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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.svg7/28/2019 Four Basic Operations of Arithmetic
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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/Salary7/28/2019 Four Basic Operations of Arithmetic
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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.svg7/28/2019 Four Basic Operations of Arithmetic
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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
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