Solve (1/4-99/100)(1/4-98/100)...(frac{1}{4}-frac{2}{100})(frac{1}{4}-frac{1}{100})

$$( \frac{ 1 }{ 4 } - \frac{ 99 }{ 100 } )( \frac{ 1 }{ 4 } - \frac{ 98 }{ 100 } )...( \frac{ 1 }{ 4 } - \frac{ 2 }{ 100 } )( \frac{ 1 }{ 4 } - \frac{ 1 }{ 100 } )$$

Evaluate

$$\frac{2701}{5000}=0.5402$$

Solution Steps

Least common multiple of 4 and 100 is 100. Convert \frac{1}{4} and \frac{99}{100} to fractions with denominator 100.

$$\left(\frac{25}{100}-\frac{99}{100}\right)\left(\frac{1}{4}-\frac{98}{100}\right)$$

Since \frac{25}{100} and \frac{99}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-99}{100}\left(\frac{1}{4}-\frac{98}{100}\right)$$

Subtract 99 from 25 to get -74.

$$\frac{-74}{100}\left(\frac{1}{4}-\frac{98}{100}\right)$$

Reduce the fraction \frac{-74}{100} to lowest terms by extracting and canceling out 2.

$$-\frac{37}{50}\left(\frac{1}{4}-\frac{98}{100}\right)$$

Reduce the fraction \frac{98}{100} to lowest terms by extracting and canceling out 2.

$$-\frac{37}{50}\left(\frac{1}{4}-\frac{49}{50}\right)$$

Least common multiple of 4 and 50 is 100. Convert \frac{1}{4} and \frac{49}{50} to fractions with denominator 100.

$$-\frac{37}{50}\left(\frac{25}{100}-\frac{98}{100}\right)$$

Since \frac{25}{100} and \frac{98}{100} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{37}{50}\times \frac{25-98}{100}$$

Subtract 98 from 25 to get -73.

$$-\frac{37}{50}\left(-\frac{73}{100}\right)$$

Multiply -\frac{37}{50} times -\frac{73}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-37\left(-73\right)}{50\times 100}$$

Do the multiplications in the fraction \frac{-37\left(-73\right)}{50\times 100}.

$$\frac{2701}{5000}$$

Factor

$$\frac{37 \cdot 73}{2 ^ {3} \cdot 5 ^ {4}} = 0.5402$$