260}\). This tells us how 65 relates to 260. Ratios can be expressed in different ways: as fractions, with a colon (like 65:260), or in words ('65 to 260'). The process of finding a percentage involves understanding this ratio and then transforming it into a percentage value. Ratios provide a simple way to express relationships and can easily be simplified for more understandable numbers.
simplifying fractions
Simplifying a fraction means reducing it to its smallest equal fraction by dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). For the fraction \(\frac{65}{260}\), the GCD is 65. By dividing both the numerator and the denominator by 65, we get \(\frac{1}{4}\). Simplifying fractions makes calculations easier and helps us understand the relationship between numbers more clearly.
percentage conversion
Converting a simplified fraction to a percentage involves multiplying by 100, because percent means 'per hundred'. For example, we simplify \(\frac{65}{260}\) to \(\frac{1}{4}\). To convert \(\frac{1}{4}\) to a percentage, we multiply it by 100: \[ \frac{1}{4} \times 100 = 25\text{%}\text{.} \] This tells us that 65 is 25 percent of 260. Converting to percentage form is useful because it provides a common way to compare different ratios.

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