**LANDLORD **– (noun) See LET.

**LATERAL** – (adjective) means side. For examples of lateral surfaces see diagram 33.

**LATITUDE **– (noun) 1. In normal use, latitude means freedom to do things without strict rules or boundaries. “When he went to university he had much more latitude for his abilities. The father did not trust his son so he did not give him much latitude. ” 2. In geography latitude is used to locate places on the surface of the earth. The equator is called 0 degrees. The parallel circles above and below the equator that are approximately 110 km apart are called degrees of latitude. Look up LONGITUDE as well. If you know the latitude and longitude of a place then you can find its exact position on a map. Get your teacher to demonstrate this to you. See diagram 53.

**LAW** – (noun) When people live together they have to agree on what is right and what is wrong. For example if it was alright to take someone else’s things then no one would be able to live properly because he would never be sure that he would have the things that he needs to survive. See SURVIVE. What people agree is wrong, like to steal and to kill, is made into ‘law’ by the government of the people of a country. If someone breaks the law he will be taken to court where he has a chance to show that he did not do what he is accused of. See ACCUSE. If he is found to be innocent then he goes free. See INNOCENT. If he is found guilty then he will have to go to prison or pay a fine. See GUILTY & FINE.

**LAWYER **– (noun) A lawyer is a person who has studied the law and whose job it is to give people advice about the law. “When he could not get the man to pay him the money he went to see his lawyer for advice on what he should do.” When legal documents are needed like when a house is sold one uses a lawyer to draw up the document. See LEGAL & DOCUMENT.

**LEAVE** – (verb) 1. Leave means to go away. When are you leaving? 2. Leave also means to allow to stay in a particular condition. See PARTICULAR & CONDITION.” It is hot, please leave the door open. Leave the cup on the table. Do not leave you r school books behind”. 3. – (noun) Leave is also the name of the time a workman gets when he does not have to work and can have a holiday. He has his two weeks leave in January. 4. Leaves is the plural of a leaf that you get on a tree. “The wind blew all the leaves off the trees.

**LEDGER** – (noun) A ledger is a book that is used to keep a final record of all transactions in a business. See TRANSACTION & BOOKKEEPING.

**LEFT** 1. – (noun) Left means the side where West is when you face North. See POINTS OF THE COMPASS. When you face North, West will be on your left side and East on your right side. South will be behind you. See diagram 39. 2. – (verb) Left is also the past of leave. See LEAVE.

**LEGAL** – (adjective) means according to the law. See ACCORDING TO. “It is not legal to take someone’s money away from him. He gave me good legal advice which enabled me to avoid paying a parking fine. ” See DOCUMENT.

**LEND** – (verb) means to let someone have something of yours that he will have to give back to you sometime later. “I will lend you a book. Please lend me some money. ” The past of lend is lent. “ Yesterday he lent me this book, but I will give it back today.

**LENGTH** – (noun) The length of something is its distance from one end to the other.” The length of this book is 15 cm.

**LESSEN** – (verb) means to get smaller or less in amount or size.” After some time the heavy rain lessened to a drizzle. After the sun goes down the heat will lessen. The bright light will lessen as evening comes.

**LESSON **– (noun) A lesson is anything that is learned or taught. “He is having extra English lessons. The teacher gave us a lesson on Maths. When he burnt his finger on the kettle it taught him a lesson not to play near hot things.

**LESS THAN **means something is smaller than something else. See INEQUALITIES. “15 is less than 20.

**LET** – (verb) 1. Let means to allow. “Please move out of the way and let me get through. She would not let him kiss her. “2. Let also has a meaning to do with houses. If you own a house that you do not live in then if you allow another person to live in it and if they pay you some money each month then you say you let the house to them. The person who owns the house is called the landlord. The person who pays the money rents the house. The amount of money he pays each month is called the rent. He is called the tenant. Examples: “He is my landlord and I am his tenant. He lets me the house for a rent of R200 each month.

**LEVER **– (noun) A lever is a rigid bar used to move heavy objects. See BAR, RIGID & FULCRUM. See Diagram 38.

**LIABLE –** (adjective) 1. Liable means likely or possible. See LIKELY & POSSIBLE. “High mountains are liable to have snow on them in winter. A person who drives a car after drinking a lot of beer or wine is liable to have an accident. “2. Liable also means to be responsible especially according to the law. “ A person who causes an accident is liable to pay for the cost of the repairs to the damages he caused. ” See DAMAGE.

**LIABILITY **– (noun) In business a liability is something you owe or must pay. It is the opposite of asset. See OPPOSITE. “A debt is a liability.” See DEBT.

**LIKELY** – (adverb) to happen means that there is a good chance that that will happen. “Cold weather is likely in winter. You are likely to feel tired after climbing that high mountain.

