What is the Identity Property of One?

S3-SA4-0144

Grade Level:

Class 7

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 unchanged. It means that 1 is the 'identity' for multiplication, as it doesn't change the value of the number it's multiplied with.

Simple Example

Quick Example

Imagine you have 5 delicious ladoos. If you multiply the number of ladoos by 1, you still have 5 ladoos (5 x 1 = 5). The number of ladoos doesn't change, just like multiplying any number by 1 doesn't change its value.

Worked Example

Step-by-Step

Let's find the product of 125 and 1.

Step 1: Write down the numbers to be multiplied: 125 and 1.
---Step 2: Apply the Identity Property of One, which says any number multiplied by 1 stays the same.
---Step 3: So, 125 multiplied by 1 will be 125.
---Step 4: Write the multiplication equation: 125 x 1 = 125.

Answer: The product of 125 and 1 is 125.

Why It Matters

Understanding this property is crucial for simplifying complex equations in Algebra and for calculations in Computer Science. It's used in areas like Data Science to scale data without changing its inherent value, and in Physics for unit conversions, ensuring quantities remain consistent.

Common Mistakes

MISTAKE: Thinking that multiplying by 1 changes the number to 1. (e.g., 7 x 1 = 1) | CORRECTION: Remember that multiplying by 1 keeps the original number the same. (7 x 1 = 7)

MISTAKE: Confusing it with the Identity Property of Zero (addition). (e.g., thinking 5 x 1 = 5 + 0) | CORRECTION: The Identity Property of One is for multiplication. The Identity Property of Zero is for addition, where adding 0 keeps the number the same.

MISTAKE: Forgetting to apply it when simplifying expressions. (e.g., leaving 'x * 1' as 'x * 1' instead of just 'x') | CORRECTION: Always simplify 'number * 1' to just 'number' in expressions to make them easier to work with.

Practice Questions

Try It Yourself

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

QUESTION: If a shopkeeper sells 'p' number of pens and multiplies this quantity by 1, how many pens does he have? | ANSWER: p

QUESTION: Simplify the expression: (25 + 15) x 1 - 10. | ANSWER: 30

MCQ

Quick Quiz

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

5 + 0 = 5

5 x 1 = 5

5 x 0 = 0

5 / 1 = 1

The Correct Answer Is:

Option B, 5 x 1 = 5, correctly shows that multiplying any number by 1 results in the same number. Options A and C are properties of zero, and option D is incorrect.

Real World Connection

In the Real World

When you download a movie on your phone, if the download speed is stable, the data transfer rate multiplied by 1 second will give you the amount of data transferred in that second. This property ensures calculations of data flow and bandwidth remain consistent and accurate in Computer Science and Engineering.

Key Vocabulary

Key Terms

IDENTITY PROPERTY: A property where an operation with a specific number (identity element) leaves the original number unchanged. | MULTIPLICATION: The mathematical operation of scaling one number by another. | UNCHANGED: Remaining the same; not altered. | IDENTITY ELEMENT: The number that, when used in an operation, leaves the original number unchanged (for multiplication, it's 1).

What's Next

What to Learn Next

Great job understanding the Identity Property of One! Next, you can explore the 'Identity Property of Zero' for addition and subtraction. Knowing both will strengthen your foundational math skills for algebra.