x(1-1%2F5)x(1-1%2F6)x(1-1%2F7)x(1-1%2F8).jpeg "(1-1/4)x(1-1/5)x(1-1/6)x(1-1/7)x(1-1/8)")
Simplifying a Series of Multiplications
Let's look at the expression: (1-1/4)x(1-1/5)x(1-1/6)x(1-1/7)x(1-1/8)
This might seem daunting at first, but there's a neat pattern we can exploit to simplify it.
Simplifying Each Factor
First, let's simplify each factor:
- (1-1/4) = 3/4
- (1-1/5) = 4/5
- (1-1/6) = 5/6
- (1-1/7) = 6/7
- (1-1/8) = 7/8
Now our expression becomes: (3/4) x (4/5) x (5/6) x (6/7) x (7/8)
Canceling Common Factors
Notice how many of the numerators and denominators cancel out:
- The '4' in the numerator of the first factor cancels with the '4' in the denominator of the second factor.
- The '5' in the numerator of the second factor cancels with the '5' in the denominator of the third factor.
- This pattern continues until we reach the last factor.
Final Result
After all the cancellations, we are left with: 3/8
Therefore, (1-1/4)x(1-1/5)x(1-1/6)x(1-1/7)x(1-1/8) = 3/8