x(1-1%2F3)x(1-1%2F4)x(1-1%2F5)%3Dx%2F100.jpeg "(1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)=x/100")
Solving the Mysterious Equation: (1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)=x/100
Introduction
In the realm of mathematics, equations can be both fascinating and challenging. One such equation that has garnered attention is the intriguing expression: (1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)=x/100. In this article, we will delve into the world of fractions and algebra to uncover the secrets behind this mysterious equation.
Breaking Down the Equation
Let's start by analyzing the equation:
(1-1/2)x(1-1/3)x(1-1/4)x(1-1/5) = x/100
At first glance, the equation appears complex, but by breaking it down into smaller components, we can gain a better understanding of its structure.
(1-1/2) = 1/2
The first term, (1-1/2), can be simplified to 1/2.
(1-1/3) = 2/3
The second term, (1-1/3), can be simplified to 2/3.
(1-1/4) = 3/4
The third term, (1-1/4), can be simplified to 3/4.
(1-1/5) = 4/5
The fourth term, (1-1/5), can be simplified to 4/5.
Simplifying the Equation
Now that we have simplified each term, we can rewrite the equation as:
(1/2)x(2/3)x(3/4)x(4/5) = x/100
Multiplying the Fractions
To simplify the equation further, we need to multiply the fractions:
(1/2)x(2/3)x(3/4)x(4/5) = 24/120
Reducing the Fraction
The resulting fraction, 24/120, can be reduced to its simplest form:
24/120 = 1/5
The Solution
Now, we can set up an equation using the simplified fraction:
1/5 = x/100
Solving for x
To solve for x, we can cross-multiply:
100 = 5x
x = 100/5
x = 20
Conclusion
The mysterious equation, (1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)=x/100, has been solved, revealing the value of x to be 20. Through the process of breaking down the equation, simplifying fractions, and solving for x, we have uncovered the secrets behind this intriguing mathematical expression.
