simplify 16/21

Guri Bee

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17-10-2024

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Simplifying Fractions: 16/21 and Beyond

Understanding how to simplify fractions is a fundamental skill in mathematics. It allows us to represent numbers in their most basic form, making them easier to work with and comprehend. Let's explore how to simplify the fraction 16/21, and delve into the broader concepts of simplifying fractions.

Simplifying 16/21

The fraction 16/21 is already in its simplest form. This is because the numerator (16) and denominator (21) have no common factors other than 1.

What does it mean to simplify a fraction?

Simplifying a fraction means finding an equivalent fraction that is expressed with the smallest possible whole numbers in the numerator and denominator. This is achieved by dividing both the numerator and denominator by their greatest common factor (GCD).

Example:

Let's take the fraction 12/18. The GCD of 12 and 18 is 6.

1. Divide both numerator and denominator by 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3.

2. The simplified fraction is 2/3.

Why simplify fractions?

• Clarity: Simplified fractions are easier to understand and visualize.
• Comparisons: Simplifying makes it easier to compare fractions.
• Calculations: Simplified fractions are easier to use in calculations, especially when adding, subtracting, multiplying, or dividing fractions.

How to find the GCD:

• Listing factors: List all the factors of the numerator and denominator. The greatest common factor is the largest number that appears in both lists.
• Prime factorization: Break down the numerator and denominator into their prime factors. The GCD is the product of all the prime factors they share.

Beyond 16/21: Additional Examples

1. 24/36: The GCD of 24 and 36 is 12. Dividing both by 12, we get 2/3.

2. 5/10: The GCD of 5 and 10 is 5. Dividing both by 5, we get 1/2.

Important Note:

Always remember that simplifying a fraction does not change its value. It merely expresses the same value in a simpler form.

In Conclusion:

Simplifying fractions is a crucial mathematical skill that facilitates understanding and calculation. While 16/21 is already in its simplest form, this article has explored the process of simplification, highlighting its importance and showcasing various examples.