Less Than or Equal to

Less Than or Equal to
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In this mini-lesson, we will explore the concept of 'less than or equal to'. As we do that, we will be covering less than or equal to symbol in words, less than or equal to examples, and greater than symbol in a sentence.

We already know symbols for 'greater than \((>\))', 'less than \((<)\)' and 'is equal to \((=)\)'.

We also know that:

  • The 'greater than' symbol is used to show that one quantity is greater than the other quantity.
  • The 'lesser than' symbol is used to show that one quantity is lesser than the other quantity.
  • The 'is equal to' symbol is used to show that two quantities are equal.

Greater than, lesser than and is equal to symbols with examples are shown.

What if we have to say that some quantity is either less than or equal to a number?

Let us consider this example.

James works at a departmental store, and he is paid on an hourly basis.

illustration of less than or equal to

He can work for a maximum of 8 hours per day.

Do you know what’s meant by the term 'maximum', here?

This means James can work for less than or equal to 8 hours per day in the store.

Lesson Plan

What is Less Than or Equal To?

'Less than or equal to', as the name suggests, means something is either less than or equal to another thing.

'Less than or equal to' can also be expressed as 'at most', 'no more than', 'a maximum of', and 'not exceeding'.

Less than or equal to can also be expressed as At most, No more than etc

 
tips and tricks
Tips and Tricks
  1. The words 'maximum', 'at most' and 'lesser than or equal to' etc. correspond to the sign \(\mathbf{\leq }\).
  2. The words 'minimum', 'at least' and 'greater than or equal to' etc. correspond to the sign \(\mathbf{\geq }\).

What Is the Symbol of Less Than or Equal To?

'Less than or equal to' is represented by the symbol  '\(\leq\).'

"Less than or equal to" symbol

This symbol is nothing but the 'less than' symbol with a sleeping line under it.

Less Than or Equal To Symbol in Words

We know that \(2\) is less than \(8\)

This obviously means that \(2\) is less than or equal to \(8\)

Hence, we represent it as \(2 \leq 8\), using the 'less than or equal to' symbol in between \(2\) and \(8\).

Less than or equal to symbol: The symbol shows the less than sign with a sleeping line under it.

However, using the 'less than or equal to' symbol in the case of numbers doesn't make much sense because either '<' or '=' is sufficient to represent the relationship.

So when do we normally use 'less than or equal to'?

Let us learn about this next.


When to Use Less Than or Equal To Signs?

We come across certain statements involving the signs '\(\leq\)' and '\(\geq\)' which are called inequalities.

Here are some comparison symbols and their examples along with their meanings.

Symbol Example  Meaning

Less than or equal to, \(\leq\)

\(x \leq 7\)

The value of \(x\) is less than or equal to \(7\).

\(-5 \leq x \leq 3\)

The value of \(x\) should lie between \(-5\) and \(3\) inclusive of both values.
Greater than or equal to, \(\geq\)

\(x \geq 2\)

The value of \(x\) is greater than or equal to \(2\).

\(2 \geq x \geq -1\)

The value of \(x\) should lie between \(-1\) and \(2\) inclusive of both values.

You can find the symbols for 'less than' and 'greater than' by clicking here. You can also see how to write less than symbol and greater than symbol in sentences here.


Use of Less Than or Equal To in Algebra

In algebra, it is not always possible to translate a statement problem using an equation.

When any two numbers or expressions are related by the symbols \(>\), \(<\), \(\leq\), and \(\geq\), it forms an inequality.

Less Than or Equal To Activity

You can try the following activity to understand what is less than or equal to.


Solved Examples

Here are some less than or equal to examples.

Example 1

 

 

Your classroom can occupy at most 60 study tables.

"Less than or equal to" Example: A classroom can occupy maximum 60 tables.

Express this statement using the less than or equal to symbol.

Solution

Let's represent the number of study tables by the variable \(x\).

It is given that the classroom can occupy a maximum of 60 study tables.

So, this can be represented by a simple inequality.

\(\therefore\) \(x \leq 60\)
Example 2

 

 

Charles had \(18\) chocolates which he was going to distribute to his friends on his birthday.

Since the box was open, he lost some chocolates on the way.

Less than or equal to example: A boy with chocolates.

If \(x\) is the number of chocolates that Charles currently has, write an inequality that represents this situation.

Solution

Number of chocolates Charles had initially = \(18\)

Since he lost some chocolates, the number of chocolates with him currently is less than \(18\)

\[ x < 18 \,\,\,\,\, \cdots (1)\]

We know that the number of chocolates should be a non-negative quantity. Hence,

\[x \geq 0\]

This inequality can also be written as:

\[0 \leq x \,\,\,\,\, \cdots (2)\]

From the inequalities (1) and (2),

\(\therefore\) \({0 \leq x < 18}\)
Example 3

 

 

Jolly's teacher asked her to find the numbers that belong to the set as shown on the blackboard.

"Less than or equal to" Example: Show the numbers expressed as a set here.

Can you help her?

Solution

We know that \(Z\) is the set of integers.

The given set is:

\[\{x \in Z| x \leq 4\}\]

This means that we have to find all the integers that are less than or equal to 4

Since the set of integers is infinite, the numbers that belong to the given set are:

\(\therefore\)   \({...,-3, -2, -1, 0, 1, 2, 3, 4}\)
Example 4

 

 

A taxi charges Rs. 50 for the first kilometer and Rs.12 for each subsequent kilometer.

"Less than or equal to" Example: A taxi charges fare. express that as an inequality.

But Katie has no more than Rs. 800 to spend on a ride.

Can you give an inequality to express this situation?

Solution

Let's use the variable \(k\) to represent the kilometers she covers after the first kilometer.

No more than is the keyword to note that this statement can be written as an inequality.

This means Katie can't spend more than Rs. 800 on the ride.

So, the inequality is,

"Less than or equal to" Example: Way to write an inequality

\(\therefore\) The inequality is \(50+ 12k \leq 800\).
 
important notes to remember
Important Notes
  1. Same numbers can either be added or subtracted on both sides of an inequality without changing the sign of inequality.
  2. Same positive numbers can either be multiplied or divided on both sides of an inequality without changing the sign of inequality.
  3. Same negative numbers can either be multiplied or divided on both sides of an inequality and the sign of inequality gets reversed.

Interactive Questions

Here are a few activities for you to practice. Select/type your answer and click the 'Check Answer' button to see the result.

 
 
 
 
 
 

Let's Summarize

The mini-lesson targeted on this page was about the fascinating concept of less than or equal to. The math journey around less than or equal to starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. 

We hope you enjoyed learning about Less Than or Equal To with the simulations and practice questions. Now, you will be able to easily solve problems on less than or equal to symbol in words, less than or equal to examples, and greater than symbol in a sentence.

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Frequently Asked Questions (FAQs)

1. How do you type less than or equal to?

Less than or equal to is represented by the symbol \(\leq\).

2. What does less than or equal to mean?

Less than or equal to means that you can't have more than something, you must have either less than or equal to something.

3. What is the symbol for less than 1?

Less than 1 can be represented as \(< 1\).

  
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