How to Arrange Numbers & Fractions from Least to the Greatest?

 

How to Arrange Numbers & Fractions from Least to the Greatest?

In mathematics, numbers can be arranged in ascending order or descending order. Ascending order refers to the arrangement of numbers from least to greatest. On the other hand; when numbers are arranged from the greatest to the least, it is referred to as descending order. We will confine ourselves to only arranging numbers from least to greatest.

In this article, we will provide a comprehensive guide to arranging the number. We will learn how to write whole, negative, fractions, and decimal numbers in ascending order. At last, we will solve different examples to understand it better. 

Let’s dive in and explore the art of arranging numbers.

What is Ascending or Increasing order?

Ascending or increasing order refers to arranging a set of numbers from the smallest value to the largest value. In ascending order; each number is greater than the previous number. Mathematically, ascending order is denoted by the symbol "<" (less than). 

For example, consider a set of numbers 3, 7, 1, 5, and 2. 

These numbers would be arranged as 1, 2, 3, 5, and 7 in ascending order.

It can be represented in ascending order as:

1 < 2 < 3 < 5 < 7

This representation indicates that the number on the left is smaller than the number on the right. 

Methods for arranging the whole numbers from least to greatest 

Whole numbers are non-negative integers, including zero and all positive integers. Here are the step-by-step methods for arranging the whole numbers in ascending order. 

1. Write the smallest number among the given set of whole numbers. This will be the starting point for the arrangement. 
2. Compare the smallest number with the remaining numbers in the set. 
3. Repeat the comparison until all the numbers are arranged in ascending order. 
4. Once you have arranged all the numbers double-check your work to ensure accuracy. 

Arranging the decimal number from least to greatest 

Follow the following steps for arranging the decimal numbers from least to greatest.

1. Start by comparing the whole number parts of the decimal numbers. If there are differences in the whole number parts, the number with the smaller whole number part is the smallest.
2. If the whole number parts are the same, move on to compare the tenths place digit of each decimal number. The number with the smaller digit in the tenth place is the smallest.
3. If the tenth-place digits are the same, move on to compare the hundredth-place digits. Continue this process for each subsequent decimal place until all the decimal numbers are compared.

Ordering fractions from least to greatest 

Here is a step-by-step method for ordering fractions in ascending order using two techniques: 

• Making the denominators the same 
• Converting them to decimal form.

Making the Denominators the Same

1. Identify the fractions you want to arrange.
2. Find a common denominator for all the fractions. Determine the least common multiple (LCM) of the denominators.
3. Convert each fraction to an equivalent fraction with the common denominator by multiplying both the numerator and denominator by the appropriate factors.
4. Compare the numerators of the fractions and order them from least to greatest.
5. Write down the fractions in ascending order.

Converting Fractions to Decimal Form

• Convert each fraction to decimal form by dividing the numerator by the denominator.
• Compare the decimals obtained for each fraction and order them from least to greatest.
• Write down the fractions in ascending order based on their decimal equivalents.

An ordering fraction calculator can be used to arrange the fractions in ascending orders according to the above methods to get the result in a fraction of a second.

Also check: Maths Handwritten short notes Class 11 And 12

Writing negative numbers in ascending order

To write the negative number in ascending order, follow these steps:

1. Gather the negative numbers that you want to arrange in ascending order.

2. Start by comparing the absolute values of the negative numbers. The number with the smaller absolute value is closer to zero and therefore considered smaller in magnitude.

3. If two negative numbers have the same absolute value, the number with the negative sign is considered smaller.

4. Order the negative numbers based on the comparisons made in the previous steps. Write them down in ascending order, from the smallest (closest to zero) to the largest (farthest from zero).

Solved Examples 

Example 1:

Arrange the following fraction from least to greatest.

1/3, 1/6, 2/9, 7/15 

Solution: 

Step 1: Determine the least common multiple (LCM) of the denominators (3, 6, 9, and 15).

2	3, 6, 9, 15
3	3, 3, 9, 15
3	1, 1, 3, 5
5	1, 1, 1, 5
	1, 1, 1, 1

LCM of 3, 6, 9, 15 = 2 × 3 × 3 × 5 = 90

Step 2: Convert the fraction to an equivalent fraction with a common denominator of 90.

1/3 = (1 × 30)/ (3 × 30) = 30/90

1/6 = (1 × 15)/ (6 × 15) = 15/90

2/9 = (2 × 10)/ (9 × 10) = 20/90

7/15 = (7 × 6)/ (15 × 6) = 42/90

Step 3: Compare the numerators of the fractions and arrange them in ascending order.

15/90 < 20/90 < 30/90 < 42/90

Step 4: Write down the fractions in ascending order.

The fractions arranged from least to greatest are 1/6, 2/9, 1/3, and 7/15.

Alternative Methods 

Step 1: Convert each fraction to decimal form by dividing the numerator by the denominator.

1/3 = 0.333

1/6 = 0.167

2/9 = 0.222

7/15 = 0.467

Step 2: As the whole number parts are the same, move on to compare the tenths place digit of each decimal number. The number with the smaller digit in the tenth place is the smallest.

0.167 < 0.222 < 0.333 < 0.467

Step 3: Write down the fractions in ascending order.

The fractions arranged from least to greatest are 1/6, 2/9, 1/3, and 7/15.

Example 2:

Arrange the following number in ascending order.

-456, -459, -680, -970, -999

Solution: 

In his example, -456 is the largest number and -999 is the smallest number out of the given numbers. 

By arranging the numbers in ascending order, we can see the progression from the smallest to the largest number.

The given integers can be arranged in ascending order as follows:

-999 < -970 < -680 < -459 < -456.

Conclusion

In this article, we have discussed the concept of ordering the number from least to greatest. We learned how to arrange different types of numbers and fractions in ascending order. We solved different examples for readers to understand this concept in a better manner.