x(1-3%2F7)x(1-3%2F10)x(1-3%2F13)x(1-3%2F16).jpeg "(1-3/4)x(1-3/7)x(1-3/10)x(1-3/13)x(1-3/16)")
Simplifying a Series of Multiplications
This article explores the simplification of the following expression:
(1 - 3/4) x (1 - 3/7) x (1 - 3/10) x (1 - 3/13) x (1 - 3/16)
Let's break it down step-by-step:
1. Simplifying Individual Fractions
First, we need to simplify each of the individual fractions within the parentheses.
- (1 - 3/4) = 1/4
- (1 - 3/7) = 4/7
- (1 - 3/10) = 7/10
- (1 - 3/13) = 10/13
- (1 - 3/16) = 13/16
2. Multiplying the Simplified Fractions
Now we can multiply the simplified fractions together:
(1/4) x (4/7) x (7/10) x (10/13) x (13/16)
Notice something interesting: many of the numerators and denominators cancel out!
3. Canceling Out Common Factors
- The '4' in the numerator of the first fraction cancels out with the '4' in the denominator of the second fraction.
- The '7' in the numerator of the second fraction cancels out with the '7' in the denominator of the third fraction.
- This pattern continues, with the '10', '13', and finally the '16' canceling out.
4. The Final Result
After canceling out the common factors, we are left with:
(1/16)
Therefore, the simplified value of the expression:
(1 - 3/4) x (1 - 3/7) x (1 - 3/10) x (1 - 3/13) x (1 - 3/16) = 1/16