Understanding fractions is crucial in many aspects of mathematics and everyday life. Simplifying fractions by reducing them to their lowest terms is an essential skill that helps in solving various mathematical problems efficiently. In this guide, we will explore the concept of simplified fractions and provide you with a step-by-step process to simplify any fraction.

What is a simplified fraction?

A simplified fraction, also known as a reduced fraction or fraction in lowest terms, is a fraction where the numerator and denominator have no common factors other than 1. In other words, there is no whole number by which both the numerator and denominator can be divided without leaving a remainder.

Why should you simplify fractions?

Simplifying fractions not only makes them easier to work with but also provides a more concise representation of the original fraction. Simplified fractions are particularly helpful when comparing or performing operations on fractions, such as addition, subtraction, multiplication, and division.

How to simplify fractions

To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator. Once you have the GCD, divide both the numerator and denominator by it. This process eliminates any common factors and reduces the fraction to its lowest terms. Here’s a step-by-step guide:

  • Step 1: Find the GCD of the numerator and denominator.
  • Step 2: Divide both the numerator and denominator by the GCD.
  • Step 3: The resulting fraction is the simplified fraction in lowest terms.

Example:

Let’s take the fraction 24/36 and simplify it:

  • Step 1: Find the GCD of the numerator (24) and denominator (36). The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The largest number that appears in both lists is 12, so the GCD is 12.
  • Step 2: Divide both the numerator and denominator by the GCD (12). 24/12 = 2 and 36/12 = 3.
  • Step 3: The simplified fraction is 2/3.

Tips and Tricks:

  • If the numerator and denominator have a common factor other than 1, continue dividing by the GCD until no further simplification is possible.
  • Remember that multiplying or dividing both the numerator and denominator by the same non-zero number does not change the value of the fraction, but it may not be in its lowest terms.
  • When dealing with more complex fractions, it may be helpful to factorize the numerator and denominator to identify common factors.

Simplifying fractions is a fundamental skill that helps in various mathematical scenarios. By reducing fractions to their lowest terms, we obtain a more concise representation and facilitate calculations involving fractions. Remember to find the greatest common divisor and divide both the numerator and denominator by it to simplify fractions effectively.

Now that you have a better understanding of simplified fractions, you can confidently tackle fraction-related problems with ease!

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