Final answer:
To subtract 12 3/5 from 4 1/3, both mixed numbers are converted to improper fractions and the least common denominator is found to be 15. After performing the subtraction and simplifying, the result is 8 4/15, which is not among the provided options.
Step-by-step explanation:
To subtract the mixed numbers 12 3/5 and 4 1/3, convert them to improper fractions. For 12 3/5, multiply 12 (the whole number) by 5 (the denominator) and add 3 (the numerator) to get 63/5 (12x5+3). For 4 1/3, multiply 4 by 3 and add 1 to get 13/3 (4x3+1).
Now subtract the two improper fractions: 63/5 - 13/3. To subtract fractions, they must have the same denominator. Find the least common denominator (LCD), which is 15, and convert the fractions.
63/5 is equivalent to 189/15 (because 63x3=189) and 13/3 is equivalent to 65/15 (because 13x5=65). Now, subtract 189/15 - 65/15 to get 124/15. This can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 1, so the fraction is already in its simplest form.
Finally, convert the improper fraction back to a mixed number. 124/15 is 8 with a remainder of 4, so the mixed number is 8 4/15. Therefore, the result of subtracting 12 3/5 - 4 1/3 is 8 4/15, which does not match any of the provided options, meaning there might be a mistake in the multiple choices.