20/100 simplified as a fraction
The Correct Answer and Explanation is :
The correct answqer is: ( \frac{1}{5} )
To simplify the fraction ( \frac{20}{100} ), we need to find the greatest common divisor (GCD) of the numerator (20) and the denominator (100) and divide both by this number.
Step 1: Find the GCD
- Prime Factorization:
- For 20, the prime factors are ( 2^2 \times 5^1 ).
- For 100, the prime factors are ( 2^2 \times 5^2 ).
- Common Factors:
- The common prime factors are ( 2^2 ) and ( 5^1 ).
- To find the GCD, we take the lowest power of each common factor:
- ( 2^2 = 4 )
- ( 5^1 = 5 )
- Therefore, the GCD is ( 4 \times 5 = 20 ).
Step 2: Divide Numerator and Denominator by the GCD
Now that we have the GCD (20), we divide both the numerator and the denominator by this number:
[
\frac{20 \div 20}{100 \div 20} = \frac{1}{5}
]
Conclusion
Thus, the simplified form of ( \frac{20}{100} ) is ( \frac{1}{5} ).
Explanation
Fractions are a way to represent a part of a whole, and simplifying fractions makes them easier to understand and work with. The process of simplification involves reducing a fraction to its simplest form, where the numerator and denominator share no common factors other than 1.
In this case, ( \frac{20}{100} ) can also be understood in practical terms. If you think of it as 20 out of 100, this is equivalent to 20%, which is the same as saying you have one part of a five-part whole. Therefore, simplifying helps not just in mathematical terms but also in real-life applications, like understanding percentages or ratios. Simplified fractions are easier to compare and compute, making them essential in various fields, including finance, cooking, and statistics.
Thus, ( \frac{20}{100} ) simplifies to ( \frac{1}{5} ), which clearly conveys the same ratio in a more manageable form.