Which equation demonstrates the multiplicative identity property
The Correct Answer and Explanation is:
The equation that demonstrates the multiplicative identity property is:5×1=55 \times 1 = 55×1=5
Explanation:
The multiplicative identity property states that any number multiplied by 1 remains unchanged. This is because 1 is known as the multiplicative identity in mathematics. The essence of this property is that 1 does not alter the value of other numbers when used in multiplication.
Here’s why this is true:
- Multiplication is a binary operation that combines two numbers to produce a third number. For example, when multiplying 5 by 1, we are essentially asking, “How many times should 1 be added to itself to get 5?” Since multiplying by 1 does not change the original value of 5, the answer is simply 5.
- The property is fundamental in many areas of mathematics, especially in algebra and arithmetic, as it allows us to simplify equations, expressions, and operations. For example, in solving equations, one might multiply both sides by 1, and the equation will remain unchanged, making the process easier or more manageable.
Why it matters:
- This property helps in defining the behavior of multiplication, distinguishing it from other operations like addition or subtraction.
- It also ensures that 1 serves as the “neutral element” in multiplication, just like 0 serves as the “neutral element” in addition. This symmetry is important in many mathematical proofs and operations.
In summary:
The multiplicative identity property tells us that multiplying any number by 1 leaves the original number unchanged. This simple but powerful rule is vital in understanding and manipulating equations in algebra and beyond.
