Reduce the fraction 20/72 to the simplest form
The Correct Answer and Explanation is :
To reduce the fraction ( \frac{20}{72} ) to its simplest form, follow these steps:
Step 1: Find the Greatest Common Divisor (GCD)
The first step in simplifying a fraction is to find the Greatest Common Divisor (GCD) of the numerator (20) and the denominator (72). The GCD is the largest number that divides both 20 and 72 without leaving a remainder.
- Factors of 20: ( 1, 2, 4, 5, 10, 20 )
- Factors of 72: ( 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 )
The common factors of 20 and 72 are 1, 2, and 4. The greatest of these is 4, so the GCD of 20 and 72 is 4.
Step 2: Divide Both the Numerator and Denominator by the GCD
Next, divide both the numerator and the denominator of the fraction by the GCD, which is 4:
[
\frac{20}{72} \div 4 = \frac{20 \div 4}{72 \div 4} = \frac{5}{18}
]
Step 3: Verify the Result
To verify that ( \frac{5}{18} ) is in its simplest form, check if the numerator (5) and the denominator (18) have any common factors other than 1.
- Factors of 5: ( 1, 5 )
- Factors of 18: ( 1, 2, 3, 6, 9, 18 )
Since the only common factor is 1, ( \frac{5}{18} ) cannot be reduced any further, and this is the simplest form of the fraction.
Conclusion:
The simplified fraction is ( \frac{5}{18} ).
Explanation of the Process
The process of simplifying a fraction involves reducing it to its lowest terms, which means making sure the numerator and denominator have no common factors other than 1. The method relies on finding the GCD, dividing both the numerator and denominator by this number, and ensuring that the fraction cannot be reduced further. This helps make the fraction easier to understand and work with, especially in mathematical operations or real-life applications.