Babylonian mathematics
This free course looks at Babylonian mathematics. You will learn how a series of discoveries has enabled historians to decipher stone tablets and study the various techniques the Babylonians used for problem-solving and teaching. The Babylonian problem-solving skills have been described as remarkable and scribes of the time received a training far in advance of anything available in medieval Christian Europe 3000 years later. Author(s): Creator not set

This free course, Squares, roots and powers, reminds you about powers of numbers, such as squares and square roots. In particular, powers of 10 are used to express large and small numbers in a convenient form, known as scientific notation, which is used by scientific calculators.

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This OpenLearn course provides a sample of level 1 study in Author(s): The Open University

Except for third party materials and otherwise stated in the acknowledgements section, this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence.

Course image: russellstreet in Flickr made available under
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The rules for multiplying positive and negative numbers can be illustrated by the table below.

Multiplying a positive number by a positive number gives a positive answer.

Multiplying a negative number by a positive number gives a negative answer.

Multi
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Next consider subtraction of a negative number. In terms of Thomasâ€™s piggy bank, subtracting a negative number is the same as taking away one of his IOUs. If his mother says â€˜you have been a good boy today so Iâ€™ll take away that IOU for Â£3â€™ this is equivalent to him being given Â£3.

So, âˆ’ (âˆ’3) = 3. Does this correspond with the number line interpretation of subtracting a negative number?

Consider the evaluation of 8 âˆ’ âˆ’3. Continue to think o
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## Activity 56

Evaluate each of the following and give an example from everyday life to illustrate the sum (e.g. Thomas's piggy bank).

• (a) âˆ’4 âˆ’ 6

• (b
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How about other fractions? What is 6 Ã· ? This means how many Author(s): The Open University

## Activity 46

Evaluate each of the following.

• Author(s): The Open University

The same rules about the order of calculations apply to decimals as apply to whole numbers.

## Calculations are performed in the following order:

Brackets;

Powers (e.g. squaring or cubing a number);

Division and Multiplication (performed in the order written, left to
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## Activity 31

Insert brackets in the following calculations to emphasise the order in which a scientific calculator would perform them, then do the calculations by hand and on your calculator, with and without the bracke
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You may have noticed that sometimes the order in which calculations are carried out seems to matter and sometimes it does not. When using a calculator, it is very important to know the order in which it will do calculations. It is not always the order in which you enter them.

Although written English is read from left to right, this is not the case for all written languages (Chinese is read top to bottom, right to left). With mathematics, the order of the written operations does not alw
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Division is probably the most awkward of the four arithmetic operations. Since you may have a calculator, you do not need to be able to carry out complicated divisions by hand, but you do need to carry out simple divisions in order to check your calculator calculations. Division is the reverse process of multiplication. The quantity 12 Ã· 3 tells us how many times 3 goes into 12. Since 4 Ã— 3 = 12, 12 Ã· 3 = 4.

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## Activity 22

Carry out the following calculations, without using a calculator.

• (a) A million pound lottery prize minus a three hundred pound administrative charge.

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When you are adding or subtracting whole numbers, an important thing to keep in mind is the place value of the figures. It is often a good idea to set out the numbers in columns before doing the arithmetic.

## Example 11

• (a) There are 4
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In order to compare quantities, it is best to express them in the same units.

## Example 10

Three children have just measured their own heights in metric units. Isaac says â€˜My height is 1098â€™, Jasmine says â€˜My height is 112â€™ and Kim says â€˜Mine is 1.1â€™. What units were
Author(s): The Open University

The basic metric unit for capacity is the litre, usually denoted by the symbol l (though sometimes an uppercase L is used to avoid confusion with the number 1).

In the SI system, units such as cubic metres (m3), cubic centimetres (cm3) and cubic millimetres (mm3) are used. These two systems are linked because:

1 ml = 1 cm3

The animation below i
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The basic SI unit for length is the metre, abbreviation m.

The animation below illustrates how to convert between the most commonly used units of length, kilometres (km); metres (m); centimetres (cm); millimetres (mm) and micrometres (Î¼m).

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The basic SI unit for mass is the kilogram, symbol kg

The tonne (t) which is equivalent to 1000 kg and is a metric unit is often used alongside the SI units.

The animation below illustrates how to convert between the most commonly used units of mass, the metric tonne (t); the kilogram (kg); the gram (g); the milligram (mg) and the microgram (Î¼g).

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## Activity 17

A person's height is given as 1.65 m. What is this in centimetres?

1.65 m is 165 cm (multiply by 100).

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A great advantage of the metric system of units is that conversion between units within the system is particularly easy. For example, â€˜Â£1 is worth 100pâ€™ is converting one pound into pence. To convert pounds to pence, you multiply by 100. So Â£2 is 200p, and Â£2.63 is 263p. (Remember that to multiply by 100, you move the digits two places to the left in the place value table.)

To convert from pence to pounds, you need to reverse this process, i.e. to divide by 100 (moving the
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