Fractions, decimals and percentages: Practice Questions

A shopkeeper marks up the cost price of an antique vase by \( 40\% \). Later, he offers a discount of \( 25\% \) on this marked price. What is the shopkeeper\'s overall percentage profit or loss on the original cost price?

Work out the value of the following expression, giving your answer as a decimal:

\( \left( \frac{3}{5} + 0.25 \right) \div \frac{1}{2} \)

Express the recurring decimal \( 0.4\dot{7} \) as a fraction in its simplest form.

Convert the mixed number \( 3 \frac{1}{4} \) into a percentage.

A company's production quota increased from 3200 units last month to 4160 units this month. Calculate the percentage increase in production.

Write $$ \frac{7}{8} $$ as a decimal and a percentage.

Work out \( 2 \frac{1}{3} \div \left( \frac{1}{2} + \frac{1}{4} \right) \). Give your answer as a mixed number in its simplest form.

A water tank is \( \frac{3}{8} \) full. After adding \( 35 \) litres of water, the tank becomes \( \frac{2}{3} \) full. Calculate the total capacity of the tank in litres.

The population of City X is \( 200\,000 \) and is increasing at a compound rate of \( 5\% \) per year. The population of City Y is \( 250\,000 \) and is decreasing at a compound rate of \( 2\% \) per year.

(a) Calculate the population of City X after \( 3 \) years, to the nearest whole number.

(b) Calculate the population of City Y after \( 3 \) years, to the nearest whole number.

(c) Calculate the difference in population between the two cities after \( 3 \) years as a percentage of the original difference in population.

In a school library, \( 45\% \) of the books are fiction. Of the fiction books, \( \frac{2}{3} \) are novels and the rest are short stories.

(a) Calculate the number of short stories as a percentage of the total number of books in the library.

(b) There are \( 180 \) short stories in the library. Calculate the total number of books in the library.