Simplify 15/20 To Lowest Terms In 5 Easy Steps

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Simplifying fractions is an essential math skill that can seem daunting at first, but with a step-by-step approach, it becomes manageable. In this article, we will break down the process of simplifying 15/20 to its lowest terms in 5 easy steps.

Understanding the Concept of Simplifying Fractions

Simplifying fractions involves reducing a fraction to its simplest form by dividing both the numerator and the denominator by the greatest common divisor (GCD). The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.

Why Simplify Fractions?

Simplifying fractions is important because it helps to:

• Reduce the complexity of mathematical expressions
• Make calculations easier and more accurate
• Improve understanding of mathematical concepts
• Enhance problem-solving skills

Step 1: Find the Greatest Common Divisor (GCD)

To simplify 15/20, we need to find the GCD of 15 and 20. The factors of 15 are 1, 3, 5, and 15, while the factors of 20 are 1, 2, 4, 5, 10, and 20. The greatest common factor of 15 and 20 is 5.

How to Find the GCD

There are several methods to find the GCD, including:

• Listing the factors of each number
• Using the prime factorization method
• Applying the Euclidean algorithm

Step 2: Divide the Numerator and Denominator by the GCD

Now that we have found the GCD (5), we can divide both the numerator (15) and the denominator (20) by 5.

15 ÷ 5 = 3 20 ÷ 5 = 4

The simplified fraction is 3/4.

Why Divide by the GCD?

Dividing both the numerator and the denominator by the GCD ensures that the fraction is reduced to its simplest form. This is because the GCD is the largest number that divides both numbers without leaving a remainder.

Step 3: Check if the Fraction is in its Simplest Form

The fraction 3/4 is already in its simplest form, as there are no common factors between 3 and 4.

How to Check if a Fraction is Simplified

To check if a fraction is simplified, you can:

• Look for common factors between the numerator and the denominator
• Use the prime factorization method to verify that the fraction is in its simplest form

Step 4: Write the Simplified Fraction

The simplified fraction is 3/4.

Importance of Writing Simplified Fractions

Writing simplified fractions is crucial in mathematics, as it helps to:

• Avoid errors in calculations
• Improve understanding of mathematical concepts
• Enhance problem-solving skills

Step 5: Verify the Simplified Fraction

To verify the simplified fraction, we can multiply the numerator and the denominator by the GCD (5) to ensure that we get the original fraction.

3 × 5 = 15 4 × 5 = 20

The original fraction is 15/20, which verifies that the simplified fraction is indeed 3/4.

Why Verify Simplified Fractions?

Verifying simplified fractions is essential to ensure that the fraction is accurate and reliable. This helps to:

• Avoid errors in calculations
• Improve understanding of mathematical concepts
• Enhance problem-solving skills

By following these 5 easy steps, you can simplify fractions with confidence and accuracy. Remember to always find the GCD, divide the numerator and denominator by the GCD, check if the fraction is in its simplest form, write the simplified fraction, and verify the simplified fraction.

We hope this article has helped you understand the concept of simplifying fractions and how to simplify 15/20 to its lowest terms. If you have any questions or need further clarification, please don't hesitate to ask.