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Chapter 6: Problem 38

Find fraction notation. Simplify. $$ 55 \% $$

Short Answer

Expert verified
The simplified fraction is \(\frac{11}{20}\).

Step by step solution

01

Convert percentage to fraction

To convert 55% to a fraction, write it as \(\frac{55}{100}\).
02

Simplify the fraction

Find the greatest common divisor (GCD) of 55 and 100. The GCD of 55 and 100 is 5. Divide both the numerator and the denominator by 5. So, \(\frac{55 \div 5}{100 \div 5} = \frac{11}{20}\).

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Key Concepts

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

percent to fraction conversion
Understanding how to convert a percentage to a fraction is a fundamental math skill. A percentage represents a number out of 100. For example, 55% means 55 out of 100. To convert a percentage to a fraction, you simply write the percentage number over 100. So, 55% becomes \(\frac{55}{100}\). This fraction can often be simplified, which means finding an equivalent fraction that is easier to work with.
greatest common divisor
Simplifying a fraction involves dividing both the numerator (top number) and the denominator (bottom number) by the greatest common divisor (GCD). The GCD is the largest number that can evenly divide both numbers.
For our fraction \(\frac{55}{100}\), we need to find the GCD of 55 and 100.
First, list the factors of each number:
  • Factors of 55: 1, 5, 11, 55
  • Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
The largest common factor is 5. So, the GCD of 55 and 100 is 5. By dividing both the numerator and the denominator by 5, we can simplify the fraction:
\(\frac{55 \div 5}{100 \div 5} = \frac{11}{20}\).
fraction notation
Fraction notation is a way of expressing numbers that are not whole. It uses two numbers separated by a slash. The top number is called the numerator, and the bottom number is called the denominator. For example, in the fraction \(\frac{55}{100}\), 55 is the numerator and 100 is the denominator.
When you simplify a fraction, you are looking for the equivalent fraction where both the numerator and the denominator cannot be divided further by the same number except 1.
Fractions are simplified by dividing both parts by their GCD.

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Most popular questions from this chapter

Multiply and simplify. $$ \frac{4}{15} \times \frac{3}{20} $$

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