Final answer:
To divide 2 1/9 by 3 1/3, convert each to an improper fraction, multiply by the reciprocal of the divisor, then reduce to lowest terms. The final answer is 19/30, corresponding to option a.
Step-by-step explanation:
To divide the mixed numbers 2 1/9 by 3 1/3 and reduce the answer to lowest terms, we first convert each mixed number to an improper fraction.
The improper fraction for 2 1/9 is (2 × 9 + 1)/9, which equals 19/9.
Similarly, 3 1/3 as an improper fraction is (3 × 3 + 1)/3, which equals 10/3.
Next, we divide the two improper fractions by multiplying the first fraction by the reciprocal of the second fraction. In other words, (19/9) × (3/10). Multiplying these gives us (19 × 3)/(9 × 10), which simplifies to 57/90.
Finally, we reduce the fraction 57/90 to its lowest terms by finding the greatest common divisor, which is 3 in this case, and dividing both the numerator and the denominator by this number.
The result is 19/30, which corresponds to option a.