What is 4/20 simplified
The Correct Answer and Explanation is :
To simplify the fraction ( \frac{4}{20} ), we need to find the greatest common divisor (GCD) of the numerator (4) and the denominator (20).
Steps to Simplify ( \frac{4}{20} )
- Find the GCD:
- The factors of 4 are 1, 2, and 4.
- The factors of 20 are 1, 2, 4, 5, 10, and 20.
- The largest common factor is 4.
- Divide the Numerator and Denominator by the GCD:
- Divide both the numerator and the denominator by the GCD (4):
[
\frac{4 \div 4}{20 \div 4} = \frac{1}{5}
]
Thus, ( \frac{4}{20} ) simplified is ( \frac{1}{5} ).
Explanation
When simplifying fractions, the goal is to reduce them to their simplest form, which means finding an equivalent fraction where the numerator and denominator have no common factors other than 1.
The process begins by determining the GCD of the numerator and the denominator. The GCD is the largest number that divides both numbers without leaving a remainder. In our case, both 4 and 20 share several factors, but the largest is 4.
Once we identify the GCD, we divide both the numerator and denominator by this value. This step maintains the equality of the fraction since we are effectively multiplying both parts by the same number (in this case, dividing by 4).
The final fraction, ( \frac{1}{5} ), cannot be simplified further because 1 is the only factor of the numerator, while 5 is a prime number with no factors other than 1 and itself. Simplifying fractions is a valuable skill in mathematics, as it can make calculations easier and provide clearer insights into the relationships between numbers.
In conclusion, the simplified form of ( \frac{4}{20} ) is ( \frac{1}{5} ).