In your day-to-day life, you will observe that comparison is something unavoidable. We compare various quantities based on several parameters. For instance, children compare the number of chocolates, toys, and even friends one has when compared to the other. Furthermore, we compare scores of exams conducted at the national and international levels. Comparison of ranks and IQ score determines the ranking and intelligence of individuals. In mathematics, we compare two or more numbers. Whenever there is an inequality among the number of objects, there comes the word “greater than or less than”. For this purpose, two terms are extensively used: “greater than” and “less than”. Moreover, you will see the symbols > and < are used for greater than and less than respectively. These words can be replaced with the help of symbols. And you can explore how these symbols are used to show the relation between two numbers and how it saves time. The concept of comparison of numbers is fun and interesting. It is one of the easiest lessons in mathematics.
Let us go through a situation and try to understand the comparison taking place in our day-to-day life. Two friends Sam and Ryan were having a conversation. Sam said today it’s hot. Yesterday it was not that hot. Ryan said no Sam weather is not that hot today. Now, how can you solve this conflict?
A comparison of temperatures over two days can help us. This requires the temperature of both days. Further, they can search on the internet and get the numerical value of the temperature in degrees and compare. And then, they can see which is greater and conclude accordingly hence this will resolve the conflict between Sam and Ryan.
The story of comparing numbers doesn’t end here. You can compare your weight, height, marks, etc. with others. Further, you can compare prices of different items like food, clothes, books, groceries, etc.
When you say you can compare the price of different items, that means you can even compare decimal numbers. Because prices are very often in decimal numbers.
Importance of Symbols
With the help of symbols, you can save yourself from writing long sentences to share your idea of comparison. Eventually, using symbols makes it easy and convenient to write comparison sentences.
Greater than Symbol
Greater than symbol is a mathematical sign used to represent inequality between two numbers. As you observe the style of the symbol is very closely related to the mathematical meaning of greater than. This symbol is written in between two quantities. The quantity which is more in value, size or the parameter being compared will be on the wide end i.e., to the left of the symbol. While on the right side of the symbol next to the pointed end we will have the smaller one. To show inequality among the quantities in consideration you can use the greater than symbol. And you can avoid using long sentences to share the idea of comparison.
For Example:
Since 4 by its value is greater than 3.
Example 1:
Which is a greater number 5 or 1?
Here, 5 is greater than 1.
Mathematically, we can represent it as 5 > 1
The rules to represent using the > symbol can be listed as given below:
- A symbol > is like two equal slant lines meeting at an acute angle toward the right side.
- The greater number will always be followed by the > symbol, prior to the wide end.
- The symbol > is followed by the smaller number, post the pointed vertex.
Equal to sign
It represents the equality between two similar numbers. A symbol used is “=”.
Example-
30 and 30. Here thirty is equal to 30.
Mathematically it is represented as- 30=30.
Tricks to remember the greater than symbol
Forms of the > sign
We can use a combination of the greater than and the equal sign to represent quantities that can be greater than or equal to. It is denoted by ≥. If we say x is greater than or equal to y then we write it as x ≥ y. This statement is true in both the cases of x > y or x = y.
Example: Pass grade (P) = 35 and above.
Shera scores 35 and Veera scores 67. Mathematically Shera’s score is equal to the pass grade while Veera’s score is greater than the pass grade. Hence both of them receive the grade P.
We can write the condition as P = score ≥ 35.
TRICK TO REMEMBER THE SIGN:
The angular bracket opens to that side which has a large number.
OR
Alligator Method
The alligator method is a way where you can easily relate the greater than and less than signs with the open mouth of a crocodile. Imagine the symbol as the mouth of a crocodile. And the crocodile opens its mouth to that side where there is a greater number. The greater numbers make the crocodile open its mouth wide. This method helps a kid to memorize the symbol with its meaning in the early phases of learning about these symbols.
Example: Compare the numbers 989 and 456.
The number 989 is greater than 456.
So, the crocodile will open its mouth towards the left side.
Hence, we will write this as
989 > 456.
SOME EXAMPLES OF GREATER THAN SYMBOLS:
Comparing Whole Numbers and Integers
- 5 and -5.
