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3 Subtraction rules – order matters

It’s important to remember that subtraction has different rules from addition.

For example, when you add up numbers, it doesn’t matter what order you add them up in. So 6 + 4 is exactly the same as 4 + 6. The result is 10 in both cases.

But in subtraction, order matters. So 6 – 4 is different from 4 – 6.

With the first, you start with 6, subtract 4, and are left with 2.

But with the second you start with 4 and if you subtract 6, which is a bigger number, you a
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Learning outcomes

After studying this course, you should be able to:

  • subtract one number from another

  • subtract using decimals

  • practise your subtraction skills.


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4.2 Fractions

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 ÷ 4 = 1½
  • 6 ÷ 4 = 1.5

A fraction is really just another way of expressing a division because ½ means
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3 Division rules – order matters

An important thing to remember about division is that it has different rules from multiplication.

For example when you multiply two numbers together, it doesn’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 ÷ 4 is different from 4 ÷ 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
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3.1 Health personnel in Thailand

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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1.5 Summary

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.

Figure 1.8Author(s): The Open University

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5.8 Sample variance

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, …, 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
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5.1 Measures of location

Everyone professes to understand what is meant by the term ‘average’, 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 ‘a typical adult female in Britain is 160 cm tall’ would be understood by most people who heard it. Obviously not all adult females in Britain are the same
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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.


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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.

   1 + 2 × 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
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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).


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2.1 Using estimations

Approximations are most useful when it comes to making rough estimates –
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1.5 Significant figures

Sometimes it doesn’t make sense to round to a specific number of decimal places. If, say, you were calculating the cost of fencing at £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 × 185 × 0.3048. (Conversion of feet to metres was given in Author(s): The Open University

Examples

  • 1.   The condition ‘is equal to’ is a relation on any set of real numbers because, for any x, y in the set, the statement ‘x is equal to y’ is either definitely true or definitely false. This relation is usually denoted by the symbol =. For this relation, each real number in the set is related only to itself!

  • 2.   The condition ‘is less than’ is a relation on any set of real numbers, and we usually
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3.3 Operations in modular arithmetic

The Division Algorithm tells us that all the possible remainders on division by an integer n lie in the set

We denote this set by Author(s): The Open University

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2.1 What is a complex number?

We will now discuss complex numbers and their properties. We will show how they can be represented as points in the plane and state the Fundamental Theorem of Algebra: that any polynomial equation with complex coefficients has a solution which is a complex number. We will also define the function exp of a complex variable.

Earlier we mentioned several sets of numbers, including Author(s): The Open University

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Keep on learning

Study another free course

There are more than 800 courses on OpenLearn for you to
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