Final answer:
The equivalent mixed number to one and six-eighths is one and twelve-sixteenths because when both are simplified, they equal one and three-fourths.
Step-by-step explanation:
To find the equivalent mixed number to one and six-eighths, we must first simplify the fraction six-eighths. When simplifying fractions, we look for the greatest common divisor (GCD) that can divide both the numerator and the denominator. In this case, the GCD of 6 and 8 is 2. Dividing both by 2, we get three-fourths (3/4). Now, we look at the options given: one and six-sixteenths, one and six-tenths, one and twelve-sixteenths, and one and twelve-eighths.
Option A: One and six-sixteenths remains unsimplified, and its simplest form is one and three-eighths which does not equal one and three-fourths.
Option B: One and six-tenths is in simplest form but clearly does not equal one and three-fourths as the denominators are different.
Option C: Simplifying one and twelve-sixteenths by dividing both the numerator and the denominator by 4, we get one and three-fourths, which is indeed equivalent to one and six-eighths.
Option D: Simplifying one and twelve-eighths by dividing both the numerator and the denominator by 8, we get one and one-half, which is not equivalent to one and six-eighths.