Page 274 - Ganit Kaushal

(b) The starting floor is +3 and we need to go to the target floor –1.

\ We need to go down by 4 floors. So, the movement needed is –4. (–ve sign shows downward
movement.)

Hence, we have (–1) – (+3) = (– 4).
(c) The starting floor is –2, and we need to go to the target floor +2.
\ We need to go up by 4 floors. So, the movement needed is +4.
Hence, we have (+2) – (–2) = (+4).

10.5 COMPARISON OF NUMBERS USING FLOORS

Four friends — Jiya, Asha, Bina and Aman went to visit the Building of Fun. Thereafter, they went to different
floors according to their choices.
Jiya is fond of art, so, she went to visit the Art Gallery. Asha is looking for some good books, so she is in the
Books Library. Bina is in the Cinema Hall. Aman wants to purchase some toys, so he went to the Toy Store.

Based on the above information, can you answer the following questions:
Who is on the highest floor, and who is on the lowest floor?
Yes, you are right! Jiya is on the highest floor (+3) and Aman Note
is on the lowest floor (−2). All negative number floors
So, you understand that (+3) > (−2). are below the floor 0. So, all
Can you arrange them in descending order of their floors? negative numbers are less than
Yes, it’s as: Jiya → Bina → Asha → Aman 0. All the positive number floors

 (+3) > (+2) > (−1) > (−2) are above floor 0. So, all positive
numbers are greater than 0.
It is understandable that lower floors lie below the higher floors.
Ex. Imagine the Building of Fun with more floors. Compare the numbers and fill in the boxes with
< or >: (NCERT)
(a) –10 −12 (b) –10 +17
Sol. (a) –10 > −12 [ Floor –12 lies below –10.] (b) –10 < +17 [ Floor –10 lies below +17.]

10.6 INTEGERS

Now, imagine a Building of Fun that has an unending number of floors above and below the ground level.
Then we can imagine the lift inside it that will move up positive floors, +1, +2, +3, and so on, without an end.
Similarly, it will go down negative floors −1, −2, −3, and so on, without an end. Such unending positive and
negative numbers, along with zero, are called Integers. They go both ways from 0 as written below:
…, – 4, – 3, – 2, – 1, 0, 1, 2, 3, 4, …

1, 2, 3, 4, … are called positive integers and …, – 4, – 3, – 2, – 1 are called negative integers.
The integer 0 is neither positive nor negative.
To add and subtract even larger integers, imagine a lift that can go upwards forever and downwards forever,
starting from level 0. Let’s just call it an ‘Infinite Lift’!

We can use this imagination to add and subtract any integers we like.
For example: Suppose we want to carry out the subtraction + 2000 – (–200). We can imagine a lift with 2000
levels above the ground and 200 levels below the ground.

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