14 72 simplified

Charlotte

2 min read

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01-03-2025

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Fractions can seem daunting, but simplifying them is a fundamental math skill. This guide breaks down how to simplify 14/72, and provides you with the tools to tackle any fraction reduction problem. We'll cover the concept of greatest common factors (GCF), and offer step-by-step instructions. By the end, you'll confidently simplify fractions.

Understanding Fraction Simplification

Simplifying a fraction means reducing it to its lowest terms. This means finding the largest number that divides both the numerator (top number) and the denominator (bottom number) evenly. This number is called the greatest common factor (GCF).

The goal isn't to just find any common factor; it's to find the greatest one. This ensures the fraction is in its simplest, most efficient form.

Finding the Greatest Common Factor (GCF) of 14 and 72

To simplify 14/72, we first need to find the GCF of 14 and 72. There are several ways to do this:

1. Listing Factors

List all the factors of 14 and 72:

• Factors of 14: 1, 2, 7, 14
• Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

The largest number appearing in both lists is 2. Therefore, the GCF of 14 and 72 is 2.

2. Prime Factorization

This method is particularly useful for larger numbers. Let's find the prime factorization of 14 and 72:

• 14: 2 x 7
• 72: 2 x 2 x 2 x 3 x 3 = 2³ x 3²

The common prime factor is 2 (only one 2 appears in the prime factorization of 14). Therefore, the GCF is 2.

Simplifying 14/72

Now that we know the GCF is 2, we can simplify the fraction:

1. Divide both the numerator and the denominator by the GCF (2):

   14 ÷ 2 = 7 72 ÷ 2 = 36

2. The simplified fraction is: 7/36

Therefore, 14/72 simplified is 7/36.

How to Simplify Fractions: A Step-by-Step Guide

Follow these steps to simplify any fraction:

1. Find the GCF: Use either the listing factors method or prime factorization to determine the greatest common factor of the numerator and denominator.
2. Divide: Divide both the numerator and the denominator by the GCF.
3. Check: Ensure the resulting fraction cannot be further simplified. If the numerator and denominator only share a GCF of 1, the fraction is in its simplest form.

Practice Problems

Try simplifying these fractions using the steps outlined above:

• 12/18
• 25/75
• 36/48

Conclusion

Simplifying fractions like 14/72 is a crucial skill in mathematics. By understanding the concept of the greatest common factor and applying the steps outlined above, you can confidently reduce fractions to their simplest form. Remember, practice makes perfect, so keep working through examples to build your proficiency.