Simplifying Fractions: Understanding 22/52
Fractions represent a part of a whole. Simplifying a fraction means reducing it to its simplest form, where the numerator and denominator have no common factors other than 1. Let's explore how to simplify the fraction 22/52.
Finding the Greatest Common Factor (GCD)
The key to simplifying fractions is finding the greatest common factor (GCD) of the numerator and denominator. The GCD is the largest number that divides both numbers evenly.
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Factorization: Start by finding the factors of both 22 and 52:
- Factors of 22: 1, 2, 11, 22
- Factors of 52: 1, 2, 4, 13, 26, 52
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Identify the GCD: The greatest common factor of 22 and 52 is 2.
Simplifying the Fraction
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Divide by the GCD: Divide both the numerator (22) and the denominator (52) by the GCD (2):
22 ÷ 2 = 11 52 ÷ 2 = 26
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Simplified Fraction: The simplified fraction is 11/26.
Verification
To ensure the fraction has been simplified correctly, check if the numerator and denominator have any common factors other than 1. In this case, 11 and 26 only share the factor 1, meaning the fraction 11/26 is in its simplest form.
Conclusion
Simplifying fractions like 22/52 involves finding the GCD and dividing both the numerator and denominator by it. This process results in a simplified fraction, 11/26, representing the same value as the original fraction but in its simplest form.