**LIMIT **– (verb) 1. Limit means to stop something going more than a certain point. See CERTAIN. “You must limit your speed to 80 kilometres per hour or you will have to pay a speeding fine.” See FINE. 2. – (noun) A limit means a certain point beyond which one should not go or cannot go for some reason. “The speed limit is 120 kph on this road. The limits of the field are shown by a fence. “3. In maths limit means a value towards which a mathematical sequence approaches, but never exceeds. For example the limit of the sequence for the natural logarithm e is 2,718182 – (to 6 decimal places). See ‘#>e #.

**LIMITED** 1. Limited means kept down in amount. “The dog was tied with a long piece of rope which gave him limited “- (adjective)” freedom. The children were limited “- (verb)” to one piece of cake each. ” 2. When the word limited is used to do with a business it means that if the business does not do well and a lot of money is owed then the amount of money that has to be paid is limited to a certain amount. See PROPRIETARY LIMITED COMPANY.

**LINE **– (noun) 1. In maths the word line usually means a straight line. 2. A straight line is the shortest distance between two points. When you want to draw a straight line on a piece of paper you usually use a ruler – (also called a straight edge) and a pen or a pencil.

**LINEAR EQUATION **– (noun) A linear equation is an equation the graph of which is a straight line. y = ax + c is the formula for a linear equation. Try plotting the graph from this equation for x = 1, x = 2 and x = 3 given that the values of a is 2 a nd c is 3. A linear equation is an equation which is a polynomial equation which has the unknowns to the power 1 – (to the degree 1). For example 4x + 6y = 5 is a linear equation. See POLYNOMIAL, POWER & DEGREE.

**LINE SEGMENT **– (noun) A line segment is part of a line between two points on that line. See diagram 49. Segment has another meaning in maths. See definition at SEGMENT.

**LIQUID** – (noun) 1. Liquid means something that will flow like water. “Oil is a thick liquid. It flows slowly. Petrol and water are” “also liquids. “ 2. Liquid can also be used as an adjective meaning flowing like water. “Petrol is more liquid than oil.” See FLOW. 3. When used to do with money liquid has a special meaning. When you talk about Liquid Assets – (See ASSET) you mean assets that are cash or can easily be sold and turned into cash. Cash in the bank, gold coin, money on short term deposit – (See TERM), stock of a kind that is easy to sell would all be called Liquid Assets. Money loaned to someone who cannot quickly pay you back, Buildings, Plant and Equipment, raw materials of a kind that are not easily sold would not be called Liquid Assets.

**LITERAL** – (adjective) means according to the exact meanings of the words used. The literal meaning of ‘He is a very big man,’ is exactly what these words mean. However if you say ‘He is as heavy as a horse’ you also mean that he is a very big man, but you cannot take the literal meaning because no man is as heavy as a horse.

**LITRE **– (noun) A litre is a measure of volume. “A litre of petrol is enough for your car to reach home.

**LOAN** – (noun) A loan is an amount of money that is lent to someone. “I am going to the Building Society to get a loan to buy this house. “ A loan has to be repaid. See LEND.

**LOCATE** – (verb) 1. Locate means to find the place of something. “Look at the map and locate Johannesburg.” 2. It also means to put in a place. “He decided to locate his shop in the main street.

**LOCATION **– (noun) means a place where something is.” What is the location of Johannesburg? Johannesburg is in the Southern Transvaal.

**LOCUS** – (noun) A locus is a set of points which satisfies one or more conditions. For example a circle is a locus of all the points which are equidistant from a fixed point which is called its centre. All the points make up a curved line which is called a circle. The condition here is that all the points must be the same distance from the centre point. That distance is called the radius. See diagram 34. See EQUIDISTANT & CONDITION. What would be the locus of the points that are all the same distance from a straight line?

**LOG** – (noun) is short for logarithm.

**LOG TO THE BASE OF**: See LOGARITHM.

**LOGARITHM **– (noun) First look up the word EXPONENT. In the following table the first two columns are two different ways of writing the same numbers. Look at the first number 1000. 1000 is equal to 10 cubed which is written 10&>3 &>. 100 is written 10&>2 &> & so on. You will see that you can also express numbers less than 1 in this way. 0,01 is 10&>-2 &> for example. The rule is that the minus exponent is one more than the number of zeros on the right hand side of the decimal comma. Now the logarithm of a number to the base 10 is the number of times that 10 must be multiplied together to give that number. So you will see that the logarithm to the base 10 of 1000 is 3. This is shown in a shortened form in column 3. You will also see that the logarithm to the base 10 of 100 is 2 and the log to the base 10 of 0,01 is -2 and so on.

