1. Number Systems Integers Positive & Negative Numbers

2. History of Integers The Babylonians were the first civilization to come up with the concept of zero, to signify that something was missing The idea of negative numbers and zero in mathematics can be traced back to India about 620 BCE and a man named Brahmagupta. He used them to calculate the debts and fortunes of the nobility We still use the rules he created today. This idea spread into Arabia in the 10 th Century and from there eventually made its way into European mathematics in the 15 th century.

3. Integers Integers are positive and negative whole numbers, including zero. … -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, … Can you think of situations where negative numbers are used? Banking & FinanceTemperature GolfLifts We define the set of integers using; Z was first used by a group of European mathematicians trying to organise numbers into groups. Zahlen is German for zero.

4. Positive Numbers Positive number A number greater than zero. 0123456 If there is no sign written in front of a number then you can assume it is positive. So 1 = +1 2 = + 2e.t.c

5. Negative Numbers Negative number A number less than zero The sign to the left of the number tells you if it is positive or negative. 0123456-2-3-4-5-6

6. Opposite Numbers or Zero Pairs Opposite Numbers Numbers that are the same distance from zero in the opposite direction 0123456-2-3-4-5-6 and

7. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 When the number is positive, count to the right. When the number is negative, count to the left. + -

8. Adding & Subtracting Integers 0123456-2-3-4-5-6 + - +3 - 5 = -2

9. Adding & Subtracting Integers 0123456-2-3-4-5-6 + - +6 - 4 = +2

10. Adding & Subtracting Integers 0123456-2-3-4-5-6 + - +3 - 7 =-4

11. Adding & Subtracting Integers 0123456-2-3-4-5-6 - + -3 + 7 =+4

12. Multiplying Integers What we know already or that a positive number multiplied by a positive number = a positive number What about Well you could think about this as So we can say that a negative number multiplied by a positive number = a negative number.

13. The Double Negative Rule I didn’t not eat a massive amount of chocolate on Halloween Night! What happens in English when we have two negatives together in a sentence? The sentence becomes positive The same thing happens in maths, for example So we can say that a negative number multiplied by a negative number = a positive number.

14. Multiplying Integers What we know already (zero pairs) So what about well if we consider this and use the distributive rule Written out fully this becomes (Rule on previous slide) So we can say that a negative number multiplied by a negative number = a positive number.

15. Dividing Integers The same rules we have for multiplication applies for division. A positive number divided by a positive number = a positive number. A negative number divided by a positive number = a negative number. A negative number divided by a negative number = a positive number.

16. Questions