<prompt> Explain why the following fraction is equivalent to 14416  <response>: The fraction 416 is equivalent to 14 because both fractions represent the same value. A fraction can be simplified by dividing both the numerator and the denominator by a common factor. In this case, 4 is a common factor of both the numerator and the denominator of 416. When we divide both by 4, we get 44 1 and 164 4, so the simplified fraction is 14. Alternatively, we can think of this in terms of multiplication. For example, if we multiply the numerator and denominator of the fraction 14 by 4, we get 1x44x4, or 416. Since both fractions can be derived from the other through multiplication or division by the same number, they represent the same value and are equivalent. 