If you want to subtract without using a calculator, you need to know off by heart what you get if you subtract any number up to 10 from any bigger number up to 20. All the possible combinations are shown in the table below.

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Now that youâ€™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
Author(s): The Open University

Subtracting whole numbers such as 52 from 375 is fairly straightforward. Subtracting decimal numbers such as 6.892 from 223.6 uses the same process but with one extra step â€“ you have to line the decimal points up first.

Rather than arranging your two numbers so that they line up on the right-hand side, you need to line up the decimal points, regardless of how many numbers there are after the decimal point. In the example below, the top number has one number after the decimal point. It
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If the digit at the top of any column in your subtraction is smaller than the digit at the bottom of the same column, you need to borrow (or carry) from the next column on the left.

There is an example of this below. Click on each step in turn to see how to carry out the calculation.

Active content not displayed. This content req
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If the numbers you want to subtract 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.

Write your starting number at the top with the number you want to subtract from it underneath. Because the order in which you subtract one number from another matters, it is important to put the correct numbers on top and bottom. Then draw a line underneath.

Write the numbers so the digits form columns and they
Author(s): The Open University

After studying this course, you should be able to:

• subtract one number from another

• subtract using decimals

• practise your subtraction skills.

Author(s): The Open University

Instead of putting the two left over biscuits back in the tin, you might instead decide to break them into halves and then give one of the resulting four halves to each person so that everyone receives a total of one and a half biscuits. In this case, the answer has to be expressed as a fraction or the equivalent decimal number:

• 6 Ã· 4 = 1Â½
• 6 Ã· 4 = 1.5

A fraction is really just another way of expressing a division because Â½ means
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An important thing to remember about division is that it has different rules from multiplication.

For example when you multiply two numbers together, it doesnâ€™t matter what order you multiply them in. So 8 x 4 is exactly the same as 4 x 8. The result is 32 in both cases.

But in division, order matters. So 8 Ã· 4 is different from 4 Ã· 8.

The answer to the first is 2. If you multiply 4 by 2 you get 8.

But the answer to the second is 0.5 (a half). If you multiply 8 by
Author(s): The Open University

There are practically no new theories or new principles in this section. We shall work through some examples, and you will see how basic techniques and approaches that you have already learned can be combined to allow you to use tabular data efficiently.

## Example 3.1 Health personnel in Thailand

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In this section you have been introduced to the boxplot. This is a graphic that represents the key features of a set of data. A typical boxplot is shown in Figure 1.8.

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It is worth noting that a special term is reserved for the square of the sample standard deviation: it is known as the sample variance.

## The sample variance

The sample variance of a data sample x 1, x 2, â€¦, xn
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5.6 Quartiles and the interquartile range

The first alternative measure of dispersion we shall discuss is the interquartile range: this is the difference between summary measures known as the lower and upper quartiles. The quartiles are simple in concept: if the median is regarded as the middle data point, so that it splits the data in half, the quartiles similarly split the data into quarters. This is, of course, an over-simplification. With an even number of data points, the median is defined to be the average of the middle two: de
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5.2.2 Birth weights of infants with SIRDS

The data in Table 3 are the birth weights (in kg) of 50 infants suffering from severe idiopathic respiratory distress syndrome. There are two groups of infants: those who survived the condition (there were 23 of these) and those who, unfortunately, did not. The data have not been sor
Author(s): The Open University

5.1 Measures of location

Everyone professes to understand what is meant by the term â€˜averageâ€™, in that it should be representative of a group of objects. The objects may well be numbers from, say, a batch or sample of measurements, in which case the average should be a number which in some way characterises the batch as a whole. For example, the statement â€˜a typical adult female in Britain is 160 cm tallâ€™ would be understood by most people who heard it. Obviously not all adult females in Britain are the same
Author(s): The Open University

2.3 Infants with SIRDS

The data in Table 3 are the recorded birth weights of 50 infants who displayed severe idiopathic respiratory distress syndrome (SIRDS). This is a serious condition which can result in death.

## Author(s): The Open UniversityLicense informationRelated contentCopyright Ã‚Â© 2016 The Open University

3.2 Have I used the correct order for my calculation?

When calculating an answer it is important that you give careful consideration to the order of operations used in the calculation. If you are using a mixture of operations remember that certain operations take priority in a calculation. Consider the following, apparently, simple sum.

Â Â Â 1 + 2 Ã— 3 = ?

What answer would you give?

Did you give 7 as your response, or 9?

The correct answer is 7 but can you explain why?

If you have a calculator handy, check that it
Author(s): The Open University

2.1.1 Try some yourself

## Activity 14

Measurement of a ceiling gives a length of 6.28 m and a width of 3.91 m.

• (a) Make a rough estimate of the area of the ceiling (the length times the width).

Author(s): The Open University

2.1 Using estimations

Approximations are most useful when it comes to making rough estimates â€“
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1.5 Significant figures

Sometimes it doesnâ€™t make sense to round to a specific number of decimal places. If, say, you were calculating the cost of fencing at Â£10.65 per metre, for a garden boundary, the length of which had been given to you as 185 feet, then you would want to multiply 10.65 Ã— 185 Ã— 0.3048. (Conversion of feet to metres was given in Author(s): The Open University