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Chapter 7: Problem 36

9 is what percent of 15?

Short Answer

Expert verified
9 is 60% of 15.

Step by step solution

01

Understand the Formula

To find what percent one number is of another, use the formula \( \text{percent} = \left( \frac{\text{part}}{\text{whole}} \right) \times 100 \). Here, 9 is the 'part' and 15 is the 'whole'.
02

Substitute the Numbers

Plug in the numbers into the formula: \( \text{percent} = \left( \frac{9}{15} \right) \times 100 \).
03

Calculate the Fraction

First, calculate the fraction \( \frac{9}{15} \). Simplify it to get \( \frac{3}{5} \).
04

Convert Fraction to Decimal

Convert the simplified fraction \( \frac{3}{5} \) to a decimal by dividing 3 by 5 to get 0.6.
05

Convert Decimal to Percent

Multiply the decimal 0.6 by 100 to convert it to a percentage. Therefore, \( 0.6 \times 100 = 60 \).

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Key Concepts

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

Fraction Simplification
When working with fractions, simplification is a critical skill. This means you reduce the fraction to its simplest form. A fraction is simplified by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.
Take the fraction \( \frac{9}{15} \) as an example. Both 9 and 15 can be divided by 3, which is their GCD. When you divide both by 3, you get \( \frac{3}{5} \). Now, \( \frac{3}{5} \) is in its simplest form since 3 and 5 share no common divisor other than 1.
Simplifying fractions
  • Makes them easier to work with.
  • Helps in further calculations like converting to decimals or percentages.
  • Aids in comparing fractions more conveniently.
Converting Fractions to Decimals
Converting fractions to decimals is a straightforward process. You simply need to divide the numerator by the denominator. This can be done using long division or a calculator.
For instance, to convert \( \frac{3}{5} \) to a decimal, divide 3 by 5. You will get 0.6 as the decimal representation of the fraction.
Why convert fractions to decimals?
  • Decimals are often easier to understand in everyday situations.
  • They make some calculations simpler, like adding and subtracting.
  • Decimals help compare values more intuitively, especially when dealing with percentages.
Converting Decimals to Percentages
The transition from decimals to percentages is a simple operation that involves moving two decimal places to the right or, equivalently, multiplying the decimal by 100. This conversion helps in expressing numbers in a way that's easy to comprehend, especially in financial and statistical terms.
Using our decimal 0.6 from the previous example:
  • To convert 0.6 to a percentage, multiply by 100: \( 0.6 \times 100 = 60 \).
  • This tells us that 9 is 60 percent of 15, making it easy to interpret and compare.
Why use percentages?
  • They are a common way to express parts of a whole.
  • Percentages simplify comparisons across different contexts because they standardize values for easy interpretation.
  • Understanding percentages is crucial in various real-life situations, from grades to financial interest rates.

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