Solve 70/72-1-1/1+frac{70{72}}

$$\frac{ 70 }{ 72 } -1- \frac{ 1 }{ 1+ \frac{ 70 }{ 72 } }$$

Evaluate

$$-\frac{1367}{2556}\approx -0.534820031$$

Solution Steps

Reduce the fraction \frac{70}{72} to lowest terms by extracting and canceling out 2.

$$\frac{35}{36}-1-\frac{1}{1+\frac{70}{72}}$$

Convert 1 to fraction \frac{36}{36}.

$$\frac{35}{36}-\frac{36}{36}-\frac{1}{1+\frac{70}{72}}$$

Since \frac{35}{36} and \frac{36}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-36}{36}-\frac{1}{1+\frac{70}{72}}$$

Subtract 36 from 35 to get -1.

$$-\frac{1}{36}-\frac{1}{1+\frac{70}{72}}$$

Reduce the fraction \frac{70}{72} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{36}-\frac{1}{1+\frac{35}{36}}$$

Convert 1 to fraction \frac{36}{36}.

$$-\frac{1}{36}-\frac{1}{\frac{36}{36}+\frac{35}{36}}$$

Since \frac{36}{36} and \frac{35}{36} have the same denominator, add them by adding their numerators.

$$-\frac{1}{36}-\frac{1}{\frac{36+35}{36}}$$

Add 36 and 35 to get 71.

$$-\frac{1}{36}-\frac{1}{\frac{71}{36}}$$

Divide 1 by \frac{71}{36} by multiplying 1 by the reciprocal of \frac{71}{36}.

$$-\frac{1}{36}-1\times \frac{36}{71}$$

Multiply 1 and \frac{36}{71} to get \frac{36}{71}.

$$-\frac{1}{36}-\frac{36}{71}$$

Least common multiple of 36 and 71 is 2556. Convert -\frac{1}{36} and \frac{36}{71} to fractions with denominator 2556.

$$-\frac{71}{2556}-\frac{1296}{2556}$$

Since -\frac{71}{2556} and \frac{1296}{2556} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-71-1296}{2556}$$

Subtract 1296 from -71 to get -1367.

$$-\frac{1367}{2556}$$

Factor

$$-\frac{1367}{2556} = -0.5348200312989045$$