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Chapter 7: Problem 12

Convert the given percent to a fraction, and simplify the result. $$ 5 \% $$

Short Answer

Expert verified
5% as a fraction is \( \frac{1}{20} \).

Step by step solution

01

Convert Percent to Fraction

Start by converting 5% to a fraction. Remember that a percent is a part per hundred, so 5% can be written as \( \frac{5}{100} \).
02

Simplify the Fraction

Next, simplify the fraction \( \frac{5}{100} \). Find the greatest common divisor of 5 and 100, which is 5. Divide both the numerator and the denominator by 5: \( \frac{5}{5} = 1 \) and \( \frac{100}{5} = 20 \). This gives us \( \frac{1}{20} \).

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Key Concepts

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

Simplifying Fractions Made Easy
Simplifying fractions is a process that makes fractions as simple as they can be. The goal is to ensure that both the numerator (top number) and the denominator (bottom number) no longer share any common factors other than 1. This is called putting the fraction in its 'simplest form'.

Here are the basic steps to simplify:
  • First, identify the greatest common divisor (GCD) of the numerator and the denominator. This is the largest number that divides both numbers evenly.
  • Divide both the numerator and the denominator by the GCD.
  • The result is your simplified fraction.
Applying these steps makes working with fractions easier and often more intuitive.
Understanding the Greatest Common Divisor (GCD)
The greatest common divisor, or GCD, is an essential concept when working with fractions. It is the largest number that can evenly divide two numbers without any remainder. Finding the GCD allows us to simplify fractions efficiently.

To find the GCD, you can:
  • List all the factors of both the numerator and denominator.
  • Identify the largest factor that appears in both lists.
For example, when simplifying the fraction \( \frac{5}{100} \), the factors of 5 are [1, 5] and the factors of 100 are [1, 2, 4, 5, 10, 20, 25, 50, 100]. The greatest common factor is 5, which simplifies the fraction to \( \frac{1}{20} \).

This method ensures that the fraction is reduced to its simplest form, making it easier to work with in calculations or comparisons.
Navigating Basic Arithmetic Steps
Basic arithmetic steps are fundamental operations that we use daily, such as addition, subtraction, multiplication, and division. These operations become crucial when converting percentages to fractions and simplifying them.

When you convert a percentage like 5% to a fraction, you take it as a part out of 100, forming \( \frac{5}{100} \). The next arithmetic step is simplifying the fraction by division. This involves:
  • Dividing the given numbers by their GCD, found through basic division operations.
  • Ensuring the results can't be divided further without leaving a remainder.
Understanding these steps allows for easier manipulation and conversion of numbers, reinforcing basic arithmetic skills that are essential for solving more complex problems efficiently.

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