1. CH- 6-INTEGERS

2. 6.1Introduction The numbers with a negative sign are less than zero. These are called negative integers.

3. 6.1.1Tag me with a sign Some numbers carry a minus sign. For example : profit and loss are opposite situations and if profit is represented by+ sign, loss can be represented by-sign & if earnings are represented by + sign,then the spendings may be shown by a – sign.

4. 6.2 INTEGERS The first numbers be discovered were natural numbers i.e. 1,2,3,4,…If we include zero to the collection of natural no., we get a new collection of no. known as whole no. i.e. 0,1,2,3,4,…If we put the whole no. and the negative no. together, the new collection of no. will look like 0,1,2,3,4,5,…,-1,-2,-3,-4,-5,… and this collection of no. Is known as integers. The collection of 1,2,3,..are said to be positive integers and -1,-2,- 3,..are said to be negative integers.

5. 6.3.1ADDITION OF INTEGERS ON A NUMBER LINE 1)Let us add 3 and 5 (on number line. Ans-On the number line, we first move 3 steps to the right from 0 reaching 3, then we move 5 steps to the right of 3 and reach 8. thus we get 3+5 =8.

6. 2] Let us add -3 and -5 on the number line. Ans- On the number we first move 3 steps to the left of 0 reaching -3, then we move 5 steps to the left of -3 and reach -8. Thus, [- 3] + [-5] =-8.

7. [3]Find the sum of (+5) and (-3) on the number line. On the number line first we move to the right of 0 five by steps reaching 5.T hen we move 3 steps to the left of five reaching 2.

8. [4]Find the sum of [-5]and [+3] on the number line. First we move 5 step s of to the left of 0 reaching d-5 and then from this point we move 3 steps to the right. We reach the point -2.

9. ADDITIVE INVERSE Numbers such as 3 and -3,2 and -2, when added to each other give sum zero. They are called additive inverse of each other. Example – add 3 and -3. We first move from 0 to +3 and then from +3, we move 3 points to left and reach 0.

10. SUBTRACTION OF INTEGERS WITH THE HELP OF NUMBER LINE Let us subtract -8-(-10) using number line. On the number line, from -8 we will move 10 steps towards right. We each at 2. Thus - 8-(-10) = 2.

11.  When a positive integer is added to an integer, the resulting integer becomes greater than the given integer. 1. When a negative integer is added to an integer, the resulting integer become less than the given integer.  To add a positive integer we move towards the right.  On number line and for adding a negative integer we move towards left.  When we subtract a negative integer we get a greater integer.