1. Done by- Group 2 Grade: 6 Section :A Marula(leader) Mahima, Aman, Nikitha, Prateeksha, Raj Z

2. Content: i. History and need of negative numbers ii. Application of integers iii. Discovery of integers iv. Background of the mathematician: Brahmagupta v. Use of integers in real life vi. Citations vii. Acknowledgement

3. History and need of negative numbers Negative integers were found in 1000 B.C.E by the Chinese. It’s first in the east was made by Greece. In India it was termed as ‘debts’. It became famous in the 16 th century.

4. Application of integers It is easy to recognize numbers in the real world. For example, highways have posted speed limits that are represented in numbers. People who have obtained a driver’s license understand this system of numbers. They know that if the posted limit is 110 km/h and they drive 120 km/h, they could be fined. Maps have numbers to give directions and information. Positive integers are included in the set of whole numbers {0, 1, 2, 3, …}. It is relatively easy to see how positive integers affect the world. The implications of negative integers however, may be less obvious.

5. Mathematician who discovered negative numbers Brahmagupta describes operations on negative numbers. He first describes addition and subtraction, The sum of two positives is positives, of two negatives negative; of a positive and a negative [the sum] is their difference; if they are equal it is zero. The sum of a negative and zero is negative, that of a positive and zero positive, [and that] of two zeros zero.... A negative minus zero is negative, a positive [minus zero] positive; zero minus zero is zero. When a positive is to be subtracted from a negative or a negative from a positive, then it is to be added. He goes on to describe multiplication, The product of a negative and a positive is negative, of two negatives positive, and of positives positive; the product of zero and a negative, of zero and a positive, or of two zeros is zero.

6. Brahmagupta was an Indian mathematician and astronomer. Brahmagupta wrote important works on mathematics and astronomy. In particular he wrote Brahmasphutasiddhanta, in 628. The work was written in 25 chapters and Brahmagupta tells us in the text that he wrote it at Bhillamal which today is the city of Bhinmal. This was the capital of the lands ruled by the Gurjara dynasty.

7. Use of Integers in Real life  We use integers in our lives because they are everywhere in our life and we use them all the time. We use them in school and we read them in our daily lives like in work, even when you read time, you are looking at integers.  Integers help us every day in many ways. They are all around us. We represent profit and loss with integers, while using the lift, we have the minus sign for the floors below the basement. Some escalators also use the positive and negative signs for going up and going down. We also use integers in sports, to represent the deduction of points, or the points gained.

8. the temperature of three different places Here the bar starts from 0 and goes up or down depending on the sign -2 o c -1 o c 0oc0oc

9. use of Integers in Sports Hockey  each line of players records a plus or a minus.  If the other team scores on your line, that is a minus.  If someone on your line scores a goal, that is plus.  If neither team scores, the result is zero.

10. Hockey stadium

11. Altitude  Geographically, we represent sea level with integers.  Below sea level is represented with negative integers for example- i. death valley in California is 86m below sea level which is -86. ii. Antarctica is 2,538m below sea level which is -2,538.  When geography specialists study the difference between a mountain which is above sea level, and a sea which is below sea level they use negative integers. Example-Mount Everest is 8848m above sea level and the bottom dead sea is 409m below sea level.

12. Banks  Negative integers are used to represent debits.  Positive integers are used to represent credits  When there is an increase in the share value it is a positive integer.  When there is a decrease in the share value it is a negative integer

13. RULES ADDITION AND SUBTRACTION Same signs keep and add, Different signs subtract, Take the sign of the bigger absolute value, And then you’ll be exact! MULTIPLICATION AND DIVISION SPON works! S-Same Signs, P-Positive, O-Opposite Signs, N- Negative

14. Citations www.wikipedia.com www.google.com www.wikianswer.com

15. Acknowledgement: We thank Bhagya ma’am for her support to make our power point presentation a very big success, allowing us to get such a wonderful opportunity. thank you!!!