COMPARING AND ORDERING WHOLE NUMBERS

The set of all non negative integers is whole numbers.

That is,

W = {0, 1, 2, 3, 4, .......}

We use number line to compare and order whole numbers.

That is,  if we want to compare two whole 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 whole 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 Whole Numbers

Example 1 :

Compare the whole numbers 3 and 6.

Solution :

Let us locate the two whole 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 :

Compare the whole 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.

Ordering Whole Numbers

Question :

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

Solution :

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

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

Thus, we get

1, 3, 5, 6, 9, 12

Real World Problems

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 whole 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

Problem 3 :

Write <, > or = in the blank.

a) 1385 ____ 1300 + 30 + 105

b) 20104 _____ 20000 + 4 + 100

Solution :

a) 1385 > 1335

b) 20104 = 20104

Problem 4 :

Martine puts number cards in the order shown below.

Which number can Martine put on the empty card?

A) 659      B) 821      C) 722     D) 584

Solution :

By observing the numbers in the list, it is arranged from least to greatest.

The required number should be greater than 673 and lesser than 729. So, the answer is 722.

Problem 5 :

Marco has 342 photos in an album. Rosa has 297 photos. Hideki has more photos than both Marco and Rosa. Which shows how many photos Hideki could have?

A) 189      B) 382    C) 287   D) 314

Solution :

Number of photos Macro has = 342

Number of photos Rosa has = 297

Number of photos Hideki has is greater than Macro and Rosa. So, the answer is 382, Option B is correct.

Problem 6 :

Daryl writes these numbers on a number line.

Which number can Daryl write to fill in the blank?

A) 5,780     B) 5,049    C) 6,417     D) 6,704

Solution :

The required number should lie in between 5078 and 6147.

5078 < 5780 < 6147

So, the answer is option B.

Problem 7 :

An airplane travels 45,890 miles. The next week it travels 37,604 miles. The following week it travels 40,098 miles. Which shows the miles in order from greatest to least?

A) 40,098; 37,604; 45,890   B) 45,890; 37,604; 40,098

C) 37,604; 40,098; 45,890    D) 45,890; 40,098; 37,604

Solution :

First time the distance covered by airplane = 45890 miles

Second time the distance covered = 37604 miles

Third time the distance covered = 40098 miles

Ordering from greatest to least,

45890, 40098, 37604

So, option D is correct.

Problem 8 :

A company ships 35,809 pears and 21,790 plums. It also ships more apples than plums, but fewer apples than pears. Which shows how many apples could have been shipped?

A)  35,908   B) 21,097     C) 34,118    D) 40,055

Solution :

• Number of pears = 35809
• Number of plums = 21790

Number of appples should be greater than plums and lesser than pears. So, the answer is option C. Number of apples is 34118.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.