I am a fraction equivalent to \(\frac{45}{60}\). If you multiply my denominator by my numerator, the product will be 192. What fraction am I?

Question

15-02-2024
Mathematics

College

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I am a fraction equivalent to \(\frac{45}{60}\). If you multiply my denominator by my numerator, the product will be 192. What fraction am I?

Answer :

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KurtDavies KurtDavies · Answer 1 · 2024-01-17T12:42:21-05:00

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.