1.4.1 Try some yourself

Activity 5

Convert each of the following fraction ratios to decimal ratios.

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1.4 Converting ratios from fractions to decimals

Although ratios are often given as fractions, they can also be expressed as decimals. You need to deal with a mixture of fractions and decimals, and to compare ratios given in either form, so you need to be able to convert between the two forms.

Example 4

The ratio of the circ
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1.2 Expressing ratios

To make short crust pastry, one recipe book says ‘use one part of fat to two parts of flour’; another recipe says ‘use fat and flour in the ratio of one to two’; and yet another says ‘use half as much fat as flour’. These are different ways of expressing the same ratio. Ratios are often expressed as fractions. So in this case:

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Learning outcomes

After studying this course, you should be able to:

  • work with simple ratios

  • convert between fractions, decimals and percentages

  • explain the meaning of ratio, proportion and percentage

  • find percentages of different quantities

  • calculate percentage increases and decreases.


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References

Ahmed, A. (1987) Better Mathematics, London, HMSO.
DfEE (2001) Key Stage 3 National Strategy: Framework for Teaching Mathematics: Years 7, 8 and 9, London, DfEE.
NCTM (1989) Curriculum and Evaluation Standards for School Mathematics Reston VA, National Council of Teachers of Mathematics.

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Keep on learning

Study another free course

There are more than 800 courses on OpenLearn for you t
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Conclusion

In this course you have been introduced to the difference between mathematical content and processes. You have worked on the do–talk–record (DTR) framework for learning mathematics.


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1.2.3 Process

Mathematical processes are different from content in that they overarch the subject and are not thought of as hierarchical. A list of processes could contain:

  • problem-solving (including investigating);

  • mathematical modelling;

  • reasoning;

  • communicating;

  • making connections (including applying mathematics); and

  • using tools.

Each of the six processes listed here repre
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1.1 Experiences of learning mathematics

You will come to this course with many memories of mathematics, both as a teacher and a learner. It may help if you start by recalling memories of learning mathematics and making a record of them in your notebook.

When you work on a task, get into the habit of having your notebook to hand to record your thinking. Use the notebook in any way that helps you to think about the work you have done. Some people find it helpful to divide a page into two columns using the left-hand side to reco
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5 Approaches to problem solving

You should not expect always to be able to read a problem and then just write down the answer. When you are faced with a written mathematical question or problem to solve, read it carefully. It is important that you get to grips with the question in two ways: first, that you absorb the information given; and second, that you find out what the question is really asking. Your solution will link the two. This method can be summarised by the following questions.

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