<< Chapter < Page Chapter >> Page >

Letters and arithmetic

The simplest thing that can be done with numbers is adding, subtracting, multiplying or dividing them. When two numbers are added, subtracted, multiplied or divided, you are performing arithmetic Arithmetic is derived from the Greek word arithmos meaning number . . These four basic operations can be performed on any two real numbers.

Mathematics as a language uses special notation to write things down. So instead of:

one plus one is equal to two

mathematicians write

1 + 1 = 2

In earlier grades, place holders were used to indicate missing numbers in an equation.

1 + = 2 4 - = 2 + 3 - 2 = 2

However, place holders only work well for simple equations. For more advanced mathematical workings, letters are usually used to represent numbers.

1 + x = 2 4 - y = 2 z + 3 - 2 z = 2

These letters are referred to as variables , since they can take on any value depending on what is required. For example, x = 1 in [link] , but x = 26 in 2 + x = 28 .

A constant has a fixed value. The number 1 is a constant. The speed of light in a vacuum is also a constant which has been defined to be exactly 299 792 458 m · s - 1 (read metres per second). The speed of light is a big number and it takes up space to always write down the entire number. Therefore, letters are also used to represent some constants. In the case of the speed of light, it is accepted that the letter c represents the speed of light. Such constants represented by letters occur most often in physics and chemistry.

Additionally, letters can be used to describe a situation mathematically. For example, the following equation

x + y = z

can be used to describe the situation of finding how much change can be expected for buying an item. In this equation, y represents the price of the item you are buying, x represents the amount of change you should get back and z is the amount of money given to the cashier. So, if the price is R10 and you gave the cashier R15, then write R15 instead of z and R10 instead of y and the change is then x .

x + 10 = 15

We will learn how to “solve” this equation towards the end of this chapter.

Addition and subtraction

Addition ( + ) and subtraction ( - ) are the most basic operations between numbers but they are very closely related to each other. You can think of subtracting as being the opposite of adding since adding a number and then subtracting the same number will not change what you started with. For example, if we start with a and add b , then subtract b , we will just get back to a again:

a + b - b = a 5 + 2 - 2 = 5

If we look at a number line, then addition means that we move to the right and subtraction means that we move to the left.

The order in which numbers are added does not matter, but the order in which numbers are subtracted does matter. This means that:

a + b = b + a a - b b - a if a b

The sign means “is not equal to”. For example, 2 + 3 = 5 and 3 + 2 = 5 , but 5 - 3 = 2 and 3 - 5 = - 2 . - 2 is a negative number, which is explained in detail in "Negative Numbers" .

Commutativity for addition

The fact that a + b = b + a , is known as the commutative property for addition.

Multiplication and division

Just like addition and subtraction, multiplication ( × , · ) and division ( ÷ , /) are opposites of each other. Multiplying by a number and then dividing by the same number gets us back to the start again:

Questions & Answers

List and explain four factors of production
Vuyo Reply
capital labour entrepreneur natural resources
What is supply
Ogodo Reply
when the supply decreases demand also decreases
types of demand and the explanation
akin Reply
what is demand
akin Reply
other things remaining same if demend is increases supply is also decrease and if demend is decrease supply is also increases is called the demand
if the demand increase supply also increases
you are wrong this is the law of demand and not the definition
Demand is the willingness of buy and ability to buy in a specific time period in specific place. Mian you are saying law of demand but not in proper way. you have to keep studying more. because its very basic things in Economics.
Demand is the price of Quantity goods and services in which consumer's are willing and able to offer at a price in the market over a period of time
what is commercialization?
Doris Reply
How to talk loan for bank?
Alfred Reply
what is the meaning of gpa?
Ritisha Reply
Answer: GPA stands for Grade Point Average. It is a standard way of measuring academic achievement in the U.S. Basically, it goes as follows: Each course is given a certain number of "units" or "credits", depending on the content of the course.
what is small and Microbuisenes
tadesse Reply
What is fiscal policy
Who is the funder of Economic
founder , that is Adam Smith
what is model
Daniel Reply
The wealth of Nations
Yusuf Reply
the wealth of nations, is it the first?
Yes very sure it was released in 1759
thank you Yusuf.
then when did he died?
17 July 1790 Born: 16 June 1723, Kirkcaldy, United Kingdom Place of death: Panmure House, Edinburgh, United Kingdom
that's my today questions, thank you Yusuf it's bed time see u after.
what is fiscal policy
kemigisha Reply
what's mode?
Umar Reply
mode is the highest occurring frequency in a distribution
mode is the most commonly occurring item in a set of data.
Please, what is the difference between monopoly and monopsony?
Olaleye Reply
is there monopsony word?
I have no idea though
please, in which year Adam smith was born?
monopsony is when there's only one buyer while monopoly is when there's only one producer.
who have idea on Banter
like trade by barter?
Monopoly is when there's excessively one seller and there is no entry in the market while monopsony is when there is one buyer
Adam smith was born in 1723
 (uncountable) Good humoured, playful, typically spontaneous conversation. verb (intransitive) To engage in banter or playful conversation. (intransitive) To play or do something amusing. (transitive) To tease mildly.
which book Adam smith published first? the first book of Adam smith pls.
wealth on nation, 1776
what is market power and how can it affect an economy?
Gab Reply
market power:- where a firm is said to be a price setter.market power benefits the powerful at the expense of others.
Market power refers to the ability of a firm (or group of firms) to raise and maintain price above the level that would prevail under competition is referred to as market or monopoly power. The exercise of market power leads to reduced output and loss of economic welfare
find information about the national budget
three branches of economics in which tourism is likely to figure
Makgotso Reply
What are those three branches?
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Siyavula textbooks: grade 10 maths [caps]. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11306/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: grade 10 maths [caps]' conversation and receive update notifications?