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1.8 Simplest form of a fraction

The fraction , is the simplest form of all its equivalent fractions, because it cannot be ‘simplified’ further (by dividing top and bottom by the same whole number called a common factor<
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4.1 Understanding the question

Before you can attempt a question, you must read and understand it. This may sound obvious but you will need to know, before you start, what is expected by way of an answer. In particular, you will need to know the meaning of the instructions contained in the question. This section contains a discussion of the precise meanings attached to words like ‘find’, ‘show’, ‘write down’ and ‘determine’ in mathematics questions. The different types of instruction are illustrated by posi
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4.3 Making a plan

How you respond to this suggestion will depend on what sort of person you are. Many of us are great planners with timetables and lists for every part of our lives; others just get on with the priorities and everything else follows in due course. Planning is no guarantee everything will get done or that deadlines will be met, but the process of making a plan makes you focus on what the task entails and gives direction and purpose to your study. Studying does demand that most students need to p
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Introduction

This course considers the way that judges make law, how the common law system works and the advantages and disadvantages of a system like the British one that relies heavily on such rules and rule making. The course will set out the basic differences between ‘civil code’ systems and ‘common law’ systems, and consider the relationship between judge-made law and statutory law.

This OpenLearn course provides a sample of Level 1 study in
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3.14 Mixed numbers

In order to do arithmetic with mixed numbers like , it is often best to write them as a simple fraction, that is, one number over another.

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4 OpenMark quiz

Now try the quiz and see if there are any areas you need to work on.


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3.5 Several calculations and using brackets

Sometimes you may want to make several calculations in succession, and the order in which the calculations are performed may or may not be significant. For example, if you want to add 12 + 7 + 13, it makes no difference which of these two processes you adopt:

add the 12 and 7 first, to give 19, and then the 13, to give 32;

or

add the 7 and 13 first, to give 20, and then add this to 12 to give 32 again.

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4 OpenMark quiz

You might like to make some notes on the course for your own use later. Here is an example of a student's notes.

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Introduction to analysis
This free course is an introduction to analysis which looks at real numbers and their properties, with a particular emphasis on inequalities. Section 1 starts by revising rational numbers and their decimal representations. Then, real numbers are introduced as infinite decimals. Section 2 looks at rules for manipulating inequalities and finding the solution set of an inequality. Section 3 looks at various techniques for proving inequalities. Section 4 introduces the concept of a least upper bound
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Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

References

Hartley, T.C. (1998) The Foundations of European Community Law, Oxford, Oxford University Press, pp. 11–13.
Tempest, M. (2004) ‘EU leaders sign constitution’, Guardian, 29 October.
Wright, G. and Jeffrey, S. (2004) ‘Q&A: the European constitution’, Guardian, 26 March.

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6.5 The principle of subsidiarity

This is defined in Article 5(1) EC and 5(2) EC. It requires decision-making bodies with responsibility for larger areas to perform only those functions that decision-making bodies with responsibility for smaller areas cannot fulfil themselves. For instance, the Treaty requires the Community to take action ‘only if and in so far as the objectives of the proposed action cannot be sufficiently achieved by the Member States …’ and can ‘by reason of the scale or effects of the proposed act
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6 1 The relationship between EU law and domestic law

It is important to understand the relationship between EU law and the domestic (national) law of the EU member states. This is guided by a number of important principles.


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5.3.4 Recommendations and opinions

These have no binding force and therefore are ineffective as Community law. However, they can have ‘persuasive authority’. If a recommendation or opinion is ignored, it may later be followed up with a stronger legislative initiative, such as a decision or directive.

Activity 4 The EU law
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5.3.3 Decisions

A decision is an individual act emanating from an EU institution and addressing particular individuals, firms or EU member states. It is a legal tool designed to allow the Community institutions to order that a measure be taken in an individual case. The decision therefore, unlike the regulation or directive, is of individual application, and is binding only upon the persons to whom it is addressed.


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5.1 EU law

The main sources of EU law are:

  • EU primary legislation, represented by the treaties

  • EU secondary legislation, in the form of regulations, directives, decisions, recommendations and opinions

  • rulings on cases brought before the European Court of Justice.

EU law is created by the legislative powers with which the EU member states have invested the EU institutions. The law created by EU institutions is also bin
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3.2.1 Try some yourself

Activity 18

Write down the coordinates of the points A, B, C, D and E.

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3.3 HIV testing in sub-Saharan Africa

Example 3.2 HIV testing in sub-Saharan Africa

In developed countries, the standard method for testing whether a person is infected with the virus HIV, that causes AIDS, is to carry out a blood test. Provided such a test is carried out long enough after the initial infection occu
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1.2 Boxplot activity

Activity 1 Drawing a boxplot: chondrite meteors

5.10 Symmetry and skewness

For many purposes the location and dispersion of a set of data are the main features of its distribution that we might wish to summarise, numerically or otherwise. But for some purposes it can be important to consider a slightly more subtle aspect: the symmetry, or lack of symmetry, in the data.

Example 4: Fami
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