Less Than Equal To Symbol

The less than equal sign is very important in our day-to-day activities in addition to being vital in mathematics and related disciplines.

An example of the daily use of the less than equal to symbol and concept could be that suppose a worker is working in the industry. In his contract, he was told that he can be paid a maximum of 2500 rupees per day. The maximum here brings the less than equal to the concept in play by suggesting that he can either be paid less than 2500 rupees per day or he can also be paid 2500 rupees per day depending on his performance and the workload that day.

This means the workers in the industry can be paid ≤ 2500 rupees per day.

What does the less than equal to sign mean in mathematics?

Like many other symbols, the less than equal to sign in mathematics belongs to the symbols of the inequalities category. The mathematical meaning when this sign is used between two values is that the value on the left side of the less than equal to sign is either less than the value on the right side of the sign or it is equal to the value on the right side. Both can be possible when we are using the less than or equal to sign between two numbers or variables.

For example

25x ≤ 25y

The above equation can mean two things. One can be that 25x as a whole variable is less than 25y. This can be possible if the value of x is less than the value of y. The less than equal to sign also means that 25x can be equal to 25y. This is possible when the values of both x and y are equal to each other. When we have used the less than or equal to sign ≤ that means that we have represented both the above-mentioned situations by using one symbol only.

How to use the less than equal to sign?

Now that we know what the less than equal to sign looks like, what it means when there is a greater than equal to sign between two values, and what is the mathematical significance of this sign, we should move on to knowing which situations can this less than equal to sign be used in.

For example

A situation in which we set the maximum limit for anything. Suppose if we say that an employer hires someone and tells him that the maximum we pay our delivery guys is 15,000 rupees per month. What the employer means by using the word maximum is that they cannot pay their delivery guys more than 15,000 rupees a month which automatically means that their monthly wage can be either 15,000 rupees or less than 15,000 rupees. So this entire situation can be summed up as

The employer pays his workers ≤ 15,000 rupees per month.

Another situation when the less than equal sign can come to play is algebraic equations. We can use it between two variables indicating that the first variable, which is stated before the less than equal to sign is either smaller than or equal to the second variable, which is used after the less than equal to symbol.

For example

If an algebraic equation goes like 2x+4y ≤ 3a+6b

This complex equation can simply mean two things, either that the sum of 2x and 4y is less than the sum of 3a and 6b or the sum of the former is equal to the sum of the latter. This depends upon the values of the four variables used in this specific equation i.e. x, y, ‘a’, and b.

Another condition in which the less than equal sign can be used is if we wish to set a limit for something between two values. This means that if we want to consider all the values between two values inclusive of the two limiting values, we can use the greater than or equal to sign.

For example

2 ≤ x ≤ -6

The above equation means that the value of the variable x lies between 2 and -6. This means that the value can either be any number that falls between 2 and -6 or it can also be 2 or -6 itself.

How to type the less than equal to symbol?

Now that it has been established that what the less than equal symbol looks like, what it means, and what is its mathematical significance, we need to figure out how to type this sign on our electronic devices.

The less than equal sign is considered a complex symbol so it will not be lying in plain sight on your desktop or phone keyboards. One has to look for it and there are certain steps to be followed to be able to use it on Windows, Mac, Microsoft office, and phone separately. All of those steps are listed below separately.

Type less than equal to sign on PC windows

  1. Press the Num Lock key so that it stops functioning as a cursor pad, then hold down the alt key and then type 41436 on the Num pad and then release the alt key
  2. Open Num Lock, press 2264 then type ALT+x button at the same time
  3. Using the ALT+8804 short key

Type less than equal to sign on Mac

On Mac, the less than equal to ≤ character can be achieved by pressing option, comma, and the ≤ by pressing option period. It can also be achieved by “option” + “,”

Type less than equal to sign on Microsoft office

The Microsoft office has been used as a collective term for Microsoft word, excel, and PowerPoint because all of these applications have the same way to insert the symbol of concern for us right now that is less than equal to the symbol ≤.

  1. Go to the insert tab from the taskbar at the top of your page
  2. Click on symbols from the right side of the toolbar
  3. For that click “More symbols” from the very bottom of the drop-down menu
  4. Choose mathematical operations in the subset box. This is where you will find the less than equal sign if you look closely.

Type less than equal to sign on iPhone

Type less than equal to sign on android

Sadly the iOS keyboard does not have a direct key for the less than equal to ≤ sign. One has two options to use the symbol on their iPhone. One is to copy and paste the symbol from anywhere on the internet and the other is to create a shortcut yourself.

Now creating a shortcut can be a long process and it will benefit only those users who use a certain simple on regular basis. So if your requirement for the less than or equal to symbol is a one-time thing, feel free to copy and paste it from anywhere. For those users who wish to create a shortcut on their keyboard, the following steps are to be followed:

  1. Go to settings then to general
  2. From there go to the keyboard
  3. Then select text replacement
  4. Create a new shortcut
  5. Paste “≤” into the Phrase field.
  6. Type “≤+” into the Shortcut field.
  7. Save

As with Apple, the android keyboard also does not offer any direct key for the less than equal to sign but with some elaborate steps, it can be achieved. The best possible solution to the problem is to copy and paste it from the internet.

If that does not seem sustainable to you or it is not exactly the solution you are looking for then you can download some third-party apps from the Google Play Store which can allow you to use a variety of symbols and characters on your android device including complex symbols like the less than equal to sign.

Codes of less than equal symbol

From the above-mentioned discussion, it is clear that adding the less than or greater than equal to sign for that matter is an elaborate and tedious process. For someone who needs to use it multiple times in their work, following these long steps every time you need to use it might not be the best option. For that, there are shortcuts and codes.

Difference from other signs

It is to be noted that the less than equal to sign is ≤ which is different from the less than sign i.e. < and the equality sign i.e. =. It is also worth mentioning that the less than equal to sign is not to be used in place of the much less than sign <<, the less than sign < and other signs of the sort.

This confusion is expected since the less than equal to sign has two components, the less than sign and equal to sign. An example will be explained below to assist your concepts.

The less than sign is used in situations when we know for sure that the number or variable on the left side of the sign is indeed smaller than the one on the right.

For example 32<40. In this example we have used numbers so it is very obvious that 32<40. We can also explain this with the help of certain variables like x<y that means the value of x is less than the value of y

The equal to sign is used in situations where the variable on the left is equal to the variable on the right.

For example if we say y=4 and x=y so we can automatically establish that x is equal to 4 also since x and y are equal

The less than equal to sign however means that either the variable on the left side of the sign is less than the one on the right or it can also be equal to the one on the right.

For example if we say 2a ≤ 2b that means that either 2a is less than 2b or equal to 2b depending on the value of a and b. in such cases the value of the variables is usually not given.

Conclusion

The above-mentioned discussion is a detailed account of almost everything you need to know about the less than equal sign ≤. This article can help clear up all your concepts and confusions about the less than equal to sign. you can always leave a message as to how this can be made better.

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