5 is greater than -5.
Therefore, 5 > -5.
- -1 and -10.
-1 is greater than -10.
Therefore, -1 > -10.
Comparing Fractions
- 3/2 and 2/3
32 is greater than 23.
Therefore, 32 > 23.
Comparing Decimals
- 0.02 and 0.002.
0.02 is greater than 0.002.
Therefore, 0.02 > 0.002.
Comparing Exponents
- 26 and 25.
2^5(2×2×2×2×2=32) and 2^6(2×2×2×2×2×2=64).
This means 2^6 is greater than 2^5. Therefore, 2^6 > 2^5.
Problems
Question 1) Ram read four pages of the book and John read two more pages than Ram. Who reads a greater number of pages?
Solution:
Number of pages read by Ram = 4
Number of pages read by John = 6
6 is greater than 4. So, 6 > 4.
Hence, John read a greater number of pages.
Question 2) Sam has four notebooks and he gave one notebook to Peter. Peter already had five notebooks. Who has a greater number of notebooks?
Solution:
Number of notebooks Sam has after giving to Peter = 3
Total number of notebooks Peter has = 1+5 = 6
6 > 3.
Therefore, Peter has a greater number of notebooks.
Question 3) The base and height of a right-angled triangle ABC are 4 and 6 cm respectively. While for a right-angled triangle, PQR base and height are 10 and 20 cm respectively. Which triangle has more area?
Solution
Area of triangle ABC = 1/2×4×6=12 cm²
Area of triangle PQR = 1/2x10x20=100 cm²
12 cm² < 100 cm². Therefore, the Area of triangle PQR is greater than triangle ABC.
Question 4) Compare the following numbers:
456__________4456
550___________1000
9980___________5678
89____________89
Solution-
1) Since 456 is less than 4456. So, 456 < 4456.
2) 550 is less than 1000. So, 550 < 1000. 3) 9980 is greater than 5678. So, 9980 > 5678.
4)89 is equal to 89. So, 89=89.
Question 5) Mary got 49 marks in Math. While Natasha got 30 marks. Who got more marks?
Solution:
Marks obtained by Mary = 49
Marks obtained by Natasha = 30
49 is more than 30.
So,49 > 30.
Therefore, Mary got more marks.
Question 6) In a factory, the number of clothes manufactured in March was 567892, and in April was 597653. In which month a greater number of clothes are manufactured?
Solution:
Number of clothes manufactured in March =567892
Number of clothes manufactured in the month of April=597653
597653 is greater than 567892.
So,597653>567892. Hence in April, a greater number of clothes are manufactured.
Question 7) Put < > or = sign.
(0.001)^2 _____________ (0.001)^3
(0.01)^-1_____________ (0.01)^-2
Solution:
1) (0.001)^2=0.000001
And (0.001)^3=0.000000001
Hence, (0.001)^2 is greater than (0.001)^3.
Therefore, (0.001)^2 > (0.001)^3.
2) (0.01)^-1=1/100=100
(0.01)^-2 = 1 / (0.01 × 0.01) = 1 / 0.0001 = 10000
Hence, (0.01)^-1 < (0.01)^-2.
Question 8) There are three tables table A has a height of 1/12 meter table B has a height of 1/4 meter and table C has a height of 1/24 meter. Arrange the height of these tables in decreasing order.
Solution:
Height of table A =1/12
Height of table B =1/4
Height of table C =1/24
1/4 > 1/12 > 1/24
Hence, table B > table A > table C.
Question 9) Shreya burnt 25789 kCal in the gym on day 1 and 45876 kCal on day 2 in the gym. On which day does she burn more calories?
Calories burnt on day 1=25789
Calories burnt on day 2=45876
Hence, 45876 > 25789.
So, a greater number of calories are burnt on day 2.
Question 10) Natasha has 2500 rupees. She spent 3/5 th of the money on books and 2/5 th on groceries. Which product contributed more to her expenditure?
Money spent on books= 3/5×2500= 1500
Money spent on Grocery = 2/5×2500= 1000
1500 > 1000
Hence, she spent more money on books.
Question 11) Compare 589.256 and 589.254.
Solution:
Clearly,
589.256˃589.254
