NCERT Book Class 6 Maths Integers

Integers

6.1 Introduction

Sunita’s mother has 8 bananas. Sunita has to go for a picnic with her friends. She wants to carry 10 bananas with her. Can her mother give 10 bananas to her? She does not have enough, so she borrows 2 bananas from her neighbour to be returned later. After giving 10 bananas to Sunita, how many bananas are left with her mother? Can we say that she has zero bananas? She has no bananas with her, but has to return two to her neighbour. So when she gets some more bananas, say 6, she will return 2 and be left with 4 only.

Ronald goes to the market to purchase a pen. He has only Rs 12 with him but the pen costs Rs 15. The shopkeeper writes Rs 3 as due amount from him. He writes Rs 3 in his diary to remember Ronald’s debit. But how would he remember whether Rs 3 has to be given or has to be taken from Ronald? Can he express this debit by some colour or sign? Ruchika and Salma are playing a game using a number strip which is marked from 0 to 25 at equal intervals. 

To begin with, both of them placed a coloured token at the zero mark. Two coloured dice are placed in a bag and are taken out by them one by one. If the die is red in colour, the token is moved forward as per the number shown on throwing this die. If it is blue, the token is moved backward as per the number shown when this die is thrown. The dice are put back into the bag after each move so that both of them have equal chance of getting either die. The one who reaches the 25th mark first is the winner. They play the game. Ruchika gets the red die and gets four on the die after throwing it. She, thus, moves the token to mark four on the strip. Salma also happens to take out the red die and wins 3 points and, thus, moves her token to number 3. In the second attempt, Ruchika secures three points with the red die and Salma gets 4 points but with the blue die. Where do you think both of them should place their token after the second attempt? Ruchika moves forward and reaches 4 + 3 i.e. the 7th mark.

Whereas Salma placed her token at zero position. But Ruchika objected saying she should be behind zero. Salma agreed. But there is nothing behind zero. What can they do?

Salma and Ruchika then extended the strip on the other side. They used a blue strip on the other side.

Now, Salma suggested that she is one mark behind zero, so it can be marked as blue one. If the token is at blue one, then the position behind blue one is blue two. Similarly, blue three is behind blue two. In this way they decided to move backward. Another day while playing they could not find blue paper, so Ruchika said, let us use a sign on the other side as we are moving in opposite direction. So you see we need to use a sign going for numbers less than zero.

The sign that is used is the placement of a minus sign attached to the number. This indicates that numbers with a negative sign are less than zero. These are called negative numbers.

Do This

(Who is where?)

Suppose David and Mohan have started walking from zero position in opposite directions. Let the steps to the right of zero be represented by ‘+’ sign and to the left of zero represented by ‘–’ sign. If Mohan moves 5 steps to the right of zero it can be represented as +5 and if David moves 5 steps to the left of zero it can be represented as – 5. Now represent the following positions with + or – sign :

(a) 8 steps to the left of zero.       (b) 7 steps to the right of zero.

(c) 11 steps to the right of zero.    (d) 6 steps to the left of zero.

Please refer to attached file for NCERT Class 6 Maths Integers