Introduction to algebra
This free course is an introduction to algebra which builds on the idea of using letters to represent numbers. Section 1 looks at finding, simplifying and using formulas and includes useful tips on learning algebra. Section 2 introduces some of the terminology used in algebra and techniques such as evaluating and checking equivalence of expressions, identifying terms in an expression and collecting like terms. Section 3 looks at how to simplify terms and introduces index notation and multiplying
Conclusion This free course provided an introduction to studying Mathematics. It took you through a series of exercises designed to develop your approach to study and learning at a distance and helped to improve your confidence as an independent learner.
3.21 Division rules Lastly consider division. Dividing 8 by 2 means ‘How many times does 2 go into 8?’ or ‘What must you multiply 2 by to get 8?’. The answer is 4. So to find 8 ÷ −2, you need to ask ‘What do I have to multiply −2 by to get 8?’. The answer is −4, since −2 × −4 = 8. So 8 ÷ −2 = −4. Similarly, to find −8 ÷ −2 you need to ask ‘what do I have to mul
3.14.1 Try some yourself Evaluate the following, giving your answer in its simplest form. 3.13.1 Try some yourself Evaluate each of the following. 3.4.1 Try some yourself Look at the rules in the boxes above. Write in your own words the rules for multiplying and dividing, adding and subtracting two numbers, giving an example of each. Try some yourself For each of the following shapes, indicate the fraction of the whole shape represented by the shaded parts: 1.7.1 Try some yourself The diagram below shows an oatmeal cake marked into 12 equal portions. I want to give my sister a third of the cake. Where could I cut the cake, and what would be left over? 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 1 Ways of expressing subtraction Another way to say ‘subtract one number from another’ is to say ‘one number minus another’. And the standard sign to show this is a minus sign, which looks like this ‘–’. The expressions ‘take away’ or ‘take from’ are also used to mean subtract or minus. So the following expressions all mean the same thing: 3.4 Guidelines for graphics Data in the form of counts of individual entities (for example, people, animals, power stations) in a small set of discrete categories can be presented in bar charts or pie charts. For most purposes, bar charts are preferable. Pie charts draw particular attention to the proportions in which the entities are split between the different categories. However, they do so by representing the proportions by angles, and even when the main interest lies in the propor 3.2 Health care personnel in Thailand: activities Would it be helpful, in considering possible changes in the way health care personnel are divided into the five categories listed, to recalculate th 5.6.3 Interquartile range for the SIRDS data For the 23 infants who survived SIRDS, the lower quartile is qL =1.720 kg, and the upper quartile is qU =2.830 kg. Thus the interquartile range (in kg) is qU – qL = 2.830 – 1.720 = 1.110. 5.6.1 Quartiles for the SIRDS data For the 23 infants who survived SIRDS, the ordered birth weights are given in Table 9. The first quartile is qL = x (¼(23+1)) = x (6) = 1.720kg. The third quartile is qU = x (¾ 5.4.2 Waiting times between geyser eruptions Figure 20 shows a histogram of waiting times, varying from about 40 minutes to about 110 minutes. 5.3 The mean The second measure of location defined in this course for a collection of data is the mean. Again, to be precise, we are discussing the sample mean, as opposed to the population mean. This is what most individuals would understand by the word ‘average’. All the items in the data set are added together, giving the sample total. This total is divided by the number of items (the sample size). 3.3.1 Try some yourself A friend has been quoted a price of £25.50 per square yard for tarmac surfacing of his yard. The yard measures 6 yards by 10 feet. Here is his calculation of the total cost. What is wrong with it? cost = Try some yourself Without using your calculator solve the following calculations. (a) 3 + 5 × 2 = ? (b) 12 − 6 + 6 = ? (c) 6 + (5 + Learning outcomes After studying this course, you should be able to: round a given whole number to the nearest 10, 100, 1000 and so on round a decimal number to a given number of decimal places or significant figures use rounded numbers to find rough estimates for calculations use a calculator for decimal calculations involving +, −, × and ÷, giving the answer to a specified accuracy (e.g. decimal places or significant figures) and checking the ans
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Activity 7 Health care personnel in Thailand: calculating percentages
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