Final answer:
The multiplication of mixed numbers 1 3/5 and 2 1/4 results in the mixed number 3 3/5 after converting to improper fractions, multiplying, and simplifying. The correct answer is option (a) 3 3/5.
Step-by-step explanation:
To solve the multiplication of mixed numbers 1 3/5 x 2 1/4, we first need to convert the mixed numbers into improper fractions. The mixed number 1 3/5 can be converted by multiplying the whole number 1 by the denominator 5 and then adding the numerator 3 (1 x 5 + 3 = 8), giving us 8/5. The mixed number 2 1/4 can be converted by multiplying the whole number 2 by the denominator 4 and then adding the numerator 1 (2 x 4 + 1 = 9), giving us 9/4.
After converting to improper fractions, we then multiply the numerators and denominators respectively. We get 72/20 when we multiply 8/5 by 9/4 (8 x 9 = 72 and 5 x 4 = 20).
Finally, we simplify the fraction 72/20 by dividing both the numerator and the denominator by their greatest common factor, which is 4. Therefore, 72/20 simplified is 18/5, which is the same as 3 3/5 when converted back into a mixed number. So, the correct answer is (a) 3 3/5.