Comparison: In our day-to-day life, we come across many situations where we can use the comparison of quantities, objects, things or numbers. Comparison compares the quantities of objects or numbers and verifies which is greater and the one which is smaller or checks whether they are equal or similar.

Most of the time, we compare one person’s height, weight, and marks with another person. The most important point we should remember in comparison is always we can compare the quantities of a similar kind only. For example, we can compare the heights of the two-person but not the height of one person to the weight of another person.

What is Comparison?

In our day to day life, we come across many situations where we can use the comparison of quantities, objects, things or numbers. Comparison is one of the most used daily activities in our life.

Most of the time, we compare one person’s height, weight, and marks with another person. The most important point we should remember in comparison is always we can compare the quantities of the similar kind only. For example, we can compare the heights of the two people but not the height of one person to the weight of another person.

Comparison compares the quantities of objects or numbers and verifies which is greater and the one which is smaller or checks whether they are equal or similar.

In Mathematics, we will compare the numbers by using mainly three special symbols that are given below:

1. Greater than \(( > )\)
2. Less than \(( < )\)
3. Equals to \(( = )\)

Comparison Symbols in Math

We will compare the numbers such as natural numbers, whole numbers, integers, fractions, and decimal numbers in mathematics. In Math, while comparing the numbers, we will use mainly three symbols: greater than, less than and equal sign.

Greater Than Type Operator

The operator used to find the greater number or quantity among the two numbers or quantities is called greater than type operator.

The open side of the greater than operator always faces towards the greater number or quantity, and the narrow endpoint of the greater than operator faces towards, the smaller number or quantity.

The number or quantity to the left of the greater than operator is greater.

Example: In the numbers \(5\) and \(2\), we know that \(5\) is greater than \(2\).

Less Than Type Operator

The operator used to find the smaller number or quantity among the two numbers or quantities is called less than type operator.

The open side of the less-than operator always faces towards the greater number or quantity, and the narrow endpoint of the less-than operator faces towards the smaller number or quantity.

The number or quantity which is to the left of less than type operator is smaller.

Example: In the numbers \(3\) and \(2\), we know that \(2\) is smaller than \(3\).

Comparison of Numbers

Comparison of numbers is the process of comparing the numbers and exploring the difference between the numbers.

Numbers with Unequal Number of Digits

While comparing the number with the unequal digits, the number with more digits is larger than the number with fewer digits is smaller.

Example:

In the numbers \(999\) and \(4,999\) is larger as it has more digits.

Numbers With the Same Number of Digits

To compare the numbers having the same digits, we compare the numbers starting from the extreme left-most digits. The number with a larger extreme left-most digit is larger among them.

If the left-most digits of the numbers are equal, we will go with the next digit towards the right to compare.

Example: Compare the numbers \(632\) and \(529\).

Here, given two numbers has three digits, comparing the left-most digits of the given numbers, \(6\) is greater than \(5\).

Thus, \(632\) is greater than \(529\).

Conclusions made based on the given rule are:

1. All two-digit numbers are greater than the one-digit numbers
2. All three-digit numbers are greater than the two-digit numbers
3. All four-digit numbers are greater than the three-digit numbers
4. All five-digit numbers are greater than the four-digit numbers, and so on.

Comparison of Fractions

We can compare the fractions for observing the interests, profits, and discounts in real-life problems. Fractions are part of the whole. Fractions with the same denominators are like fractions, and fractions with different denominators are unlike fractions.

Comparison of Like Fractions

Two fractions are said to be like fractions that have the same denominator and different numerators. While comparing the like fractions, the fraction whose numerator is larger in given like fractions is the larger fraction, and the fraction with a smaller numerator is the smaller.

Example: Compare \(\frac{6}{{17}}\) and \(\frac{{16}}{{17}}\)

1. Observing the denominators of the given fractions: \(\frac{6}{{17}}\) and \(\frac{{16}}{{17}}\)
2. Here, denominators of given fractions are the same.
3. So, comparing the numerators \(16 > 6\)
4. So, the fraction with the larger numerator is larger.

Hence, \(\frac{6}{{17}} < \frac{{16}}{{17}}\)

Comparison of Unlike Fractions

To compare fractions with different denominators, also known as unlike fractions, find the least common multiple \(({\rm{LCM)}}\) to make denominators of the fractions the same. After making their denominators equal to \({\rm{LCM,}}\) compare the numerators of the fractions.

A fraction with a larger numerator is larger and vice-versa.

Example: Compare \(\frac{1}{2}\) and \(\frac{2}{5}\)

1. Given fractions \(\frac{1}{2}\) and \(\frac{2}{5}\) are unlike fractions.
2. Find the \({\rm{LCM}}\) of \(2\,\& \,5\), so \({\rm{LCM(2,5)}}\,{\rm{ = }}\,{\rm{10}}\)
3. Now, make their denominators equal.
   \(\frac{1}{2} = \frac{1}{2} \times \frac{5}{5}\) and \(\frac{2}{5} = \frac{2}{5} \times \frac{2}{2}\,\)
4. Now, compare the fractions obtained, \(\frac{5}{{10}}\) and \(\frac{4}{{10}}\)
5. Comparing the numerators, \(5\,\, > \,\,4\)
6. The fraction with a greater numerator is the larger fraction. Thus,\(\frac{5}{{10}}\,\, > \,\frac{4}{{10}}\)

Therefore, \(\frac{5}{{10}}\,\, > \,\frac{4}{{10}}\)

Comparison of Decimal Numbers

Numbers that have both the whole number and the decimal part are called decimal numbers. We know that the decimal number with a larger whole part is the greater number.
Another way of comparing the given decimal numbers is to compare the most significant (first digit in the decimal, other than zero) numbers of the given decimals.

