122% is equivalent to what fraction in reduced terms? Write as an
improper fraction.
The Correct Answer and Explanation is :
To convert 122% to a fraction in reduced terms, we first recognize that the percent sign (%) means “per hundred.” Therefore, we can express 122% as:
[
122\% = \frac{122}{100}
]
Next, we need to reduce this fraction to its simplest form. This requires finding the greatest common divisor (GCD) of the numerator (122) and the denominator (100).
Step 1: Find the GCD of 122 and 100
To find the GCD, we can use the prime factorization method or the Euclidean algorithm. Let’s first factor both numbers:
- 122 can be factored into (2 \times 61) (where 61 is a prime number).
- 100 can be factored into (2^2 \times 5^2).
The common factor between 122 and 100 is (2).
Step 2: Divide the numerator and denominator by their GCD
Now, we can simplify the fraction by dividing both the numerator and the denominator by 2:
[
\frac{122 \div 2}{100 \div 2} = \frac{61}{50}
]
Step 3: Result
Thus, (122\%) can be expressed as the improper fraction (\frac{61}{50}).
Conclusion
In conclusion, the fraction (\frac{61}{50}) represents (122\%) in reduced terms. This process illustrates the steps required to convert a percentage into a fraction and then reduce that fraction to its simplest form. Understanding how to manipulate percentages and fractions is crucial in many fields, including finance, science, and everyday mathematics. This knowledge allows for clearer communication of quantitative information, ensuring accurate interpretations and calculations in various real-world applications.