Solve 70/80-(1-1/1+frac{70{80}})

$$\frac{ 70 }{ 80 } -(1- \frac{ 1 }{ 1+ \frac{ 70 }{ 80 } } )$$

Evaluate

$$\frac{49}{120}\approx 0.408333333$$

Solution Steps

Reduce the fraction \frac{70}{80} to lowest terms by extracting and canceling out 10.

$$\frac{7}{8}-\left(1-\frac{1}{1+\frac{70}{80}}\right)$$

Reduce the fraction \frac{70}{80} to lowest terms by extracting and canceling out 10.

$$\frac{7}{8}-\left(1-\frac{1}{1+\frac{7}{8}}\right)$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{7}{8}-\left(1-\frac{1}{\frac{8}{8}+\frac{7}{8}}\right)$$

Since \frac{8}{8} and \frac{7}{8} have the same denominator, add them by adding their numerators.

$$\frac{7}{8}-\left(1-\frac{1}{\frac{8+7}{8}}\right)$$

Add 8 and 7 to get 15.

$$\frac{7}{8}-\left(1-\frac{1}{\frac{15}{8}}\right)$$

Divide 1 by \frac{15}{8} by multiplying 1 by the reciprocal of \frac{15}{8}.

$$\frac{7}{8}-\left(1-1\times \frac{8}{15}\right)$$

Multiply 1 and \frac{8}{15} to get \frac{8}{15}.

$$\frac{7}{8}-\left(1-\frac{8}{15}\right)$$

Convert 1 to fraction \frac{15}{15}.

$$\frac{7}{8}-\left(\frac{15}{15}-\frac{8}{15}\right)$$

Since \frac{15}{15} and \frac{8}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{8}-\frac{15-8}{15}$$

Subtract 8 from 15 to get 7.

$$\frac{7}{8}-\frac{7}{15}$$

Least common multiple of 8 and 15 is 120. Convert \frac{7}{8} and \frac{7}{15} to fractions with denominator 120.

$$\frac{105}{120}-\frac{56}{120}$$

Since \frac{105}{120} and \frac{56}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{105-56}{120}$$

Subtract 56 from 105 to get 49.

$$\frac{49}{120}$$

Factor

$$\frac{7 ^ {2}}{2 ^ {3} \cdot 3 \cdot 5} = 0.4083333333333333$$