Final answer:
To simplify 36/90, Amelia should divide both the numerator and the denominator by their greatest common divisor (GCD), which is 18, resulting in a simplified fraction of 2/5.
Step-by-step explanation:
To simplify the fraction 36/90 fully in one step, Amelia needs to divide both the numerator (36) and the denominator (90) by their greatest common divisor (GCD). The GCD of 36 and 90 is 18. Dividing both the numerator and the denominator by 18, we get:
36 ÷ 18 = 2
90 ÷ 18 = 5
So the simplified form of the fraction 36/90 is 2/5.
When simplifying fractions, we find the largest number that both the numerator and denominator can be divided by evenly to reduce the fraction to its simplest form. This involves factoring and understanding the concept that multiplication and division are reciprocal operations: dividing by a number is the same as multiplying by its reciprocal.