NCERT Book Class 6 Maths The Other Side of Zero PDF Download

Chapter 10: Integers - The Other Side of Zero

More and More Numbers!

Recall that the very first numbers we learned about in the study of mathematics were the counting numbers 1, 2, 3, 4, ...

Then we learned that there are even more numbers! For example, there is the number 0 (zero), representing nothing, which comes before 1. The number 0 has a very important history in India and now in the world. For example, around the world we learn to write numbers in the Indian number system using the digits 0 to 9, allowing us to write numbers however large or however small using just these 10 digits.

We then learned about more numbers that exist between the numbers 0, 1, 2, 3, 4, ... , such as \( \frac{1}{2} \), \( \frac{3}{2} \), and \( \frac{13}{6} \). These are called fractions.

But are there still more numbers? Well, 0 is an additional number that we didn't know about earlier, and it comes before 1 and is less than 1. Are there perhaps more numbers that come before 0 and are less than 0?

Phrased another way, we have seen the number line:

[Figure: A number line showing points from 0 to 10, See in your textbook]

However, this is actually only a number 'ray', in the language we learned earlier in geometry; this ray starts at 0 and goes forever to the right. Do there exist numbers to the left of 0, so that this number ray can be completed to a true number line?

That is what we will investigate in this chapter!

Can there be a number less than 0? Can you think of any ways to have less than 0 of something?

10.1 Bela's Building of Fun

Children flock to Bela's ice cream factory to see and taste her tasty ice cream. To make it even more fun for them, Bela purchased a multistoried building and filled it with attractions. She named it Bela's Building of Fun.

But this was no ordinary building!

Observe that some of the floors in the 'Building of Fun' are below the ground. What are the shops that you find on these floors? What is there on the ground floor?

A lift is used to go up and down between the floors. It has two buttons: '+' to go up and '-' to go down. Can you spot the lift?

To go to the Art Centre from the 'Welcome Hall', you must press the '+' button twice.

We say that the button press is + + or +2.

To go down two floors, you must press the '-' button twice, which we write as - - or -2.

So if you press +1 (i.e., if you press the '+' button once), then you will go up one floor and if you press -1 (i.e., if you press the '-' button once), then you will go down 1 floor.

Lift button presses and numbers:

+++ is written as + 3
- - - - is written as - 4

What do you press to go four floors up? What do you press to go three floors down?

Numbering the floors in the building of fun

Entry to the 'Building of Fun' is at the ground floor level and is called the 'Welcome Hall'. Starting from the ground floor, you can reach the Food Court by pressing + 1 and can reach the Art Centre by pressing + 2. So, we can say that the Food Court is on Floor + 1 and that the Art Centre is on Floor + 2.

Starting from the ground floor, you must press -1 to reach the Toy Store. So, the Toy Store is on Floor -1 similarly starting from the ground floor, you must press - 2 to reach the Video Games shop. So, the Video Games shop is on Floor - 2.

The ground floor is called Floor 0. Can you see why?

Number all the floors in the Building of Fun.

Did you notice that + 3 is the floor number of the Book Store, but it is also the number of floors you move when you press + 3? Similarly, - 3 is the floor number but it is also the number of floors you go down when you press - 3, i.e., when you press - - - .

Teacher's Note

The '+' and '-' signs are not operations here; they are part of the number itself. When you write +2 or -2, the sign tells you the direction from zero (up or down), not an instruction to add or subtract. Think of them as labels on a building, not math symbols yet.

A number with a '+' sign in front is called a positive number. A number with a '-' sign in front is called a negative number.

In the 'Building of Fun', the floors are numbered using the ground floor, Floor 0, as a reference or starting point. The floors above the ground floor are numbered with positive numbers. To get to them from the ground floor, one must press the '+' button some number of times. The floors below the ground are numbered with negative numbers. To get to them from the ground floor, one must press the '-' button some number of times.

Zero is neither a positive nor a negative number. We do not put a '+' or '-' sign in front of it.

Teacher's Note

Zero is special - it is the boundary between positive and negative numbers. Many students think 0 is positive or negative, but it is neither. In the building, Floor 0 (the ground floor) is your starting point; everything above it is positive, everything below is negative.

Key Points

• Positive numbers represent values above zero and are written with a '+' sign, like +1, +2, +3.
• Negative numbers represent values below zero and are written with a '-' sign, like -1, -2, -3.
• Zero is neither positive nor negative; it is the reference point between positive and negative numbers.
• In the Building of Fun, the ground floor (Floor 0) is the starting point, with positive numbers for floors above and negative numbers for floors below.

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