What is the outcome when a number is multiplied by its inverse?

Prepare for the WEST–B Mathematics Test. Engage with multiple choice questions and explanations to boost understanding. Set yourself up for success!

Multiple Choice

What is the outcome when a number is multiplied by its inverse?

When a number is multiplied by its inverse, the outcome is always one. The inverse of a number is defined as the number that, when multiplied by the original number, results in the identity element for multiplication, which is one. For instance, if you take a number \( x \), its multiplicative inverse (or reciprocal) is \( \frac{1}{x} \). Therefore, when you multiply \( x \) by \( \frac{1}{x} \): \[ x \times \frac{1}{x} = 1 \] This relationship holds true for any non-zero number. Since the identity property of multiplication states that multiplying any number by one does not change its value, the product of a number and its inverse is indeed one. Understanding this principle is fundamental in algebra, especially in solving equations and understanding the properties of numbers.

When a number is multiplied by its inverse, the outcome is always one. The inverse of a number is defined as the number that, when multiplied by the original number, results in the identity element for multiplication, which is one. For instance, if you take a number ( x ), its multiplicative inverse (or reciprocal) is ( \frac{1}{x} ). Therefore, when you multiply ( x ) by ( \frac{1}{x} ):

[

x \times \frac{1}{x} = 1

]

This relationship holds true for any non-zero number. Since the identity property of multiplication states that multiplying any number by one does not change its value, the product of a number and its inverse is indeed one.

Understanding this principle is fundamental in algebra, especially in solving equations and understanding the properties of numbers.

More practice questions