Solve 70/77-(1-1/1+frac{70{77}})

$$\frac{ 70 }{ 77 } -(1- \frac{ 1 }{ 1+ \frac{ 70 }{ 77 } } )$$

Evaluate

$$\frac{100}{231}\approx 0.432900433$$

Solution Steps

Reduce the fraction \frac{70}{77} to lowest terms by extracting and canceling out 7.

$$\frac{10}{11}-\left(1-\frac{1}{1+\frac{70}{77}}\right)$$

Reduce the fraction \frac{70}{77} to lowest terms by extracting and canceling out 7.

$$\frac{10}{11}-\left(1-\frac{1}{1+\frac{10}{11}}\right)$$

Convert 1 to fraction \frac{11}{11}.

$$\frac{10}{11}-\left(1-\frac{1}{\frac{11}{11}+\frac{10}{11}}\right)$$

Since \frac{11}{11} and \frac{10}{11} have the same denominator, add them by adding their numerators.

$$\frac{10}{11}-\left(1-\frac{1}{\frac{11+10}{11}}\right)$$

Add 11 and 10 to get 21.

$$\frac{10}{11}-\left(1-\frac{1}{\frac{21}{11}}\right)$$

Divide 1 by \frac{21}{11} by multiplying 1 by the reciprocal of \frac{21}{11}.

$$\frac{10}{11}-\left(1-1\times \frac{11}{21}\right)$$

Multiply 1 and \frac{11}{21} to get \frac{11}{21}.

$$\frac{10}{11}-\left(1-\frac{11}{21}\right)$$

Convert 1 to fraction \frac{21}{21}.

$$\frac{10}{11}-\left(\frac{21}{21}-\frac{11}{21}\right)$$

Since \frac{21}{21} and \frac{11}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{11}-\frac{21-11}{21}$$

Subtract 11 from 21 to get 10.

$$\frac{10}{11}-\frac{10}{21}$$

Least common multiple of 11 and 21 is 231. Convert \frac{10}{11} and \frac{10}{21} to fractions with denominator 231.

$$\frac{210}{231}-\frac{110}{231}$$

Since \frac{210}{231} and \frac{110}{231} have the same denominator, subtract them by subtracting their numerators.

$$\frac{210-110}{231}$$

Subtract 110 from 210 to get 100.

$$\frac{100}{231}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2}}{3 \cdot 7 \cdot 11} = 0.4329004329004329$$