852,9025>It is possible to find the logarithms of numbers between these numbers – (between 1 and 10 or 10 and 100 and so on) This you will learn in your arithmetic class. You use tables of values to look up the logarithms of different sized numbers and the antilogs.

2272,9025>The numbers we use in our daily life are based on 10, but you can use numbers with a different base. An important set of numbers is those based on 2 because these are the numbers that a computer works with. For example 16 is 2&>4 &> . So you would say the logarithm of 16 to the base 2 is 4. This written log’>2 ‘>16 = 4. If 125 = 5&>3 &> , then what is the logarithm of 125 to the base 5? Logs are the same in algebra. In the expression a&>b &> = c, the logarithm of c to the base a is b. The short way of writing this is log’>a ‘> c = b. The opposite of a logarithm is an antilogarithm. In the above examples the antilogarithm of 3 is 1000 and the antilog of -2 is 0,01. When you see a logarithm written without a base then you can assume it is to the base 10.

**NUMBER EXPONENTIAL FORM LOGARITHM**

1000 10&>3 &> log’>10 ‘>1000 = 3

100 10&>2 &> log’>10 ‘>100 = 2

10 10&>1 &> log’>10 ‘>10 = 1

1 10&>0 &> log’>10 ‘>1 = 0

0,1 10&>-1 &> log’>10 ‘>0,1 = -1

0,01 10&>-2 &> log’>10 ‘>0,01 = -2

0,001 10&>-3 &> log’>10 ‘>0,001 = -3

To mutiply 2 numbers using logs you find their logs, using a book containing log tables, add them together and then find the antilog. To divide one number by another you subtract the log of the number you are dividing by from the log of the other number and look up the antilog of the difference. You will learn how to do this in your arithmetic class. See Appendix II.11.

**LOGARITHMIC EQUATION **– (noun) A logarithmic equation is an equation involving a logarithm of the unknown. For example log(x + 1) – log(x – 3) = 6 is a logarithmic equation.

**LOGIC **– (noun) is the subject of sensible reasoning. See SENSE & REASON. If something does not make sense then it is not based on logic and one calls it illogical which means not logical. See LOGICAL. “2 + 2 = 4 is based on logic and it makes sense. 2 + 2 = 5 is not based on logic and is not true and does not make sense.

**LOGICAL** – (adjective) means based on LOGI It therefore means something that makes sense. “The mad man muttered a whole lot of words that were not logical and I could not understand what he was trying to say. “ “The logical steps in boiling an egg are: boiling the water, putting the egg into the water and taking the egg out after 5 minutes. It would not be logical to put the egg into the cold water for 5 minutes, take it out and then boil the water. ” Se e LOGI

**LONG DIVISION **– (noun) When you are dividing by a number which is from 1 to 12 you use short division. If you know your multiplication tables well you will find short division very easy. When you want to divide by numbers from 13 upwards to any bigger number you use long division. For an explanation of long division see your arithmetic book or ask your teacher. See appendix V for multiplication tables.

**LONGITUDE** – (noun) One great circle – (see GREAT CIRCLE) that passes through the North and South poles is taken as 0 degrees. This is usually the one that passes through Greenwich in England. All the other great circles that also pass through the North and South poles that are one degree apart – (approximately 110 km at the equator) are called degrees of longitude. See Diagram 53. These lines of longitude are also called meridians. For example you would say the meridian that passes through Greenwich is 0 degrees. Look up **LATITUDE**. See diagram 53. You will see that if you know both the latitude and longitude of a place then you can find its position on a map. See MAP.

**LOOK UP **– (verb) means to go and look in a book and find the correct information. “Look up the meaning of that word in a dictionary.

**LOSS **1. Loss means something that one has lost. “The wind blew his hat away and he lost it. The loss of his hat makes him feel sad. ” 2. When one runs a business the idea is to get in more money than it takes to run the business. If one takes in less money than it is costing to run the business then the business is said to be running at a loss. The difference between the money you pay out and the money you get in is called the loss. See PROFIT.

**LOWEST COMMON MULTIPLE **– (noun) means the smallest number that some other numbers will all divide into without remainder. The smallest number that 2, 3 & 5 will all divide into is 2 x 3 x 5 = 30. You will see that 2 & 3 both divide into 6 and 3 & 5 will both divide into 15 but for all 3 to divide alright you need the number 30. You will learn in your arithmetic class a method of how to find the lowest common multiple of any group of numbers. See COMMON & MULTIPLE. The abbreviation for lowest common multiple is LCM.

**LOYAL** – (adjective) means to do what is expected from you for a person or a group of people. A person who is loyal to his king will always do what his king commands and will defend his king and fight for him. A person who is loyal to his country will be willing to fight to defend his country if it is attacked and will always try to do what is best for his country.