GROUP 16A

Negative integers can be traced to the Chinese Negative integers can be traced to the Chinese in 200 BCE.in 200 BCE.

They used red rods to represent positive They used red rods to represent positive numbers and black rods to represent negative numbers and black rods to represent negative numbers.numbers.

In India ,negative integers started appearing In India ,negative integers started appearing around AD 620 – 630 in the work of Hindu around AD 620 – 630 in the work of Hindu Brahma Gupta.Brahma Gupta.

He called the positive numbers affirmative He called the positive numbers affirmative quantities.quantities.

Chu – Shiky gave the “rule of sign”.Chu – Shiky gave the “rule of sign”. There have been various notations to represent There have been various notations to represent

negative numbers.negative numbers. The Hindus put a small circle or a dot over or The Hindus put a small circle or a dot over or

next to the number to denote it was a negative next to the number to denote it was a negative number.number.

The Chinese drew a The Chinese drew a slash through a portion slash through a portion of the number to of the number to indicate that the indicate that the number was negative.number was negative.

For temperature reading we can use integers in the following ways:

Eg: If the temperature rises by x degree it is represented as +x degree celsius.

If it falls by y degree it is represented as –y degree celsius.

DELHIDELHI 43 c43 c

39 c39 c46 c46 c

40 c40 c45 c45 c

37 c37 c40 c40 c

32 c32 cHH

LL

KASHMIRKASHMIR 7 c7 c

3 c3 c1 c1 c

-2 c-2 c3 c3 c

1 c1 c1 c1 c

-3 c-3 cHH

LL

MONDAY TUESDAY THURSDAYWEDNESDAY

What was the coldest temperature in Kashmir?

The coldest temperature was -3 degrees celsius

What was the highest temperature in Delhi ?

The highest temperature was 46 degree celsius

In addition ,subtraction: same sign In addition ,subtraction: same sign keep and add, different signs subtract keep and add, different signs subtract take the sign of the bigger absolute take the sign of the bigger absolute value.value.

+ of + = + - of - = + - of + = - + of + = + - of - = + - of + = -

+ of - = - + of - = - In multiplication if the signs are same In multiplication if the signs are same

the answer is positive opposite signs the answer is positive opposite signs give negative.give negative.

•In multiplication and In multiplication and division SPON works division SPON works THAT IS ‘ same signs THAT IS ‘ same signs positive and opposite positive and opposite signs negative’.signs negative’.

RULES

• KEY : Good (+) ; Hate (-) ; Love (+) ; Bad (-)

• If you love to love ,it is good (+) x (-) = -• If you hate to hate ,it is good (-) x (-) =

+• If you love to hate , it is bad (+) x (-) = -• If you hate to love , it is bad (- )

RULESRULES DMAS RULEDMAS RULE Dear mother and sister to remember Dear mother and sister to remember

the rule i.e. Order of operation is the rule i.e. Order of operation is DMAS rule explains when an operator DMAS rule explains when an operator

should be considered for when there should be considered for when there occur multiple operators in an occur multiple operators in an expression.expression.

•Order of operations:Order of operations:DivisionDivisionMultiplicationMultiplicationAdditionAdditionSubtraction.Subtraction.

DMAS

Negative numbers are commonly used in sports.

Eg: in hockey if a player on your side score on your line it is a plus. If a player from the other team scores on your line then it is a minus.

Negative integers are Negative integers are used to represent debits used to represent debits and positive integers for and positive integers for credit.credit.

Eg : if I deposit Rs.100/- Eg : if I deposit Rs.100/- then the balance is +100 then the balance is +100 I I withdraw Rs.50/- then my withdraw Rs.50/- then my account will show -50 account will show -50 (debit).(debit).

• Budgeting is allotting a certain amount Budgeting is allotting a certain amount of money for a particular project or of money for a particular project or work.work.

• When the allotted amount is less than When the allotted amount is less than required then the deficit is represented required then the deficit is represented by a negative integer and after the by a negative integer and after the completion of work if there is some completion of work if there is some amount left after the work is done that amount left after the work is done that amount is represented by a positive amount is represented by a positive integer.integer.

• If I get Rs.100/-as a birthday present it is represented by+100.

• If I spend Rs.75/- on paints it is denoted by -75

• +=• -=

100 +100

75 -75

50

25

I am going shopping today and I have only I am going shopping today and I have only Rs.500 to spend.Rs.500 to spend.My shopping list contains:My shopping list contains:

1kg Sugar for Rs.501kg Sugar for Rs.50 5kg rice for Rs.1505kg rice for Rs.150 1kg of mangos and bananas for Rs.1001kg of mangos and bananas for Rs.100 A fountain pen for Rs.100A fountain pen for Rs.100 2 books for Rs.502 books for Rs.50

A fancy pouch for A fancy pouch for Rs.50Rs.50

3 CDs for Rs.30 3 CDs for Rs.30 o I had only Rs.500 to I had only Rs.500 to

spend I give away spend I give away Rs.500 but I still have Rs.500 but I still have a balance of Rs.30 so a balance of Rs.30 so it is represented as -it is represented as -30.30.

LokeshLokesh Ekshetha Ekshetha AbigynaAbigyna Krut Krut RamRam AkshayAkshay

We learnt how to add, subtract , We learnt how to add, subtract , multiply and divide integers.multiply and divide integers.

We learnt how integers started and We learnt how integers started and how to perform many operations on how to perform many operations on integers.integers.

• Google .co.in/images?um=1&h1=en&tbs

=icsh%=3A1&sa=1&q=thermometers clear pictures.

• Google.co .in /imegres?imegurl=http: //math.ppst.com/banner-math-negative.

• Integers handout • www.cartoonstalk.com

We thank Bhagya We thank Bhagya maam for her maam for her valuable guidance valuable guidance and patient help.and patient help.

We thank Bhagya We thank Bhagya maam for allowing us maam for allowing us to do such a to do such a wonderful project.wonderful project.