ICSE Class 6 Maths Chapter 03 Number Line

Chapter 3: Number Line

Number Line

A number line can be used to represent all types of real numbers: -23, 0, 8, \(\frac{3}{5}\), \(2\frac{1}{5}\), \(\sqrt{2}\), \(\sqrt{5}\), etc. Here -23, 0 and 8 are integers and \(\frac{3}{5}\), \(2\frac{1}{5}\), \(\sqrt{2}\) and \(\sqrt{5}\) are non-integers. But in the current chapter we shall be dealing with the number line representing integers only.

Steps for drawing a number line:

1. Draw a straight line of any suitable length.

2. Mark points on the drawn line to divide it into the required number of equal parts.

3. Mark the centre point of the drawn straight line as zero.

4. Starting from zero, and on the right hand side of it mark the positive integers +1, +2, +3, etc., at the points marked in step 2.

Similarly, starting from zero, on the left hand side of it mark the negative integers -1, -2, -3, etc., at the points marked in step 2.

The line so obtained will be a number line of the form shown below:

[Number line graphic showing -7 through +7 with 0 in center]

Arrow-heads at the two ends of the number line show that the line as well as the integers continue up to infinity on both the positive and the negative sides.

Number Lines For Natural Numbers, Whole Numbers And Integers

1. Natural Numbers: A number line starting from 1 (one) and marked 2, 3, 4, 5, ...... at equal distances on the right hand side of 1 is called a number line representing the natural numbers (as shown below):

[Number line graphic showing 1 through 8]

The arrow-head on the right side shows that the natural numbers continue up to infinity.

2. Whole Numbers: A number line starting from 0 (zero) and marked 1, 2, 3, 4, .... at equal distances on the right hand side of 0 is called a number line representing the whole numbers (as shown below):

[Number line graphic showing 0 through 6]

The arrow-head on the right side shows that the whole numbers continue up to infinity.

3. Integers: Since integers = { ...., -3, -2, -1, 0, 1, 2, 3, 4, .... }, a number line with zero (0) marked any where on it, with positive numbers 1, 2, 3, .... marked on the

right hand side of 0 at equal distances and negative numbers -1, -2, -3, .... marked on the left hand side of 0 (zero) at the same equal distances, is said to represent integers (as shown below):

[Number line graphic showing -4 through 4 with 0 in center]

Arrow-heads on the two sides show that the integers continue up to infinity on the positive side as well as on the negative side.

1. Integers = {........., -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ..........}

2. Natural numbers = {1, 2, 3, 4, 5, 6, .........}

3. Whole numbers = {0, 1, 2, 3, 4, 5, .........}

4. Whether the number line is drawn for integers, natural numbers or whole numbers, the distance between any two consecutive numbers is always the same.

Using A Number Line To Compare Numbers

Out of any two numbers, marked on a number line, the number which is

(i) to the right is greater

(ii) to the left is smaller.

[Number line graphic showing -6 through 8]

Considering the number line drawn above:

(i) 6 is greater than 2 because it is to the right of 2

(ii) -2 is greater than -5 because it is to the right of -5

(iii) 3 is greater than -1 because it is to the right of -1

(iv) -6 is smaller than -2 because it is to the left of -2

(v) -4 is smaller than 1 because it is to the left of 1 and so on.

Thus, each number on a number line is always greater than each and every number to its left. Similarly, each number on a number line is always smaller than each and every number to its right.

For the following number line:

[Number line graphic showing -6 through 7]

(i) 7 is greater than all numbers to its left i.e. 7 is greater than each of 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, etc.

(ii) -6 is smaller than all numbers to its right i.e. -6 is smaller than each of -5, -4, -3, -2, -1, 0, 1, 2, etc.

Also. (i) Every positive number is greater than every negative number.

(ii) Zero is smaller than every positive number but greater than every negative number.

(iii) The greater the number, the smaller is its opposite.

viz. 8 is greater than 5 but -8 is less than -5

Similarly, -9 > -15 - => 9 < 15 and so on

(iv) The smaller the number, the greater is its opposite.

viz. 6 is smaller than 7 but -6 is greater than -7

Similarly, -8 < -5 - => 8 > 5, and so on.

Example 1

Using a number line, write the following numbers (integers) in ascending order of value: 3, -2, 5, 0, -7, 6 and -4.

Solution:

Draw a suitable number line and mark on it the given numbers, as shown below:

[Number line graphic showing -8 through 8 with marked points at -7, -4, -2, 0, 3, 5, 6]

Since ascending order means smaller to greater.

Therefore, the given numbers in ascending order

= -7, -4, -2, 0, 3, 5 and 6 (Ans.)

Symbol '<' means 'is less than' and symbol '>' means 'is greater than.'

Therefore, Answer to Example 1 given above can also be written as:

-7 < -4 < -2 < 0 < 3 < 5 < 6.

If required, the same numbers in descending (decreasing) order will be written as:

6, 5, 3, 0, -2, -4 and -7

or, 6 > 5 > 3 > 0 > -2 > -4 > -7

Teacher's Note

Number lines help students visualize the ordering and comparison of integers in a concrete, visual way. This concept is foundational for understanding positive and negative values in real-world contexts like temperature changes, bank account balances, and elevation above or below sea level.

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