Uses or Importance of Comparison

Comparison is the process of comparing and exploring differences between numbers or quantities. Some of the uses of comparison are listed below:

1. In real life to compare the heights and weights of the persons.
2. To compare the height and depth of the objects.
3. To observe the distances of objects.
4. In geometry, to compare the line segments, polygons etc.
5. In science, to compare the temperatures and humidity of the places.
6. To check discounts in sales.
7. In medical prescriptions given by the doctor.
8. To check the test scores of the students.

Solved Examples – Comparison

Q.1. Compare the given fractions \(\frac{6}{{13}}\,\,and\,\frac{6}{{20}}\)
Ans: Given fractions are \(\frac{6}{{13}}\,\,and\,\frac{6}{{20}}\)
Here, the fractions have the same numerator \((6)\)
If two fractions have the same numerator and different denominators, then the fraction with the least denominator is larger, and the fraction with a larger denominator is smaller.
While comparing the denominators of two fractions, \(13\) is smaller than \(20\). \((13\,\, < \,\,20)\).
So, the fraction \(\frac{6}{{13}}\)  is larger as compared to the \(\frac{6}{{20}}\)
This can be represented mathematically, \(\frac{6}{{13}} > \frac{6}{{20}}\).

Q.2. Prince home is located \(490\) metres away from the supermarket and \(4\,{\rm{km}}\) away from the city library. By comparing their distances, which is far from the home of Prince?
Ans: Given:

The distance between a library and home is \(4\,{\rm{km  = }}\,{\rm{4000}}\,{\rm{m}}\) and the distance between supermarket and home is \(490\,{\rm{m}}\).
So, comparing the above absolute values, the number with more digits is greater.
So, \(4000\,{\rm{m}}\,\,{\rm{ > }}\,\,{\rm{490}}\,{\rm{m}}\)
Therefore, the city library is far away from the Prince home.

Q.3. Keerthi has \(3\,{\rm{kg}}\) of apples, and Laxmi has \(5\,{\rm{kg}}\) of potatoes. Comparing the weights, find who has a large number of fruits or vegetables?
Ans: Given, Keerthi has \(3\,{\rm{kg}}\) of apples, and Laxmi has \(5\,{\rm{kg}}\) of potatoes

Comparing their weights, we can say that five is larger than three.
Therefore, \(5\,{\rm{kg}}\,\,{\rm{ > }}\,\,{\rm{3}}\,{\rm{kg}}\)
Hence, Laxmi has more vegetables or fruits as compared to Keerthi.

Q.4. Fill in the blanks with the proper symbols of comparison used in mathematics.
\(123\_\_\_23\)
\(111\_\_\_111\)
\(555\_\_\_1000\)
Ans: In Math, while comparing the numbers, we will use mainly three symbols: greater than, less than and equal sign
The symbols used are : \( > ,\, < ,\, = \)
\(123\,\, > \,\,23\)
\(111\, = \,111\)
\(555\,\, < 1000\)

Q.5. Compare the two line segments given below and observe the larger and smaller line segment among them.

Ans: In the above figure, by observing, the line segment \(AB’s\) length is more than the line segment \(CD\).
Thus, \(\overline {AB} \,\, > \,\,\overline {CD} \)
Therefore, line segment \(AB\) is larger, and line segment \(CD\) is smaller.

Summary

In this article, we have studied the comparison, comparing and exploring the difference of quantities or numbers. We have discussed the symbols of comparison in mathematics, such as greater than type operator, less than type operator and equal sign with examples.

This article discussed comparing numbers (numbers with the same digits and numbers with different digits), comparing like and unlike fractions, and comparing decimal numbers. We have studied the importance of comparison in our day-to-day lives and solved some questions, which helps us understand the concept easily.

Learn the Concepts on Comparing Quantities

Frequently Asked Questions (FAQs) – Comparison

Q.1. How do you compare numbers in Math?
Ans: In Math, numbers are compared by observing their place values.

Q.2. What are the comparison symbols in Maths?
Ans: The symbols of comparison used in Math are
1. Greater than \(( > )\)
2. Lessthan \(( < )\)
3. Equals to \(( = )\)

Q.3. What is the use of comparison in daily life?
Ans: In real life, the comparison is used to compare the weights, heights and marks of two persons and the distances, height and depth of the objects.

Q.4. What are the methods used to compare the fractions?
Ans: The fractions are compared by using two methods:
1. Decimal method
2. Cross-multiplication method

Q.5. What are the two mathematical concepts used in comparing the quantities?
Ans: The two concepts used in comparing quantities are
1. Ratio
2. Proportion

Now you are provided with all the necessary information on the concept of comparison and we hope this detailed article is helpful to you. If you have any queries regarding this article, please ping us through the comment section below and we will get back to you as soon as possible.