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

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

Evaluate

$$\frac{1225}{2556}\approx 0.479264476$$

Solution Steps

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

$$\frac{35}{36}-\left(1-\frac{1}{1+\frac{70}{72}}\right)$$

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

$$\frac{35}{36}-\left(1-\frac{1}{1+\frac{35}{36}}\right)$$

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

$$\frac{35}{36}-\left(1-\frac{1}{\frac{36}{36}+\frac{35}{36}}\right)$$

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

$$\frac{35}{36}-\left(1-\frac{1}{\frac{36+35}{36}}\right)$$

Add 36 and 35 to get 71.

$$\frac{35}{36}-\left(1-\frac{1}{\frac{71}{36}}\right)$$

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

$$\frac{35}{36}-\left(1-1\times \frac{36}{71}\right)$$

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

$$\frac{35}{36}-\left(1-\frac{36}{71}\right)$$

Convert 1 to fraction \frac{71}{71}.

$$\frac{35}{36}-\left(\frac{71}{71}-\frac{36}{71}\right)$$

Since \frac{71}{71} and \frac{36}{71} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35}{36}-\frac{71-36}{71}$$

Subtract 36 from 71 to get 35.

$$\frac{35}{36}-\frac{35}{71}$$

Least common multiple of 36 and 71 is 2556. Convert \frac{35}{36} and \frac{35}{71} to fractions with denominator 2556.

$$\frac{2485}{2556}-\frac{1260}{2556}$$

Since \frac{2485}{2556} and \frac{1260}{2556} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2485-1260}{2556}$$

Subtract 1260 from 2485 to get 1225.

$$\frac{1225}{2556}$$

Factor

$$\frac{5 ^ {2} \cdot 7 ^ {2}}{2 ^ {2} \cdot 3 ^ {2} \cdot 71} = 0.47926447574334896$$