Solve 70/81-(1-1/1+frac{70{81}})

$$\frac{ 70 }{ 81 } -(1- \frac{ 1 }{ 1+ \frac{ 70 }{ 81 } } )$$

Evaluate

$$\frac{4900}{12231}\approx 0.400621372$$

Solution Steps

Convert 1 to fraction \frac{81}{81}.

$$\frac{70}{81}-\left(1-\frac{1}{\frac{81}{81}+\frac{70}{81}}\right)$$

Since \frac{81}{81} and \frac{70}{81} have the same denominator, add them by adding their numerators.

$$\frac{70}{81}-\left(1-\frac{1}{\frac{81+70}{81}}\right)$$

Add 81 and 70 to get 151.

$$\frac{70}{81}-\left(1-\frac{1}{\frac{151}{81}}\right)$$

Divide 1 by \frac{151}{81} by multiplying 1 by the reciprocal of \frac{151}{81}.

$$\frac{70}{81}-\left(1-1\times \frac{81}{151}\right)$$

Multiply 1 and \frac{81}{151} to get \frac{81}{151}.

$$\frac{70}{81}-\left(1-\frac{81}{151}\right)$$

Convert 1 to fraction \frac{151}{151}.

$$\frac{70}{81}-\left(\frac{151}{151}-\frac{81}{151}\right)$$

Since \frac{151}{151} and \frac{81}{151} have the same denominator, subtract them by subtracting their numerators.

$$\frac{70}{81}-\frac{151-81}{151}$$

Subtract 81 from 151 to get 70.

$$\frac{70}{81}-\frac{70}{151}$$

Least common multiple of 81 and 151 is 12231. Convert \frac{70}{81} and \frac{70}{151} to fractions with denominator 12231.

$$\frac{10570}{12231}-\frac{5670}{12231}$$

Since \frac{10570}{12231} and \frac{5670}{12231} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10570-5670}{12231}$$

Subtract 5670 from 10570 to get 4900.

$$\frac{4900}{12231}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2} \cdot 7 ^ {2}}{3 ^ {4} \cdot 151} = 0.4006213719238002$$