To multiply 2/3 by 1 1/4, we first need to convert 1 1/4 to an improper fraction.
To do so, we multiply the whole number, which is 1, by the denominator, which is 4. Then we add the numerator, which is 1, to the result.
1 * 4 + 1 = 4 + 1 = 5
Therefore, 1 1/4 is equivalent to 5/4.
Now, we can multiply 2/3 by 5/4:
(2/3) * (5/4) = (2 * 5) / (3 * 4) = 10/12.
To simplify this fraction, we can divide the numerator and denominator by their greatest common divisor, which is 2.
(10/12) ÷ 2/2 = 5/6.
The simplified form of 2/3 multiplied by 1 1/4 is 5/6.