To find the quotient of two fractions, we need to divide the numerator of the first fraction by the numerator of the second fraction and divide the denominator of the first fraction by the denominator of the second fraction.
For the given fractions:
Numerator of the first fraction: 9
Numerator of the second fraction: 2
Denominator of the first fraction: 10
Denominator of the second fraction: 3
So, the quotient is calculated as follows:
Quotient = (Numerator of the first fraction / Numerator of the second fraction) / (Denominator of the first fraction / Denominator of the second fraction)
Quotient = (9/2) / (10/3)
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction.
Quotient = (9/2) * (3/10)
Next, multiply the numerators together and the denominators together:
Quotient = (9 * 3) / (2 * 10)
Quotient = 27 / 20
Therefore, the quotient of 9/10 and 2/3 is 27/20.