A good knowledge of fractions is essential for the eleven plus and independent school entrance exams. A student must be familiar with the following topics:

  • Simplifying fractions (equivalent fractions)
  • Change fractions to decimals
  • Change fractions to percentages
  • Change improper fractions to mixed numbers
  • Finding a fraction halfway between two other fractions
  • Arrange fractions, decimals and percentages in order
  • Add fractions with different denominators
  • Subtract fractions with different denominators
  • Multiply fractions
  • Divide fractions
  • Finding a fraction of a known quantity
  • Fractions of unknown quantities


The accompanying video shows you how to work with fractions of unknown quantities. In these questions the student must first find the unit fraction (a fraction with a numerator of 1) and then find the whole number. (Divide everything by the numerator of the fraction and then times with the denominator of the fraction.)


The most difficult questions on Fractions of unknown quantities are problems like the following example.

I spend ½ of my money on food and 1/5 on games. This left me with £21 pounds in my pocket. How much money did I have at the beginning?

In this case, the student must first add ½ and 1/5, and then subtract it from 1 to find the fraction that is left. They then need to be able to find the unit fraction to work out the amount at the beginning.