LOCATING NUMBERS ON A NUMBER LINE

Usually we locate numbers on a number line in order to compare and order numbers.

That is,  if we want to compare two numbers, first we have to locate the numbers on the number line and mark them.

The number which comes to the right of the other number is greater. The number which comes to the left of the other number is smaller.

To order the numbers, we have to locate the given numbers on the number line and mark them. Then, write the numbers from left to right to list them in order from least to greatest.

Comparing Numbers Using Number Line

Example 1 :

Locate the numbers 3 and 6 on a number line and compare them.

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 2 :

Locate the numbers 6 and 9 on a number line and compare them.

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.

Ordering Numbers Using Number Line

Question :

Locate the numbers 12, 5, 9, 6, 1, 3 on a number line and order them 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

Solving World Problems Using Number Line

Problem 1 :

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.

Problem 2 :

John recorded the following golf scores during his first week at a golf academy. In golf, a lower score beats a higher score.

Graph John’s scores on the number line, and then list the numbers in order from least to greatest.

Solution :

Step 1 :

Graph the scores on the number line.

Step 2 :

Read from left to right to list the scores in order from least to greatest.

The scores listed from least to greatest are

0, 1, 3, 5, 6, 9, 12

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