COMPARING AND ORDERING NUMBERS

We use number line 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

Example 1 :

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 2 :

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.

Ordering Numbers

Question :

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

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 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

Work with a partner. Decide which number form (fraction, decimal, or percent) is more common. Then find which is greater.

Problem 3 :

7% sales tax or 1/20 sales tax.

Solution :

7% sales tax :

7% = 7/100

= 0.07

1/20 sales tax :

1/20

To convert the denominator as 100, we should multiply both numerator and denominator by 5.

= (1/20) x (5/5)

= 5/100

= 0.05

So, 7% of sales tax is greater.

Problem 4 :

0.37 cup of flour or 1/3 cup of flour

Solution :

0.37 cup of flour :

0.37

1/3 cup of flour :

1/3

Convering it as decimal, we get

= 0.33

So, 0.37 cups of flour is greater.

Problem 5 :

3  5/8 inch wrench or 3.69 inch wrench

Solution :

3  5/8 inch wrench :

= 3  5/8

= 29/8

Dividing using long divison, we get 3.625 inch.

3.69 inch :

It is already in decimal. 3.69 inch wrench.

So, 3.69 inch wrench is greater.

Problem 6 :

12  2/3 dollars or 12.56 dollars.

Solution :

12  2/3 dollars :

= 12  2/3

= 38/3

Dividing it, we get

= 12.6 dollars.

12.56 dollars :

It is already in dollars.

So, 12  2/3 dollars is greater.

Problem 7 :

93% test score or 7/8 test score

Solution :

93% test score :

93% = 93/100

= 0.93

7/8 test score :

= 7/8

Dividing it, we get

= 0.875

So, 93% of test score is greater.

Problem 8 :

5  5/6 fluid ounces or 5.6 fluid ounces

Solution :

5  5/6 fluid ounces :

5  5/6 = 35/6

Dividing it, we get

= 5.833

5.6 fluid ounces :

It is already in decimal.

So, 5  5/6 fluid ounces is greater.

Problem 9 :

Compare and order the numbers from least to greatest.

38%, 8/25, 0.41

Solution :

Simplifyinf 38% :

38% = 38/100

= 0.38

Simplifying 8/25 :

= 8/25

To convert the denominator of 8/25 as 100, we have to multiply both numerator and denominator by 4.

= (8/25) x (4/4)

= 32/100

= 0.32

Simplifying 0.41 :

Here 0.41 is already decimal.

By comparing these three decimals, we get the order from least to greatest as

0.32, 0.38, 0.41

8/25, 38%, 0.41

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.