Operations with Fractions: Practice Questions

Calculate the result of the following and express it in its simplest form:
\( \frac{3}{8} \times \frac{4}{9} \div \frac{1}{6} \)

Calculate the value of the following expression:
\( 5\frac{1}{4} - (2\frac{2}{3} + \frac{5}{6}) \)

Evaluate the following expression and express the result in its simplest form:
\( \frac{5}{6} \times \left( 1\frac{1}{2} - \frac{3}{4} \right) \)

Calculate \( 2\frac{2}{3} + 1\frac{1}{4} \) and express the answer as a mixed number.

Evaluate \( 4\frac{1}{2} - 1\frac{2}{3} + \frac{5}{6} \) and express the answer as a fraction in its simplest form.

Calculate the value of \( 3\frac{1}{2} \div (\frac{3}{4} + \frac{1}{2}) \) and express the answer as a mixed number.

Calculate the following and express the result as a mixed number in its simplest form:
\( \left( 2\frac{1}{3} + 1\frac{3}{4} \right) \div \frac{7}{8} \)

A local charity organizes a fundraising marathon. (a) On the first day, the charity raises \(\frac{2}{9}\) of its total target amount. On the second day, it raises \(\frac{3}{5}\) of the remaining balance. What fraction of the total target is still left to be raised after the second day?

(b) If the amount raised on the second day was \(\$14,000\) more than the amount raised on the first day, calculate the total target amount for the fundraising marathon.