Fractions (Mixed arithmetic operations): Practice Questions

Evaluate the following mixed operation with fractions:
\( (\frac{5}{6} + \frac{1}{3}) \times \frac{6}{7} \)

Evaluate the following expression and simplify your answer to a mixed number:
\( 2\frac{1}{2} - (\frac{1}{3} + \frac{5}{12}) \)

Calculate the value of the following mixed operation:
\( 3\frac{1}{5} - (1\frac{1}{2} + \frac{3}{10}) \)

Evaluate the following expression:
\( \frac{3}{5} \times (\frac{1}{6} + \frac{1}{2}) \)

Add the following fractions: \(\frac{2}{5} + \frac{3}{10}\)

A container holds \( \frac{3}{10} \) kg of salt and another container holds \( \frac{4}{15} \) kg of salt. What is the total mass of salt in the two containers in kg?

Calculate the value of the following expression and express the answer as a mixed number in its simplest form:
\( 4\frac{2}{3} - ( 1\frac{1}{2} + \frac{5}{9} ) \)

Evaluate the following expression and express the answer as a mixed number:
\( ( 2\frac{2}{3} - \frac{1}{6} ) \div 1\frac{1}{4} + \frac{2}{5} \)

A piece of ribbon is \( 5 \frac{3}{4} \) metres long. Sarah uses \( 2 \frac{1}{2} \) metres for a gift and \( \frac{5}{8} \) metres for a hair tie. How much ribbon does Sarah have left in metres?

A garden water tank is \( \frac{7}{8} \) full of rainwater. On Monday, the gardener used \( \frac{1}{5} \) of the tank's total capacity to water the vegetables. On Tuesday, he used another \( \frac{1}{4} \) of the tank's total capacity to water the flowers.
a) What fraction of the tank's total capacity was used over the two days?
b) What fraction of the tank is left full at the end of Tuesday?
c) If the total capacity of the tank is 400 litres, how many litres of water are remaining in the tank?