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Chapter 7: Problem 53

Convert each percent to a fraction. $$18 \%$$

Short Answer

Expert verified
18% is \( \frac{9}{50} \) in fraction form.

Step by step solution

01

Understand the Percentage

A percentage is simply a number out of 100. So, 18% means 18 out of 100. Our task is to express this as a fraction.
02

Convert Percentage to Fraction

Write the percentage as a fraction out of 100. Therefore, 18% becomes \( \frac{18}{100} \).
03

Simplify the Fraction

The next step is to simplify the fraction. Check for the greatest common divisor (GCD) of 18 and 100. Both numbers are divisible by 2. Divide the numerator and the denominator by 2: \( \frac{18}{100} \rightarrow \frac{9}{50} \). 9 and 50 do not have any common divisors other than 1, so \( \frac{9}{50} \) is in its simplest form.

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Key Concepts

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

Simplifying Fractions
Simplifying fractions is a fundamental skill in mathematics. It involves reducing a fraction to its simplest form. This is done by finding a common factor of the numerator and the denominator and dividing both by it.

For example, in our exercise, we start with the fraction \(\frac{18}{100}\). Our goal is to express it in its simplest form. If we divide both numbers by 2, we get \(\frac{9}{50}\). We check to see if there are any more common factors. Here, 9 and 50 do not have common factors other than 1. Hence, \(\frac{9}{50}\) is the simplest form.

Remember:
  • Begin by identifying any common divisors.
  • The simplest form occurs when you can no longer divide both numbers evenly by any number other than 1.
  • This practice not only makes a fraction easier to read but also makes it easier to work with in further calculations.
Greatest Common Divisor (GCD)
The greatest common divisor (GCD) of two numbers is the largest number that divides both of them without leaving a remainder. It is crucial when simplifying fractions.

In our example, the GCD helps us simplify \(\frac{18}{100}\) to \(\frac{9}{50}\). We found that both 18 and 100 are divisible by 2, the GCD in this scenario.

Finding the GCD involves several steps:
  • List Factors: List all factors for each number. For instance, the factors of 18 are 1, 2, 3, 6, 9, and 18, while the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
  • Identify Common Factors: The numbers 18 and 100 share the factors 1 and 2, making 2 the highest common factor.
Using the GCD ensures your fraction is simplified perfectly every time.
Basic Arithmetic
Basic arithmetic operations form the foundation of math skills necessary for fraction conversion and simplification. Regardless of the complexity, simplifying fractions relies heavily on multiplication and division.

Let's break it down:
  • Division: We use division to simplify fractions by dividing the numerator and denominator by their GCD.
  • Multiplication: Although not used in this exact example, it is crucial in ensuring the integrity of the fraction remains during the reversal process of verifying simplifications.
Understanding these simple arithmetic operations helps in fraction conversions and many other mathematical processes.

By mastering these elementary operations, you gain the capacity to simplify not only fractions but other complicated mathematical expressions as well.

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Most popular questions from this chapter

Write the simplified fractional form of each ratio or rate. 12 to 5.

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