What is the Identity Property of One? | Simple Explanation for Class 6

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What is the Identity Property of One (Numbers)?

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The Identity Property of One, also called the Multiplicative Identity Property, states that any number multiplied by 1 remains the same number. Think of 1 as a special number that doesn't change other numbers when you multiply them. It's like a mirror for multiplication.

Simple Example

Quick Example

Imagine your cricket team scored 150 runs in a match. If you multiply this score by 1, the score remains 150 runs (150 x 1 = 150). The number 1 didn't change your team's score, just like it doesn't change any number it's multiplied with.

Worked Example

Step-by-Step

Let's find the result of multiplying 789 by 1.
1. Identify the numbers given: 789 and 1.
2. Recall the Identity Property of One: Any number multiplied by 1 stays the same.
3. Apply the property: 789 multiplied by 1 means the number 789 will not change.
4. Write down the multiplication: 789 x 1.
5. State the result: 789 x 1 = 789.
Answer: The result is 789.

Why It Matters

This property is fundamental in many advanced fields like Computer Science for scaling data or in Physics when dealing with unit conversions. Engineers use it to simplify complex equations, and it's a building block for understanding more complex mathematical operations in Data Science and Cryptography.

Common Mistakes

MISTAKE: Thinking that multiplying by 1 makes the number larger or smaller. For example, 5 x 1 = 6. | CORRECTION: Multiplying by 1 always keeps the original number exactly the same. So, 5 x 1 = 5.

MISTAKE: Confusing it with adding 1. For example, 8 x 1 = 8 + 1 = 9. | CORRECTION: Addition and multiplication are different operations. 8 x 1 means 8, while 8 + 1 means 9.

MISTAKE: Believing the property only applies to whole numbers. For example, 0.5 x 1 = 1. | CORRECTION: The Identity Property of One applies to ALL types of numbers – whole numbers, decimals, fractions, and even negative numbers. So, 0.5 x 1 = 0.5.

Practice Questions

Try It Yourself

QUESTION: What is 45 x 1? | ANSWER: 45

QUESTION: A baker made 125 ladoos. If he wants to multiply this number by 1, how many ladoos will he have? | ANSWER: 125 ladoos

QUESTION: If a fraction 3/4 is multiplied by 1, what will be the new fraction? Explain your answer. | ANSWER: The new fraction will be 3/4. This is because, according to the Identity Property of One, any number (including fractions) multiplied by 1 remains unchanged.

MCQ

Quick Quiz

Which of the following statements correctly describes the Identity Property of One?

Multiplying a number by 1 makes it zero.

Multiplying a number by 1 always gives 1.

Multiplying a number by 1 keeps the number the same.

Multiplying a number by 1 increases its value by 1.

The Correct Answer Is:

Option C is correct because the Identity Property of One states that any number multiplied by 1 retains its original value. Options A, B, and D describe incorrect outcomes.

Real World Connection

In the Real World

When you use a digital scale to weigh vegetables at a grocery store, if the scale is perfectly calibrated (meaning it has a 'factor of 1'), the weight displayed is the actual weight. Similarly, in photography, if you don't apply any 'zoom' (which is like multiplying by 1), the object in the photo remains its original size relative to the frame.

Key Vocabulary

Key Terms

IDENTITY PROPERTY: A rule in mathematics where an operation (like multiplication) with a special number (like 1) leaves the original number unchanged. | MULTIPLICATION: The process of adding a number to itself a certain number of times. | PRODUCT: The result of multiplying two or more numbers. | UNCHANGED: Remaining the same; not altered.

What's Next

What to Learn Next

Great job understanding the Identity Property of One! Next, you should explore the Identity Property of Zero (for addition and subtraction). It's another fundamental property that will help you build a strong foundation in arithmetic.