ORDERING INTEGERS FRACTIONS AND DECIMALS

Ordering Integers

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

Let us look at an example to understand this. 

Example :

Order the integers -2, -5, 4, 0, -3, -1, 3 from least to greatest. 

Solution : 

Let us locate the integers -2, -5, 4, 0, -3, -1, 3 on a number line and mark them. 

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

Thus, we get

-5, -3, -2, -1, 0, 3, 4

Ordering Fractions

To order fractions, first we have to make the denominators of all the fractions same.

Then, we have to compare the numerator and order the fractions from least to greatest or greatest to least. 

Example :

Order the fractions from least to greatest : 

3/4, 2/5, 1/8

Solution :

Here, the denominators are different.

So, we have to find the least common multiple (LCM) of the denominators. 

LCM of (4, 5 and 8)  =  40. 

Now we have to make the denominator of each fraction as 40 using multiplication.

3/4 = (3 ⋅ 10)/(4 ⋅ 10) = 30/40

2/5 = (2 ⋅ 8)/(5 ⋅ 8) = 16/40

1/8 = (1 ⋅ 5)/(8 ⋅ 5) = 5/40

Now, compare the numerators of like fractions above and order them from least to greatest.

5/40, 16/40, 30/40

Substitute the corresponding original fractions.  

1/8, 2/5, 3/4

Therefore, order of the given fractions from least to greatest is

1/8, 2/5, 3/4

Ordering Decimals

Set up a table with the decimal point in the same place for each number.

Place each decimal number in the table. 

Fill in the empty squares with zeros.

Compare using the first column on the left

If the digits are equal move to the next column to the right until one number wins.

Let us look at an example to understand this. 

Example :

Order the decimal numbers 0.098, 0.123 and 0.985 from least to greatest.

Solution :

To order the given decimal numbers, first we have to write them in a table as given below. 

To get the least one, compare the numbers in the first column (Units).

We get 0 in all the three decimal numbers in the first column. 

So, let us move to the third column (Tenths) and compare the numbers.

In third column, we get 0 in 0.098.

Therefore, 0.098 is the least among the given decimal numbers.  

In the same third column, we get 1 in 0.123. 

This is the next least decimal number.  

Therefore, the order of the given decimals from least to greatest is

0.098, 0.123, 0.985

Note : 

In the third column also, if you get the same number in all the three decimal numbers, compare the numbers in the fourth column (Hundredths column) and so on. 

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