Final answer:
To divide 12/3 by 31/2, convert to improper fractions, multiply by the reciprocal, and simplify to get 10/21. This fraction cannot be reduced further, and the answer is confirmed to be less than 1, which is reasonable.
Step-by-step explanation:
To divide the mixed numbers 12/3 by 31/2, first convert each mixed number into an improper fraction. For 12/3, multiply the whole number by the denominator (1 × 3) and add the numerator to get 5/3. For 31/2, multiply the whole number by the denominator (3 × 2) and add the numerator to get 7/2.
Next, multiply the first fraction by the reciprocal of the second fraction: (5/3) × (2/7). Multiply the numerators and the denominators: (5 × 2) / (3 × 7) which equals 10/21. This is the simplified answer, and there is no further reduction possible.
To check if the answer is reasonable, you can estimate. Since 12/3 is just slightly over 1 and 31/2 is more than 3, you would expect the division result to be less than 1, which 10/21 is.
Learn more about Dividing Mixed Numbers