What is the quotient of 2 1/6 divided by 1 1/3? Simplify the answer, if possible.
To divide 2 1/6 by 1 1/3, we need to convert the mixed numbers into improper fractions.
To convert 2 1/6 into an improper fraction, we multiply the whole number (2) by the denominator of the fraction (6), and then add the numerator (1). This gives us (2 * 6) + 1 = 12 + 1 = 13. Therefore, 2 1/6 as an improper fraction is 13/6.
Similarly, to convert 1 1/3 into an improper fraction, we multiply the whole number (1) by the denominator of the fraction (3), and then add the numerator (1). This gives us (1 * 3) + 1 = 3 + 1 = 4. Therefore, 1 1/3 as an improper fraction is 4/3.
Now we can divide 13/6 by 4/3. To do this, we multiply the reciprocal of the divisor and multiply the numerators and denominators:
(13/6) / (4/3) = (13/6) * (3/4) = (13 * 3) / (6 * 4) = 39/24.
The quotient of 2 1/6 divided by 1 1/3 is 39/24. This fraction can be further simplified by finding the greatest common divisor (GCD) of the numerator and denominator.
The GCD of 39 and 24 is 3. Dividing both the numerator and denominator by 3 gives us:
39/24 = (39/3) / (24/3) = 13/8.
Therefore, the simplified quotient is 13/8.