Rational numbers are a major category of numbers which can be expressed exactly in terms of a numerator and a denominator of arbitrary integral values. Whole numbers are a subset of these in which the denominator is exactly one - and is therefore usually not written down!
This document describes the exercises on this site which deal with rational numbers and provides an index to the individual exercises in each of the groups below.
Each of the exercises in the following groups contains 20 individual examples to be worked through. Where available separate answer sheets are also linked to from the corresponding exercise.
- Factorisation - this is the first of two groups of preliminary exercises designed to introduce the basic activities involved in handling rational numbers which are not already covered in the whole number arithmetic exercises. This group only contains five exercises which are themselves introductory to the normalisation group which follows.
- Normalisation - this second preliminary group of
exercises is provided to give practice in normalising rational numbers from
the form which may result from some earlier evaluation of an involved
expression - having already attempted all of the previous group of
facctorisation exercises. All answers to all exercises in this and other
groups below are expected to be given in normalised form - ie there are no
common prime factors in numerator and denominator!
- Two digits, one factor - answers.
- Three digits, two prime factors - answers.
- Four digits, up to three prime factors - answers.
- Additive numerators - common factors - answers.
- Additive numerators, different factors - answers.
- Additive denominators - common factors - answers.
- Additive denominators, different factors - answers.
- Numerator expressions - answers.
- Denominator expressions - answers.
- Mixed expressions - answers.
- Multiplication - rational number multiplication - NOT YET AVAILABLE!
- Division - division of rational numbers - no modulus or remainder operations are available for rational number arithmetic here - NOT YET AVAILABLE!
- Addition - the use of addition operators with rational numbers! - NOT YET AVAILABLE!
- Subtraction - simple subtraction of rational numbers - NOT YET AVAILABLE!
- Expressions - a range of expressions involving rational and whole numbers using all kinds of valid arithmetic operator - NOT YET AVAILABLE!
