36 : 99 reduced

Daniel Parker

2 min read

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26-02-2025

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The fraction 36/99 represents a part of a whole. To understand it better, and to make calculations easier, we need to simplify it. This process is called reducing a fraction to its lowest terms. This article will guide you through reducing 36/99.

Finding the Greatest Common Divisor (GCD)

The key to simplifying fractions lies in finding the greatest common divisor (GCD) of the numerator (36) and the denominator (99). The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.

There are several ways to find the GCD:

1. Listing Factors:

• Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
• Factors of 99: 1, 3, 9, 11, 33, 99

The largest number that appears in both lists is 9. Therefore, the GCD of 36 and 99 is 9.

2. Prime Factorization:

This method involves breaking down both numbers into their prime factors.

• 36: 2 x 2 x 3 x 3 = 2² x 3²
• 99: 3 x 3 x 11 = 3² x 11

The common prime factors are 3² (or 9). Therefore, the GCD is 9.

3. Euclidean Algorithm:

This is a more efficient method for larger numbers. It involves repeatedly applying the division algorithm until the remainder is 0.

1. Divide 99 by 36: 99 = 2 x 36 + 27
2. Divide 36 by 27: 36 = 1 x 27 + 9
3. Divide 27 by 9: 27 = 3 x 9 + 0

The last non-zero remainder is 9, so the GCD is 9.

Reducing the Fraction

Once we've found the GCD (which is 9), we can reduce the fraction by dividing both the numerator and the denominator by the GCD:

36 ÷ 9 = 4 99 ÷ 9 = 11

Therefore, the simplified fraction is 4/11.

Verification

To verify our answer, we can check if 4 and 11 share any common factors other than 1. Since they don't, we know that 4/11 is in its simplest form.

Conclusion

Reducing 36/99 to its lowest terms involves finding the greatest common divisor of 36 and 99, which is 9. Dividing both the numerator and denominator by 9 results in the simplified fraction 4/11. Understanding this process is crucial for simplifying fractions and making mathematical calculations more efficient. Remember to always check for common factors after simplification to ensure you've reached the lowest terms.