By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.
In this question we should simplify a rational number into its simplest form based on two facts. First, that all natural numbers except 1 and the prime numbers are products of prime numbers and, second, the simplification of the fraction can be done by using the following algebra property:
(a · c)/(b · c) = a/b, where a, b, c are natural numbers. (1)
Along with power properties.
Now we proceed to simplify the rational number:
48/192 = (2⁴ × 3) / (2⁶ × 3)
48/192 = 1 / 2²
48/192 = 1 / 4
By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.
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