What is the 'less than or equal to' symbol (≤)? | Simple Explanation for Class 4

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What is the 'is less than or equal to' symbol (≤)?

Grade Level:

Class 4

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

The 'is less than or equal to' symbol (≤) is used in maths to show that one number or value is either smaller than another number, or exactly the same as that number. It combines two ideas: 'less than' and 'equal to'.

Simple Example

Quick Example

Imagine your school says you need to score 33 marks or less (≤ 33) in a test to get a 'D' grade. This means if you score 33, you get a 'D'. If you score 30, you also get a 'D'. But if you score 35, you don't get a 'D' because 35 is not less than or equal to 33.

Worked Example

Step-by-Step

Problem: Is 5 ≤ 7 true or false? --- Step 1: Understand the symbol. '≤' means 'less than or equal to'. --- Step 2: Check the 'less than' part. Is 5 less than 7? Yes, 5 is smaller than 7. --- Step 3: Since the 'less than' part is true, the entire statement is true. (We don't even need to check the 'equal to' part if one part is true). --- Answer: True, because 5 is less than 7.

Why It Matters

Understanding 'less than or equal to' is super important for coding, engineering, and even managing money! Doctors use it to check if a patient's temperature is safe, and game developers use it to set score limits. It helps us make decisions based on conditions.

Common Mistakes

MISTAKE: Thinking '≤' means only 'less than'. For example, saying 5 ≤ 5 is false. | CORRECTION: Remember the 'or equal to' part. 5 ≤ 5 is true because 5 is equal to 5.

MISTAKE: Confusing '≤' (less than or equal to) with '≥' (greater than or equal to). | CORRECTION: The open side of the symbol always faces the larger number, and the equal sign below means 'can also be the same'. Think of '≤' as the smaller number pointing to the bigger one.

MISTAKE: Not checking both conditions (less than AND equal to). | CORRECTION: For a statement like 'A ≤ B' to be true, A must either be strictly smaller than B, OR A must be exactly the same as B. If either condition is met, the statement is true.

Practice Questions

Try It Yourself

QUESTION: Is 10 ≤ 8 true or false? | ANSWER: False

QUESTION: A bus can carry a maximum of 50 passengers. If 'P' is the number of passengers, write an inequality using '≤' to show this. | ANSWER: P ≤ 50

QUESTION: Reema has Rs. 100. She wants to buy a book that costs 'B' rupees. If she can buy the book, write an inequality using '≤'. If the book costs Rs. 105, can she buy it? | ANSWER: B ≤ 100. No, she cannot buy it because 105 is not less than or equal to 100.

MCQ

Quick Quiz

Which of these statements is TRUE?

7 ≤ 6

9 ≤ 9

15 ≤ 10

4 ≤ 3

The Correct Answer Is:

Option B is correct because 9 is equal to 9. The 'less than or equal to' symbol means either less than or equal to. All other options show a number that is greater than the second number, making them false.

Real World Connection

In the Real World

When you use a mobile data plan, your provider might say you get 2 GB of data per day. This means your daily usage 'D' must be D ≤ 2 GB. If you use 2 GB, it's fine. If you use 1.5 GB, it's also fine. But if you use 2.1 GB, you might get charged extra or your speed will reduce!

Key Vocabulary

Key Terms

INEQUALITY: A mathematical statement comparing two values that are not equal, using symbols like <, >, ≤, ≥ | LESS THAN: Smaller in value | EQUAL TO: Having the same value | SYMBOL: A mark or character used to represent something | CONDITION: A requirement that must be met for something to happen

What's Next

What to Learn Next

Great job learning about 'less than or equal to'! Next, you can explore the 'greater than or equal to' symbol (≥) to complete your understanding of inequalities. Then you can move on to solving simple inequalities with variables!