Lesson 10, Topic 1
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# The Number Line

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Many of the numbers we use represent situations, which have direction as well as size. The numbers which have direction and size are called directed numbers.

Once a direction is chosen as positive+, the opposite direction is taken as negative .

Looking at the number line, you will observe that the numbers increase in value as you move from left to the right of the scale.

For example:

-5  is on the right of -6, so -5 is greater than -6. This means that -6 is less than -5.

Mathematically, the symbols ‘>’ and ‘<’ are used for greater than and less than respectively.

>  Means ‘is greater than’   i.e.  -5   >  -6

<  means “is less than” i.e. -6  <  -5.

Similarly on the number line.

-2 is on the right of -4, so -2  >  -4  or  -4  < –  2.

3 is on the right of -1. So 3  <  -1 or  -1  <   3.

8 is on the right of -7, so, 8  >  -7   or   -7  <   8.

Note:

On a number line, a number to the right is always greater than a number to the left

Example 1

Arrange these numbers in ascending order:

5,  -6,  -4,  -10,  -19,  7,  -13,  21  and 14

Solution

Ascending order means from smallest to largest.

-19, -13,  -10,  -6,  -4,  5, 7,  14.

Hint:

Note that the largest number with a negative sign is the smallest number and the largest number with a positive sign is the largest number.

Example 2

Arrange these numbers in descending order:

-3,  1, -5, 10, 6, -7 and  3.

Solution

Descending order means from largest to smallest:

10,   6,   3,   1,   -3,   -5,   and   -7.

Example 3

Arrange these numbers in ascending order:

-8,   0,  -12,  7,  -5,  4,  20,  1.

Solution

-12,   -8,   -5,   0,  1,   4,   7,  20. error: