Final answer:
To find the quotient of 2 4/9 divided by 1 1/3, convert to improper fractions, multiply by the reciprocal, and simplify to get the quotient of 11/6, or 1 5/6 as a mixed number.
Step-by-step explanation:
To determine the quotient of 2 4/9 divided by 1 1/3, first, convert the mixed numbers to improper fractions. For 2 4/9, multiply the whole number 2 by the denominator 9 and add the numerator 4 to get (2×9)+4 = 18+4 = 22, so the improper fraction is 22/9. For 1 1/3, do the same: (1×3)+1 = 3+1 = 4, so the improper fraction is 4/3.
To divide the fractions, remember the rule to multiply by the reciprocal of the second fraction. The reciprocal of 4/3 is 3/4. Now, multiply 22/9 by 3/4. When multiplying fractions, multiply the numerators and multiply the denominators: (22×3) / (9×4) = 66/36. To simplify this fraction, you can divide both the numerator and the denominator by their greatest common divisor, which is 6, resulting in 11/6. Thus, the quotient is 11/6, which is equal to 1 5/6 when converted back to a mixed number.