explain the terms surface, surface in space, disc-like neighbourhood and half-disc-like neighbourhood;

explain the terms n-fold torus, torus with n holes, Möbius band and Klein bottle;

explain what is meant by the boundary of a surface, and determine the boundary number of a given surface with boundary;

construct certa]]> By the end of this unit you should be able to:

• explain the terms surface, surface in space, disc-like neighbourhood and half-disc-like neighbourhood;

• explain the terms n-fold torus, torus with n holes, Möbius band and Klein bottle;

• explain what is meant by the boundary of a surface, and determine the boundary number of a given surface with boundary;

• construct certa]]> If the numbers you want to divide are too large for you to do the calculation in your head, you can use a calculator. Alternatively, you can do the calculation on paper. In the example below, click on each step in turn to see how to divide 126 by 6.

  Active content not displayed. This content requires JavaScript to be enabled, and a ]]> If the numbers you want to divide are too large for you to do the calculation in your head, you can use a calculator. Alternatively, you can do the calculation on paper. In the example below, click on each step in turn to see how to divide 126 by 6.

  Active content not displayed. This content requires JavaScript to be enabled, and a ]]> Now that you’ve learned how to do subtraction on paper, you might want to practice your new skills.

  To practice subtracting whole numbers, including borrowing where necessary, go to the Practice Subtracting  section of the Numbers website and click on Get sum. Then follow the instructions.

  To practise subtracting decimals, go to the Now that you’ve learned how to do subtraction on paper, you might want to practice your new skills.

  To practice subtracting whole numbers, including borrowing where necessary, go to the Practice Subtracting  section of the Numbers website and click on Get sum. Then follow the instructions.

  To practise subtracting decimals, go to the How do you write mathematics that can be read and easily understood by anyone else, such as a tutor or another student?

  It takes practice, but the following guidelines may be helpful.

  • Ensure that what you write consists of sentences. Too many people believe that mathematics is a language which is entirely made up of unfamiliar symbols. It is not. Many symbols act in part merely as abbreviations which, when read, can be translated back into spoke]]> How do you write mathematics that can be read and easily understood by anyone else, such as a tutor or another student?

    It takes practice, but the following guidelines may be helpful.

    • Ensure that what you write consists of sentences. Too many people believe that mathematics is a language which is entirely made up of unfamiliar symbols. It is not. Many symbols act in part merely as abbreviations which, when read, can be translated back into spoke]]>

      1 For each of the following calculations make suitable rough estimates before doing the calculation on your calculator and check the result.

      • (a) 22.12 ÷ 4.12

      • (b) 0.897 × ]]>

        1 For each of the following calculations make suitable rough estimates before doing the calculation on your calculator and check the result.

        • (a) 22.12 ÷ 4.12

        • (b) 0.897 × ]]> A directive is a Community act which ‘shall be binding, as to the result to be achieved, upon each Member State to which it is addressed, but shall leave to the national authorities the choice of form and methods’. A directive therefore has to be implemented by each EU member state through its own domestic legislative process. After the enactment of a directive, the EU member states will generally be given a period of time within which to bring their domestic law in line with the objectiv]]> A directive is a Community act which ‘shall be binding, as to the result to be achieved, upon each Member State to which it is addressed, but shall leave to the national authorities the choice of form and methods’. A directive therefore has to be implemented by each EU member state through its own domestic legislative process. After the enactment of a directive, the EU member states will generally be given a period of time within which to bring their domestic law in line with the objectiv]]> International human rights are part of a much wider area, public international law, which in broad terms encompasses law relating to the legal rights, duties and powers of one nation state in relation to its dealings with other nation states. These rights, duties and powers are set out in international treaties or conventions. Such treaties and conventions may be global in their application or restricted to certain regions of the world. Reference to a work on international human rights treati]]> International human rights are part of a much wider area, public international law, which in broad terms encompasses law relating to the legal rights, duties and powers of one nation state in relation to its dealings with other nation states. These rights, duties and powers are set out in international treaties or conventions. Such treaties and conventions may be global in their application or restricted to certain regions of the world. Reference to a work on international human rights treati]]> Activities 5, 8 and 9 allowed you to demonstrate numeracy skills by performin]]> Activities 5, 8 and 9 allowed you to demonstrate numeracy skills by performin]]>