# ORDERING FRACTIONS AND DECIMALS

## About "Ordering fractions and decimals"

Ordering fractions and decimals :

In Math, we use "Like fractions" method to order fractions, when we have only fractions in a sequence.

And we use "Table" method to order decimals, when we have only decimal numbers in a sequence.

In case, we have both fractions and decimals in a sequence, we have to do the following steps to order the fractions and decimal numbers.

Step 1 :

Convert all the decimal numbers as fraction using the multiples of 10 (10, 100, 1000.....) as denominators.

Step 2 :

Once we convert the decimal numbers in to fractions, all the terms in the sequence will be fractions.

Now, we can use "Like fractions" method to order the fractions.

Note :

In converting decimals into fractions, if you have one digit after the decimal point, write the decimal number as a fraction with denominator "10",

If you have two digits after the decimal point, write the decimal number as a fraction with denominator "100" and so on.

## Ordering fractions and decimals - Examples

To have better understand on "Ordering fractions and decimals", let us look at some examples.

Example 1 :

Order the numbers from least to greatest

3/4, 2/5, 0.125

Solution :

In the given sequence of numbers we have both fractions and decimal numbers.,

Let us do the following steps to order the given numbers.

Step 1 :

Convert the decimal number 0.125 as fraction.

Since there are three digits after the decimal point, we can write 0.125 as a fraction with 1000 as denominator.

Thus, we get

0.125  =  125/1000

0.125  =  1/8

Step 2 :

Now all the given terms are fractions.

They are

3/4, 2/5, 1/8

Now, we can use "Like fractions" method to order the above fractiions.

In 3/4, 2/5 and 1/8, since the denominators are different, we have to convert these fractions as like fractions in order to compare them.

To make the given fractions as like fractions, let us use the LCM method.

LCM of (4,5 and 8) = 40

Now we have to make each fraction with the common denominator 40.

Multiply both numerator and denominator of the first fraction by 10

Multiply both numerator and denominator of the second fraction by 8

Multiply both numerator and denominator of the third fraction by 5

Now we can compare the fraction and order the fraction from least to greatest

The order of the given fractions from least to greatest is

1/8, 2/5, 3/4

or

0.125, 2/5, 3/4

Example 2 :

Order the numbers from least to greatest.

5/6, 0.375, 1/4

Solution :

In the given sequence of numbers we have both fractions and decimal numbers.,

Let us do the following steps to order the given numbers.

Step 1 :

Convert the decimal number 0.375 as fraction.

Since there are three digits after the decimal point, we can write 0.375 as a fraction with 1000 as denominator.

Thus, we get

0.375  =  375/1000

0.375  =  3/8

Step 2 :

Now all the given terms are fractions.

They are

5/6, 3/8, 1/4

Now, we can use "Like fractions" method to order the the above fractions.

In 5/6, 3/8 and 1/4, since the denominators are different, we have to convert these fractions as like fractions in order to compare them.

To make the given fractions as like fractions, let us use the LCM method.

LCM of (6, 8 and 4)  =  24

Now we have to make each fraction with the common denominator 24.

Multiply both numerator and denominator of the first fraction by 4

Multiply both numerator and denominator of the second fraction by 3

Multiply both numerator and denominator of the third fraction by 6

Comparing the numerators in the above like fractions, the order of the given fractions from least to greatest is

1/4, 3/8, 5/6

or

1/4, 0.375, 5/6

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