100×b

100×b, also known as 100 times b, is a mathematical expression that represents the product of the number 100 and the variable b. In algebraic terms, it is written as 100×b or 100b, where b is a placeholder for any real number. This expression is fundamental in various mathematical contexts, including arithmetic, algebra, and calculus.

In arithmetic, 100×b is simply the result of multiplying 100 by b. For example, if b is 5, then 100×b equals 500. This operation is commutative, meaning that the order of multiplication does not affect the result; thus, b×100 also equals 500.

In algebra, 100×b is used to represent a linear function, where 100 is the coefficient and b is the variable. This function can be graphed on a coordinate plane, resulting in a straight line passing through the origin with a slope of 100. The equation can be rewritten in slope-intercept form as y = 100b, where y represents the dependent variable and b the independent variable.

In calculus, 100×b can be used to represent the derivative of a function. For instance, if the function is f(b) = 50b^2, the derivative f'(b) would be 100b, representing the rate of change of the function at any given point b.

Overall, 100×b is a versatile mathematical expression with applications in various fields, including science, engineering, and economics. Its simplicity and fundamental nature make it an essential concept in mathematics education.