Divide and express the quotient using a vinculum: \[ 22 \div 0.75 \]

To divide 22 by 0.75, we start by converting the division into a multiplication by the reciprocal of 0.75. First, we can express 0.75 as a fraction: \( 0.75 = \frac{3}{4} \). To find the reciprocal, we flip the fraction: \( \frac{4}{3} \). Now, we can rewrite the division: \[ 22 \div 0.75 = 22 \times \frac{4}{3} \] Now, we can write 22 as a fraction, which gives us: \[ 22 = \frac{22}{1} \] So the multiplication becomes: \[ \frac{22}{1} \times \frac{4}{3} = \frac{22 \times 4}{1 \times 3} = \frac{88}{3} \] Thus, the quotient is \( \frac{88}{3} \). To express this using a vinculum, we write it as: \[ \overline{88} \, / \, 3 \] This way, you clearly denote the division with a vinculum!