x(1-1%2F3%5E2)x(1-1%2F4%5E2).jpeg "(1-1/2^2)x(1-1/3^2)x(1-1/4^2)")
Evaluating the Expression: (1-1/2^2)x(1-1/3^2)x(1-1/4^2)
In this article, we will evaluate the expression (1-1/2^2)x(1-1/3^2)x(1-1/4^2) and explore its mathematical significance.
Simplifying the Expression
To evaluate the expression, we need to simplify each factor and then multiply them together.
Factor 1: (1-1/2^2)
1 - 1/2^2 = 1 - 1/4 = 3/4
Factor 2: (1-1/3^2)
1 - 1/3^2 = 1 - 1/9 = 8/9
Factor 3: (1-1/4^2)
1 - 1/4^2 = 1 - 1/16 = 15/16
Multiplying the Factors
Now, let's multiply the simplified factors together:
(3/4) × (8/9) × (15/16)
To multiply these fractions, we need to multiply the numerators (numbers on top) and multiply the denominators (numbers on the bottom), like this:
(3 × 8 × 15) / (4 × 9 × 16)
= 360 / 576
Simplifying the Result
The resulting fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 24.
360 ÷ 24 = 15
576 ÷ 24 = 24
So, the final result is:
15/24
Thus, we have evaluated the expression (1-1/2^2)x(1-1/3^2)x(1-1/4^2) and found its value to be 15/24.
