In the previous sections you saw how to divide a big number by a small number up to 10. Things get harder if you want to do a division where both the numbers are big. This kind of calculation is called long division, probably because you write the steps of the calculation out on paper in a long sequence.

The principle of doing long division is the same as when you divide by a number up to 10. The only difference is that, because the numbers involved in long division are usually too big
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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.

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In this unit, you have been introduced to a number of ways of representing data graphically and of summarizing data numerically. We began by looking at some data sets and considering informally the kinds of questions they might be used to answer.

An important first stage in any assessment of a collection of data, preceding any numerical analysis, is to represent the data, if possible, in some informative diagrammatic way. Useful graphical representations that you have met in this unit i
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The median describes the central value of a set of data. Here, to be precise, we are discussing the sample median, in contrast to the population median.

## The sample median

The median of a sample of data with an odd number of data values is defined to be the middle value of t
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In this subsection we consider, briefly, some problems that can arise with certain ways of drawing bar charts and pie charts.

Figure 5 shows what is essentially the same bar chart as Author(s): The Open University

In several different parts of the world, footprints from prehistoric human civilisations have been found preserved in either sand or volcanic ash. From these tracks it is possible to measure the foot length and the length of the stride. These measurements can be used to estimate both the height of the person who made the footprint and also whether the person was walking or running by using the following three formulas:

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

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Discount can be calculated in the same way as an increase by a percentage. For example, Â£8 with 15% discount means you actually pay

Â Â Â£8 less (15% of Â£8)

Â Â 15% of 8 = Ã— 8 = Author(s): The Open University

• (a) How much will this tennis racquet cost if VAT at Author(s): The Open University

Our everyday experience of percentages includes percentage increases (like VAT at %, or a service charge of 15%) and percentage decreases (such as a discount of 15%).

For example, Â£8 plus Author(s): The Open University

Fractions and decimals can also be converted to percentages, by multiplying by 100%.

So, for example, 0.17, 0.3 and can be expressed as percentages as follows:

Â Â 0.17 Ã— 100% = 17%;

Â Â 0.3 Ã— 100% = 30%;

Â Â Author(s): The Open University

1 Express each of the following percentages as fractions:

• (a) 40%

• (b) 8%

• (c) 70%

• (d)
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Percentages are used, particularly in newspaper articles, to indicate fractions (as in â€˜64% of the population votedâ€™) or to indicate changes (as in â€˜an increase of 4%â€™).

Percentages often indicate proportions. For example, labels in clothes indicate the various proportions of different yarns in the fabric. â€˜Per centâ€™ means â€˜per hundredâ€™ and is denoted by the symbol %. 100% is the same as the whole, or one hundred per hundred.

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1 A piece of computer software is to be developed by a team of programmers. It is estimated that a team of four people would take a year. Which of the following times is the length of time taken by three programmers?

Â Â A 1 year
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In Section 2.2 you saw that direct proportion described relationships between two quantities, where as one increased, so did the other. Sometimes as one quantity increases the other decreases instead of increasing. This is called indirect proportion. Team tasks are often an example of this. The time taken to do a job is indirectly proporti
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1 A recipe for four people calls for
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In a recipe the quantity of each ingredient needed depends upon the number of portions. As the number of portions increases, the quantity required increases. The quantity per portion is the same. This is called direct proportion. The quantity is said to be directly proportional to the number of portions. If 2 potatoes are required for one portion, 4 will be required for two portions etc. A useful method for direct proportion problems is to find the quantity for one and multiply by the
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Proportion is another way of expressing notions of part and whole. You might say that the proportion of village inhabitants who are children is a quarter, or that the proportion of fruit juice in the punch is two thirds, or that the proportion of sand in the concrete is three quarters.

All these examples involve the fractions Author(s): The Open University

1 Which is greater, 1.2 minutes or 70 seconds?