In this article, we will explore the concept of simplifying fractions, focusing on the specific example of simplifying 100/7. We will provide a step-by-step guide on how to reduce this fraction to its lowest terms and explain the importance of understanding simplified fractions. By the end of this article, you will have a solid foundation in fraction simplification and be able to confidently apply these techniques to other fractions as well.
What is a Simplified Fraction?
A simplified fraction is a fraction that has been reduced to its lowest terms, meaning that the numerator and denominator have no common factors other than 1. When a fraction is simplified, it becomes easier to work with and compare to other fractions. For example, the simplified fraction 3/9 is equivalent to 1/3, where both the numerator and denominator share a common factor of 3. Understanding the concept of simplified fractions is crucial in various mathematical operations involving fractions.
Step-by-Step Process of Simplifying 100/7
To simplify the fraction 100/7, we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both by this common factor. Let’s break down the process into steps:
Step 1: Find the Greatest Common Divisor
The GCD is the largest number that divides both the numerator and denominator without leaving a remainder. In the case of 100/7, we can determine the GCD by using methods like prime factorization or the Euclidean algorithm. Let’s use prime factorization:
Step 2: Prime Factorization of 100 and 7
Prime factorization involves breaking down a number into its prime factors, which are the prime numbers that multiply together to give the original number. For example, the prime factorization of 100 is 2^2 * 5^2, where 2 and 5 are the prime factors. In the case of 7, it is already a prime number, so its factorization is simply 7.
Step 3: Find the Common Factors
By comparing the prime factorizations of 100 and 7, we can identify the common factors. If there are no common factors other than 1, it means that the GCD is 1 and the fraction is already in its simplest form.
Step 4: Divide by the Greatest Common Divisor
If the GCD is 1, as in the case of 100/7, we divide both the numerator and denominator by 1, resulting in the fraction being its own simplified form.
Simplifying fractions is a fundamental skill in mathematics that allows us to express fractions in their lowest terms. By understanding how to simplify fractions, we can confidently work with fractions in various equations and calculations. In this article, we specifically explored the process of simplifying 100/7 and provided a step-by-step guide to help you apply the same principles to other fractions. Remember, simplified fractions make mathematical operations easier and enhance your problem-solving skills. So practice simplifying fractions and enhance your mathematical abilities!