3.19 Multiplication with negative numbers

Now that you have rules for addition and subtraction of negative numbers, think about multiplication and division.

## Example 27

Describe each of the following in terms of the number line and the value of Thomas's piggy bank:

(a) the mul

3.15.1 Subtraction on the number line

Now what about subtraction? You can think of subtraction as undoing addition: adding 3 to 8 gets you 11, and so subtracting 3 from the answer, 11, gets you back to 8. Therefore, in terms of the number line, subtracting 3 from 11 means starting at 11 and moving 3 units to the left.

## Activity 30

Carry out the following calculations, without your calculator.

(a) 3 Ã— (60 + 70).

(b) (3 Ã— 60) + 70.

(c) (70 âˆ’ 60) Ã· 5.

3.4 Did I make a rough estimate to act as a check?

When using a calculator many people have â€˜blind

## Question 1

Which of these triangles are similar?

There is another kind of symmetry which is often used in designs. It can be seen, for instance, in a car wheel trim.

Look at the trim on the left. It does not have line symmetry but

2.1 Geometric shapes – triangles

This section deals with the simplest geometric shapes and their symmetries. All of the shapes are two-dimensional â€“ hence they can be drawn accurately on paper.

Simple geometric shapes are studied in mathematics partly because they are used in thousands of practical applications. For instance, triangles occur in bridges, pylons and, more mundanely, in folding chairs; rectangles occur in windows, cinema screens and sheets of paper; while circles are an essential part of wheels, gears a

## Question 1

Find *Î³* and *Î´* in the following diagrams produced by a ship's navigator.

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

## Activity 1

A friend is painting the inside walls of a garage. So far she has used a 2 litre tin of emulsion paint and covered an area of 9 m^{2}. She needs some more paint. How much more would you advise her to

Ratios crop up often in official statistics. The government wants the teacherâ€“pupil ratio in schools to be increased to one teacher to thirty pupils or less. The birth rate has fallen: the ratio of children to women of child bearing age has gone down. It used to be 2.4 to 1, and now it is 1.9 to 1. Predictions for the ratio of working adults to retired adults is disturbing. Predictions are, that by 2030 the ratio will be two working adults to every retired person, instead of three to one no

School mathematics curricula often focus on lists of content objectives in areas like number, arithmetic, statistics, measurement, geometry, trigonometry, and algebra. A typical list of content objectives might contain over one hundred objectives to be introduced or revisited and learned each year. These can be seen as hierarchical in nature but many textbooks do not attempt to organise the objectives in ways that enable the bigger underpinning ideas to become apparent to the pupils. In addit

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.

- Author(s):

Environment: LA River

Who killed the river that runs through Los Angeles? Did you even know there was a river? Using a mix of archive and new footage , this album tells the fascinating story of a city that has ignored the benefits of its river for decades. Now waking up to the fact that it could be a green belt with more acreage than all of Central Park, river activists are fighting developers to bring back nature to central Los Angeles. Up till now the city conquered the threat of floods by concreting over the river

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Every generation faces challenges that previous generations could scarcely imagine. Twenty years ago, few people were talking about climate change, now it's one of the most hotly-contested areas in politics.
How do artists, writers, musicians and broadcasters respond when a new subject appears that is as large and significant as this? What kind of novels, plays, paintings, sculptures, movies and music begin to emerge?
â€˜Mediating Changeâ€™ is a four-part series, chaired by BBC Radio 4â€™s Que

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Who were our ancestors? How are apes and humans related? And where does the extinct Homo erectus fit into the puzzle? In this free course, Studying mammals: Food for thought, we will examine culture, tool use and social structure in both apes and humans to gain an understanding of where we come from and why we behave as we do. This is the tenth course in the Studying mammals series.
Author(s):

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Crude oil is currently our most important global source of energy. It is vital in the manufacture of many modern materials. But the worlds supply of oil is finite, its price is unstable and our reliance on oil has damaging environmental consequences. This free course, Living without oil, explains why developing alternatives to oil is an essential and urgent task for humanity.

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Commercial exploitation of nature, such as mining, fracking, or generating hydro-electric power, often damages the way the natural environment looks. What if the environment could be restored to exactly how it looked before? Would that mean that no damage had been done, that the natural environment was as valuable as it had been before the commercial exploitation? This free course, Exploring philosophy: faking nature, examines â€˜the restoration thesisâ€™, and provides an insight into philosophi

## Question 12

The writer and campaigner George Monbiot wrote the following (in *The Guardian Weekly*, 10 February 2000): 'Every time someone in the West switches on a kettle, he or she is helpting to flood Banglades

## Question 5

Information on the different albedos of various types of surface was given in Author(s):