Answer :
Final answer:
The student is looking for a fraction equivalent to 45/60 which produces a product of 192 when the fraction's denominator is multiplied by its numerator. The simplified form of 45/60 is 3/4 and the equivalent fraction that satisfies the condition is 3/64.
Explanation:
The question involves finding a fraction equivalent to 45/60 such that when the denominator of this fraction is multiplied by the fraction's numerator, the product is 192.
First, to find the equivalent fraction, we need to simplify 45/60 by dividing both the numerator and the denominator by their greatest common factor, which is 15. This simplification results in the fraction 3/4.
Now, we are asked to find a fraction which when the denominator is multiplied by the numerator gives us a product of 192.
Thus, if 'x' represents the unknown denominator of the equivalent fraction, the equation would be 3x = 192. Solving for x, we divide 192 by 3, which yields x = 64.
Therefore, the fraction equivalent to 45/60 that satisfies this condition is 3/64.
It's important to note that fractions can be simplified or transformed and that multiplication of a numerator by a new denominator can be approached systematically through algebraic methods.
