Express 15% as a fraction in its simplest form.
Answer (2)
15% can be expressed as a fraction by first writing it as \frac{15}{100}. By finding the GCD and simplifying, we get that 15% equals \frac{3}{20} in simplest form. Thus, the answer is \frac{3}{20}.
;
Convert the percentage to a fraction: 15% = 100 15 .
Find the greatest common divisor (GCD) of 15 and 100, which is 5.
Divide both the numerator and the denominator by the GCD: 100 ÷ 5 15 ÷ 5 = 20 3 .
The simplest form of the fraction is 20 3 .
Explanation
Understanding the Problem We need to express 15% as a fraction in its simplest form. This means we want to write 15% as a fraction b a where a and b are integers, and the fraction is in its lowest terms.
Converting Percentage to Fraction First, we convert the percentage to a fraction by dividing by 100: 15% = 100 15 .
Finding the Greatest Common Divisor (GCD) Next, we simplify the fraction by finding the greatest common divisor (GCD) of the numerator (15) and the denominator (100). The GCD is the largest number that divides both 15 and 100 without leaving a remainder. We can find the GCD using the Euclidean algorithm or by listing the factors of each number. The factors of 15 are 1, 3, 5, and 15. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. The greatest common factor is 5.
Simplifying the Fraction Now, we divide both the numerator and the denominator by their GCD, which is 5: 100 15 = 100 ÷ 5 15 ÷ 5 = 20 3 .
Final Answer The fraction 20 3 is in its simplest form because 3 and 20 have no common factors other than 1.
Examples
In everyday life, percentages are often used to represent discounts. For example, if a store offers a 15% discount on an item, expressing 15% as a fraction helps you calculate the exact amount of the discount. In this case, 15% is equivalent to 20 3 . So, if the item costs 20 , t h e d i sco u n tw o u l d b e \frac{3}{20} \times $20 = $3.
