Four Basic Operations of Arithmetic

7/28/2019 Four Basic Operations of Arithmetic

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Group members: Choo Yik TzeLim Yi Ming

Caroline Jiksing


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Addition:

- a mathematical operation that

represents combining collections

of objects together into a larger

collection

- is signified by the plus sign (+)


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In the picture on the right,

there are 3 + 2 applesmeaning three apples and

two other applesWhich

is the same as five apples.


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Subtraction:

- the difference between twoquantities or numbers

- is denoted by the minus sign(-)


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In the picture above, there are 5 apples

altogether. Two of the apples are rotten. So,

the total number of good apples left is five

apples minus two apples and we get three

apples (5 2 = 3)


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Meaning of addition as:

(i) Combining two sets of discreetquantities

- When two or more disjoint collections

are combined into a single collection,the number of objects in the single

collection is the sum of the number of

objects in the original collections.


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For example:

There are two sets of objects given. The first

set consist of three objects and the secondset comprises two objects. Adding up thesetwo sets of objects gives us five objects(2 + 3 = 5)
http://en.wikipedia.org/wiki/File:AdditionShapes.svg


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(ii) Increment involving continuous quantities

An increment is an increase of some amount,

either fixed or variable. The action of increasing or becoming greater.

For example one's salary may have a fixed annualincrement or one based on a percentage of its

current value.. Other example:-

2,4,6, 8 = The increment of each number is 2

5%,10%,15%= The increment of each number is5%

0.1, 0.2, 0.3= The increment of each number is 0.1

And other number that involving increment
http://en.wikipedia.org/wiki/Salaryhttp://en.wikipedia.org/wiki/Salary


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Basic facts of addition:

Commutativity Associativity Zero One Units

the terms in asumcan bereversed

left-to-right,andthe result willbethe same as thelast one.

Symbolically,if a and b areanytwo numbers,thena + b = b + a.

addition isassociativetells us that thechoice of

definition isirrelevant.For any threenumbers a, b,and c, it is truethat

(a + b) + c = a +(b + c).

Whenadding zero toany number,the quantity

does notchange; zero isthe identityelement foraddition, alsoknown as

the additiveidentity. Insymbols, forany a,a + 0= 0 + a = a.

For anyinteger a, theinteger (a + 1) isthe least integer

greater thana,also known as

the successorof a. Because ofthis succession,the value of

some a + b canalso be seen asthe bth successorof a

Tonumericallyadd physicalquantities

with units,they mustfirst beexpressedwith commonunits


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Examples of the basic facts of addition:Commutativity Associativity Zero and

oneUnits

In this case,

4 + 2 = 6is the same as

2 + 4 = 6

No matter theshaded region is the4 blocks or the 2blocks, the total sumwould be 6.

From the diagramabove,

(3 + 1) + 2= 3 + (1 + 2)= 6

The order ofoperations does notmatter.

For example, thereare two bags ofbeans. One bag hasfive beans andanother one has nobeans. So when we

add up all together,we still get 5 beans.5 + 0 = 5If the second baghas one bean, then5 + 1 = 6

1 feet = 60 inchesFor example, if ameasure of 5 feet isextended by2 inches, the sum is

(5X60) + 2 = 62We get 62 inchessince 60 inches issynonymous with5 feet.

On the other hand,it is usuallymeaningless to tryto add 3 meters and4 square meters,since those units are

incomparable
http://en.wikipedia.org/wiki/File:AdditionZero.svghttp://en.wikipedia.org/wiki/File:AdditionAsc.svghttp://en.wikipedia.org/wiki/File:AdditionComm01.svg


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Basic facts of subtraction:Non

commutativeAssociativity Zero One Units

Forsubtraction,the sequence inthemathematics

sentence mustbe statedclearly.

a b b a

Example:10 8 8 - 10

Subtraction isassociativetells us that thechoice ofdefinition is

irrelevant butthe order ofoperationsmust be stated.For any threenumbers a, b,

and c, it is truethat(a - b) + c = a -(b + c).

Any numbersubtracted byzero is theoriginalnumber and

any numbersubtractedfrom itselfequals zero.

Example:

1. 10 0 = 102. 10 - 10 = 0

When aninteger a issubtracted byone, theinteger (a - 1) is

the leastinteger lessthan a.

For example:10 1 = 9

To numericallyminus physicalquantitieswith units,they must first

be expressedwith commonunits

For example:1 m 80 cm

=100cm - 80cm=20 cm


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Relationship between addition and subtractionThere is an inverse relationship between addition and

subtraction. A number fact is made up of three

numbers. These three numbers can be used to make

up other number facts. Look at the number facts we

can make with the numbers 2, 3 and 5.

Addition Facts Subtraction Facts

2 + 3 = 5 5 3 = 2

3 + 2 = 5 5

2 = 3


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For example, 3 + 7 = 10. If a math fact is considered,

then the following are also true:

10 - 3 = 710 - 7 = 3

Similar relationships exist for subtraction, for

example 10 - 3 = 7. Then the following are also true:

3 + 7 = 107 + 3 = 10

The reason for this is that we are dealing with an

equation. An equation is balanced or the same on

either side of the equals (=) sign. If exactly the same

thing is done to both sides of the equation, it will

still be balanced or equal.


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In the example above we start with theequation 3 + 7 = 10

Subtract the same number from both sides3 + 7 - 3 = 10 - 3

On the left side the 3 and -3 produce 0 which

leaves 7 = 10 - 3 Turning the equation around to be in more

normal form 10 - 3 = 7


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THANK YOU

Four Basic Operations of Arithmetic

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