INCREASING ORDER-RULES AND EXAMPLES

INCREASING ORDER

Increasing order is the arrangement or positioning of numbers from smallest to largest. They can be done when the units of the numbers are the same or by converting all the numbers into the same units. For example, heights of students measured in feet can be arranged in an increasing order which means from smallest to the largest value in a class. 

This increase can be in any form such as numbers, alphabets, weights, heights and time as well. Increasing order can also be called ascending order. The words increasing and ascending both mean the same thing. 

As you can see in the image below, the numbers 2, 3, 5, 8, 10 and 13 are arranged in a graph to depict ascending order.

We can either use a comma ‘ , ‘ or a ‘<’ sign which means ‘less than’. The number on the right of this symbol (<) is greater than the one on the left. For example: 

2 < 3 < 5 < 8 < 10 < 13

RULES FOR ASCENDING/ INCREASING ORDER

A few rules need to be kept in mind while arranging digits in ascending order. 

1. The first number is always the smallest number.
2. The last number is always the largest number.
3. If the units of the numbers are not the same, then they must be converted to the same unit before arranging in ascending order. For example, we have quantities in kilograms and grams, then we must either convert kilograms to grams or vice versa before sorting them in increasing order.
4. The values are always in order from the smallest to the largest.

INCREASING ORDER FOR DIFFERENT TYPES OF NUMBERS

1. Negative numbers and number line

Negative numbers can also be arranged in ascending order but the rules are different for them. We will understand this concept with the help of the number line. 

The numbers to the right of 0 are positive numbers and the numbers to the left of the number line are negative numbers. The case of negative numbers is opposite to that of positive numbers. As we go leftwards on the number line, the numbers keep on falling. 

It means that the number -2 is greater than -3 or -3 < -2. As we go left to the number line, the numbers keep on decreasing. 

For example –    Arrange the given number in ascending order: -5, 6, 3, -2

In this case, the smallest number is -5. The ascending order looks like:

-5 < -2 < 3 < 6.

2. Whole numbers and natural numbers

Whole numbers start from 0 and go on till infinity whereas natural numbers start from 1 and go on till infinity. Since the numbers are positive in both types, the increasing order follows the same rules. The number 0 is the smallest number in case of whole numbers and 1 is the smallest number in case of natural numbers. 

3. Decimals and Fractions

It is easy to arrange the decimals as they also follow the normal rules. Let us understand this with an example.

We have the numbers – 1.23, 1.20, 1.36, 0.25, 0.99.

We find the smallest number by comparing the digit to the left of the decimals. Here 0.25 and 0.99 are the numbers with 0 to the left. Out of 0.25 and 0.99, we know that 25 is less than 99 so 0.25 is the smallest number. 

When we arrange them in increasing order, we get this –

0.25 < 0.99 < 1.20 < 1.23 < 1.36

For fractions, we can either convert them into decimals and compare or convert them into like fractions and then compare.

Suppose we have, \frac{1}{4}\frac{2}{3}\frac{1}{2}.

We can convert them to decimals –

{1}/{4} = 0.25

{2}/{3} = 0.66

{1}/{2} = 0.5

Now we can simply arrange them in increasing order as 0.25 < 0.5 < 0.66 and in fractions as

1 / 4<1 / 2<2 / 3

Also, we can find a common denominator. 

LCM of (2, 3, 4) = 12

We can convert the denominators of all the fractions into 12.

\frac{1 \times 3}{4 \times 3}=\frac{3}{12}

\frac{2 \times 4}{3 \times 4}=\frac{8}{12}

\frac{1 \times 6}{2 \times 6}=\frac{6}{12}

Since the denominator is the same, we can arrange them in ascending order normally based on the value of the numerator. Here 3<6<8\left(\frac{3}{12}<\frac{6}{12}<\frac{8}{12}\right). It gives us the same answer no matter what method we use.