Final answer:
To subtract 9 1/5 - 5 4/6, convert to improper fractions with a common denominator, subtract, then simplify to get the final answer, which is 3 8/15.
Step-by-step explanation:
To solve the subtraction problem 9 1/5 - 5 4/6, we need to follow a step-by-step process. First, we make sure the fractions have a common denominator. We can convert the mixed numbers to improper fractions. 9 1/5 becomes 46/5 and 5 4/6 becomes 34/6. Because these fractions don't already have the same denominators, we must find a common denominator to make subtraction possible.
We find the least common multiple (LCM) of 5 and 6, which is 30, and convert the fractions accordingly. 46/5 becomes 276/30, and 34/6 becomes 170/30. Now we have:
276/30 - 170/30 = (276 - 170)/30 = 106/30.
After this, we simplify the improper fraction 106/30. It simplifies to 3 16/30, which can be further reduced to 3 8/15 after dividing both the numerator and the denominator by 2. Thus, the final simplified answer is 3 8/15.