(1-1/4)x(1-1/5)x(1-1/6)x(1-1/7)x(1-1/8)

2 min read Jun 16, 2024
(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

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