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.





For the 11+ and Independent School Entrance Exams, pupils need to be able to do the following percentage calculations:

  • Percentages to fractions
  • Percentages to decimals
  • Percentage of an amount
  • Increase/decrease an amount by a certain percentage
  • write one number as a percentage of another number
  • simple reverse percentages

This video shows you how to find a percentage of an amount.

We first work out 10% of the amount – divide by 10

To find 5% : divide the 10% by 2

To find 2 1/2 percent : divide 5%  by 2

To find 1% – divide the amount by 100.




Prior knowledge you need to have in order to work out the size of unknown angles in triangles are:

  • Angles on straight lines add up to 180°
  • Angles around a point add up to 360°
  • When two straight lines cross the opposite angles are equal

This video starts by looking at the properties of the different types of triangles like namely scalene, isosceles, equilateral and right-angled triangle. It then covers the following angle properties:

  • Interior angles of a triangle adds up to 180°
  • Exterior angles of a triangle equals the sum of the opposite interior angles