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Chapter 6: Problem 65

Find fraction notation for the percent notations in the table below. $$ 15 \% $$

Short Answer

Expert verified
The fraction notation for 15% is \(\frac{3}{20}\).

Step by step solution

01

- Understanding Percent Notation

A percent represents a part out of 100. The term 'percent' means 'per hundred'. So, 15% is equivalent to 15 out of 100.
02

- Writing as a Fraction

To convert 15% to a fraction, write it as \[\frac{15}{100}\].
03

- Simplifying the Fraction

To simplify the fraction \[\frac{15}{100}\], find the greatest common divisor (GCD) of 15 and 100. The GCD of 15 and 100 is 5. Divide both the numerator and the denominator by their GCD (5): \[\frac{15 \div 5}{100 \div 5} = \frac{3}{20}\].

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Key Concepts

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

Percent Notation
Percent notation makes it easy to understand the proportion of a part relative to the whole. The symbol '%' signifies 'per hundred.' So, when you see a number followed by '%', it means that number is out of 100. For instance, 15% means 15 out of every 100. When converting percent notation to a fraction, remember that the fraction鈥檚 denominator is always 100 because percent means per hundred. For example, 50% equals \(\frac{50}{100}\). This first step helps break down complex ideas into understandable parts.
Fraction Simplification
Once you have written a percent as a fraction, the next step is to simplify that fraction. Simplifying a fraction means making it as simple as possible without changing its value. This involves both the numerator (top number) and the denominator (bottom number). You do this by finding the greatest common divisor (GCD) of both numbers and dividing them by it. For example, if you have \(\frac{15}{100}\), you find their GCD, which is 5, and divide both the numerator and the denominator by 5, resulting in \(\frac{3}{20}\). Simplified fractions are easier to work with and understand.
Greatest Common Divisor
The greatest common divisor (GCD) of two numbers is the largest number that divides both of them without leaving a remainder. Finding the GCD is crucial for simplifying fractions. For example, to simplify \(\frac{15}{100}\), you first need to find the GCD of 15 and 100. Prime factorization is a helpful method for finding the GCD. Break down both numbers into their prime factors: 15 is 3 脳 5, and 100 is 2 脳 2 脳 5 脳 5. The common factors are 5, so the GCD is 5. Dividing the numerator and the denominator of \(\frac{15}{100}\) by 5 simplifies the fraction to \(\frac{3}{20}\). Simplification ensures you work with the smallest numbers possible.

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