Solve (1div1024)-(1div16)/(1div64)-(1div256)

$$\frac { ( 1 \div 1024 ) - ( 1 \div 16 ) } { ( 1 \div 64 ) - ( 1 \div 256 ) }$$

Evaluate

$$-\frac{21}{4}=-5.25$$

Solution Steps

Least common multiple of 1024 and 16 is 1024. Convert \frac{1}{1024} and \frac{1}{16} to fractions with denominator 1024.

$$\frac{\frac{1}{1024}-\frac{64}{1024}}{\frac{1}{64}-\frac{1}{256}}$$

Since \frac{1}{1024} and \frac{64}{1024} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-64}{1024}}{\frac{1}{64}-\frac{1}{256}}$$

Subtract 64 from 1 to get -63.

$$\frac{-\frac{63}{1024}}{\frac{1}{64}-\frac{1}{256}}$$

Least common multiple of 64 and 256 is 256. Convert \frac{1}{64} and \frac{1}{256} to fractions with denominator 256.

$$\frac{-\frac{63}{1024}}{\frac{4}{256}-\frac{1}{256}}$$

Since \frac{4}{256} and \frac{1}{256} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{63}{1024}}{\frac{4-1}{256}}$$

Subtract 1 from 4 to get 3.

$$\frac{-\frac{63}{1024}}{\frac{3}{256}}$$

Divide -\frac{63}{1024} by \frac{3}{256} by multiplying -\frac{63}{1024} by the reciprocal of \frac{3}{256}.

$$-\frac{63}{1024}\times \frac{256}{3}$$

Multiply -\frac{63}{1024} times \frac{256}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-63\times 256}{1024\times 3}$$

Do the multiplications in the fraction \frac{-63\times 256}{1024\times 3}.

$$\frac{-16128}{3072}$$

Reduce the fraction \frac{-16128}{3072} to lowest terms by extracting and canceling out 768.

$$-\frac{21}{4}$$

Factor

$$-\frac{21}{4} = -5\frac{1}{4} = -5.25$$