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Chapter 6: Problem 62

Find fraction notation for the percent notations in the table below. $$ 26 \% $$

Short Answer

Expert verified
\( \frac{13}{50} \)

Step by step solution

01

- Understand What Percent Means

Percent means 'per 100,' so 26% is equivalent to 26 out of 100.
02

- Write the Percent as a Fraction

Since 26% means 26 out of 100, write it as a fraction: \( \frac{26}{100} \).
03

- Simplify the Fraction

Find the greatest common divisor (GCD) of 26 and 100 and simplify the fraction. The GCD of 26 and 100 is 2. Divide both the numerator and the denominator by 2: \( \frac{26 \div 2}{100 \div 2} = \frac{13}{50} \).

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Key Concepts

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

percent to fraction conversion
To convert a percent to a fraction, start by understanding what percent means. The word 'percent' comes from Latin and means 'per 100'. So, when you see a percent, it represents a number out of 100. Let's look at 26% for instance. It means 26 out of 100.
Here鈥檚 how to convert it to a fraction:
  • First, write down the percent as is but without the percent sign: 26.
  • Next, place it over 100 because percent means per 100. So, we get: \( \frac{26}{100} \).
This initial fraction is not always in its simplest form, which is where our next steps come in.
simplifying fractions
After converting the percent to a fraction, you鈥檒l often have a fraction that can be simplified. Simplifying a fraction means reducing it to its simplest form.
This involves dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD).
Here鈥檚 how to simplify the fraction \( \frac{26}{100} \):
  • First, identify the GCD of the numerator and the denominator. In this case, the GCD of 26 and 100 is 2.
  • Next, divide both the numerator and the denominator by 2:
  • \( \frac{26 \div 2}{100 \div 2} = \frac{13}{50} \)
Now, \( \frac{13}{50} \) is in its simplest form, which means it cannot be reduced further.
greatest common divisor (GCD)
The greatest common divisor (GCD) is a key concept when simplifying fractions. The GCD of two numbers is the largest number that can divide both of them without leaving a remainder.
Here鈥檚 a quick method to find the GCD:
  • List the factors of each number. Factors of 26: 1, 2, 13, 26. Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
  • Identify the largest factor that appears in both lists. Here, 2 is the greatest number that can divide both 26 and 100.
This is useful because to simplify a fraction, you need to divide both the numerator and the denominator by their GCD. Using the above example, dividing 26 and 100 by their GCD of 2 simplifies \( \frac{26}{100}\) to \( \frac{13}{50} \).

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