Maharashtra Board Class 6 Maths part 1 Chapter 3 Integers PDF Download

Integers

Let's Recall

Count how many boys, flowers and ducks there are in the picture. We have to count objects in order to find out the answer to "How many?" Numbers were created because of the need to count things in nature. We write the count of things in the form of numbers.

Let's Discuss

Dada: The numbers 1, 2, 3, 4, that we have used up to now for counting are called "counting numbers". They are also called natural numbers. But is it possible to count the stars in the sky or the grains of sand on the beach? They are innumerable and so are the natural numbers. Look at this list of natural numbers:

Natural numbers: 1, 2, 3, 4, ..., 321, 322, ..., 28573, ...

Samir: We have already learnt to add and subtract these natural numbers. But when we subtract 5 from 5 nothing remains. The zero that we write to show that, is not seen in this list.

Dada: Of course, we cannot do without "zero". The set of all natural numbers together with zero is the set of whole numbers.

Whole numbers: 0, 1, 2, 3, 4, ..., 367, 368, ..., 237105, ...

Dada: We need to use some other numbers which are not there in this group.

Salma: Which are those?

Dada: Here's an example. In Maharashtra, the temperature falls to 10 °C (10 degrees Celsius) or even 8 °C in winter, but not down to 0 °C. But in Kashmir, it may fall even below 0 °C. To show that, we need numbers that are less than zero.

Teacher's Note

Natural numbers are the numbers we use to count things. We see them every day when we count boys, books, or flowers. Whole numbers add zero to natural numbers, just like how 0 rupees means we have no money.

Exam Trick

Remember: Natural numbers start from 1, but whole numbers start from 0. Think of it like this - you have natural numbers when you count, but whole numbers when you count and include empty (zero).

Points to Remember

Counting numbers are 1, 2, 3, 4, and they are also called natural numbers.
Whole numbers are natural numbers plus zero: 0, 1, 2, 3, 4.
We need negative numbers to show temperatures below zero.
In Kashmir, the temperature can fall below 0 °C in winter.

Samir: In January, when the papers said that it was snowing in Kashmir, the temperature in Srinagar was -8 °C. How do we read that?

Dada: It is read as "minus eight degrees Celsius". When we put a minus sign (-) before any number, the number obtained is less than zero. It is called a negative number. On a thermometer, there are increasing numbers like 1, 2, 3, above 0. These are called positive numbers. The numbers below zero are -1, -2, -3, ...

Samir: Can we show negative numbers on the number line?

Dada: Of course! On the right of zero at distances of 1, 2, 3, ... units are the numbers 1, 2, 3, ... On the left of zero at 1, 2, 3, ... unit distances are the numbers -1, -2, -3, ... They are called negative numbers. The numbers 1, 2, 3, ... on the right are called positive numbers. They can be written as 1, 2, 3, ... and also +1, +2, +3, ...

Salma: On the thermometer, the positive numbers are above zero and the negative numbers are below it. On the number line, they are on the right and left sides of zero respectively. Does it mean that positive and negative numbers are on opposite sides of zero?

Dada: Correct!

Samir: Then should we use positive numbers to show height above sea level and negative numbers for depth below sea level?

Dada: You're right, too! Very good!

The "+" sign is generally not written before positive numbers. However, it is necessary to write the "-" sign of a negative number. Zero does not have any sign.

Teacher's Note

Negative numbers show things like temperature below zero or money we owe. In India, when it gets very cold in places like Kashmir, the temperature goes below 0 degrees Celsius, and we write it as -5 or -10.

Exam Trick

Remember: Minus eight (-8) is read as "minus eight degrees". The minus sign always comes first. Think of minus as "below" and plus as "above".

Points to Remember

Negative numbers are numbers less than zero with a minus sign (-) in front.
Positive numbers are numbers greater than zero and can have a plus sign (+) or no sign.
On a thermometer, positive numbers are above 0 and negative numbers are below 0.
On the number line, positive numbers are on the right side of 0 and negative numbers are on the left.
Zero has no sign and is neither positive nor negative.

Let's Learn

Integers

Positive numbers, zero and negative numbers together form a group of numbers called the group of integers.

My Friend, Maths: At The Fair, In The Lift

Look at the picture of the kulfi man. Why do you think he keeps the kulfi moulds in a mixture of salt and ice?

In a lift, the ground floor is numbered 0 while the floors below the ground level are numbered -1 and -2.

Let's Learn

Showing Integers on the Number Line

The point on a number line which is marked 0 is called the origin. On the left and right of 0, points are marked at equal distances. The numbers shown by points on the right are positive numbers and those shown by points on the left are negative numbers.

Negative numbers ... Origin ... Positive numbers

Example: Show the numbers -7 and +8 on the number line

-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8

Teacher's Note

The number line helps us see all numbers clearly - negative on the left and positive on the right. Just like how we arrange students in a line at school, we arrange numbers on a line too.

Exam Trick

Remember: The origin is at 0 in the middle. Numbers to the right are always bigger than numbers to the left. So +5 is bigger than -5 because it is on the right side of 0.

Points to Remember

An integer is a positive number, zero, or a negative number.
The origin is the point marked 0 on the number line.
Positive numbers are on the right side of 0.
Negative numbers are on the left side of 0.
All points on the number line are equally spaced apart.

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