Solve 2016/2016*frac{2016{2017}}+1/2018

$$\frac { 2016 } { 2016 \cdot \frac { 2016 } { 2017 } } + \frac { 1 } { 2018 }$$

Evaluate

$$\frac{2036161}{2034144}\approx 1.000991572$$

Solution Steps

Express 2016\times \frac{2016}{2017} as a single fraction.

$$\frac{2016}{\frac{2016\times 2016}{2017}}+\frac{1}{2018}$$

Multiply 2016 and 2016 to get 4064256.

$$\frac{2016}{\frac{4064256}{2017}}+\frac{1}{2018}$$

Divide 2016 by \frac{4064256}{2017} by multiplying 2016 by the reciprocal of \frac{4064256}{2017}.

$$2016\times \frac{2017}{4064256}+\frac{1}{2018}$$

Express 2016\times \frac{2017}{4064256} as a single fraction.

$$\frac{2016\times 2017}{4064256}+\frac{1}{2018}$$

Multiply 2016 and 2017 to get 4066272.

$$\frac{4066272}{4064256}+\frac{1}{2018}$$

Reduce the fraction \frac{4066272}{4064256} to lowest terms by extracting and canceling out 2016.

$$\frac{2017}{2016}+\frac{1}{2018}$$

Least common multiple of 2016 and 2018 is 2034144. Convert \frac{2017}{2016} and \frac{1}{2018} to fractions with denominator 2034144.

$$\frac{2035153}{2034144}+\frac{1008}{2034144}$$

Since \frac{2035153}{2034144} and \frac{1008}{2034144} have the same denominator, add them by adding their numerators.

$$\frac{2035153+1008}{2034144}$$

Add 2035153 and 1008 to get 2036161.

$$\frac{2036161}{2034144}$$

Factor

$$\frac{2036161}{2 ^ {5} \cdot 3 ^ {2} \cdot 7 \cdot 1009} = 1\frac{2017}{2034144} = 1.000991571884783$$