Question: e) \(4.8 \div \frac{33}{4}\)

Solution

To solve the problem \(4.8 \div \frac{33}{4}\), follow these steps: First, understand that dividing by a fraction is equivalent to multiplying by its reciprocal. So we need to multiply \(4.8\) by the reciprocal of \(\frac{33}{4}\). The reciprocal of \(\frac{33}{4}\) is \(\frac{4}{33}\). Rewrite the division as a multiplication: \[ 4.8 \div \frac{33}{4} = 4.8 \times \frac{4}{33} \] Next, convert \(4.8\) to a fraction to make the multiplication easier. \(4.8\) is equal to \(\frac{48}{10}\). Multiply the fractions: \[ \frac{48}{10} \times \frac{4}{33} = \frac{48 \times 4}{10 \times 33} \] Calculate the multiplication in the numerator and the denominator: \[ = \frac{192}{330} \] Simplify the fraction by finding the greatest common divisor (GCD) of \(192\) and \(330\), which is \(6\): \[ = \frac{192 \div 6}{330 \div 6} = \frac{32}{55} \] So, the answer is \(\frac{32}{55}\).