INTEGERS ON NUMBER LINES

In basic mathematics, a number line is a picture of a graduated straight line that serves as abstraction for real numbers, denoted by . Every point of a number line is assumed to correspond to a real number, and every real number to a point.

Draw a line and mark some points at equal distance on it as shown in the figure.

Mark a point as zero on it. Points to the right of zero are positive integers and are marked +1, +2, +3, etc. or simply 1, 2, 3 etc.

Points to the left of zero are negative integers and are marked –1, –2, –3 etc. In order to mark –6 on this line, we move 6 points to the left of zero.

Example 1 :

Represent +5 on the number line.

Solution :

Example 2 :

Compare the numbers 3 and 6

Solution :

Let us locate the two numbers 3 and 6 on a number line and mark them. 

Here, 6 comes to the right of 3.

Therefore "6" is greater than "3"

And 3 comes to the left of 6.  

Therefore "3" is smaller than "6"

Example 3 :

Compare the numbers 6 and 9

Solution :

Let us locate the two whole numbers 6 and 9 on a number line and mark them. 

Here, 9 comes to the right of 6.

Therefore "9" is greater than "6"

And 6 comes to the left of 9.  

Therefore "6" is smaller than "9"

Example 4 :

Order the numbers 12, 5, 9, 6, 1, 3 from least to greatest. 

Solution :

Let us locate the numbers 12, 5, 9, 6, 1, 3 on a number line and mark them. 

From the above number line, write the numbers from left to right to list them in order from least to greatest.  

Thus, we get

1, 3, 5, 6, 9, 12

Example 5 :

In 2010, Sacramento, California, received 23 inches in annual precipitation. In 2011, the city received 17 inches in annual precipitation. In which year was there more precipitation ?

Solution :

Locate the two numbers 23 and 17 on a number line and mark them.

23 is to the right of 17 on the number line.

This means that 23 is greater than 17.

We can write the above situation in terms of inequality as 23 > 17.

17 is to the left of 23 on the number line.

This means that 17 is less than 23.

We can write the above situation in terms of inequality as 17 < 23.

There was more precipitation in 2010.

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