Solve 70/82-1-1/1+frac{70{82}}

$$\frac{ 70 }{ 82 } -1- \frac{ 1 }{ 1+ \frac{ 70 }{ 82 } }$$

Evaluate

$$-\frac{2137}{3116}\approx -0.685815148$$

Solution Steps

Reduce the fraction \frac{70}{82} to lowest terms by extracting and canceling out 2.

$$\frac{35}{41}-1-\frac{1}{1+\frac{70}{82}}$$

Convert 1 to fraction \frac{41}{41}.

$$\frac{35}{41}-\frac{41}{41}-\frac{1}{1+\frac{70}{82}}$$

Since \frac{35}{41} and \frac{41}{41} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-41}{41}-\frac{1}{1+\frac{70}{82}}$$

Subtract 41 from 35 to get -6.

$$-\frac{6}{41}-\frac{1}{1+\frac{70}{82}}$$

Reduce the fraction \frac{70}{82} to lowest terms by extracting and canceling out 2.

$$-\frac{6}{41}-\frac{1}{1+\frac{35}{41}}$$

Convert 1 to fraction \frac{41}{41}.

$$-\frac{6}{41}-\frac{1}{\frac{41}{41}+\frac{35}{41}}$$

Since \frac{41}{41} and \frac{35}{41} have the same denominator, add them by adding their numerators.

$$-\frac{6}{41}-\frac{1}{\frac{41+35}{41}}$$

Add 41 and 35 to get 76.

$$-\frac{6}{41}-\frac{1}{\frac{76}{41}}$$

Divide 1 by \frac{76}{41} by multiplying 1 by the reciprocal of \frac{76}{41}.

$$-\frac{6}{41}-1\times \frac{41}{76}$$

Multiply 1 and \frac{41}{76} to get \frac{41}{76}.

$$-\frac{6}{41}-\frac{41}{76}$$

Least common multiple of 41 and 76 is 3116. Convert -\frac{6}{41} and \frac{41}{76} to fractions with denominator 3116.

$$-\frac{456}{3116}-\frac{1681}{3116}$$

Since -\frac{456}{3116} and \frac{1681}{3116} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-456-1681}{3116}$$

Subtract 1681 from -456 to get -2137.

$$-\frac{2137}{3116}$$

Factor

$$-\frac{2137}{3116} = -0.6858151476251605$$