# Ratio, Proportion and Percentages Puzzle – Critical Thinking 7

This kind of math puzzles is an educational activity for practicing children’s math skills. It’s also helpful for adults to have fun and challenge their brains!

## Challenge:

$$(1-\frac{1}{2}) × (1 -\frac{1}{2}) × (1-\frac{1}{4} ) × … × (1-\frac{1}{100} ) =$$ ?

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The correct answer is $$\frac{1}{100}$$.

First, simplify the expression.
$$(1-\frac{1}{2}) × (1 -\frac{1}{2}) × (1-\frac{1}{4} ) × … × (1-\frac{1}{100} ) =$$ ?
$$(\frac{1}{2} ) × ( \frac{2}{3}) × ( \frac{3}{4}) × … × ( \frac{99}{100}) =$$
Remove the same numbers from both numerator and denominator. For example, cancel out 2, 3, 4, … from both numerator and denominator. You’ll get:$$\frac{1}{100}$$