Solve 1997div19971941/1998+1/1999

$$1997 \div 1997 \frac { 1941 } { 1998 } + \frac { 1 } { 1999 }$$

Evaluate

$$\frac{2660004647}{2659967351}\approx 1.000014021$$

Solution Steps

Divide 1997 by \frac{1997\times 1998+1941}{1998} by multiplying 1997 by the reciprocal of \frac{1997\times 1998+1941}{1998}.

$$\frac{1997\times 1998}{1997\times 1998+1941}+\frac{1}{1999}$$

Multiply 1997 and 1998 to get 3990006.

$$\frac{3990006}{1997\times 1998+1941}+\frac{1}{1999}$$

Multiply 1997 and 1998 to get 3990006.

$$\frac{3990006}{3990006+1941}+\frac{1}{1999}$$

Add 3990006 and 1941 to get 3991947.

$$\frac{3990006}{3991947}+\frac{1}{1999}$$

Reduce the fraction \frac{3990006}{3991947} to lowest terms by extracting and canceling out 3.

$$\frac{1330002}{1330649}+\frac{1}{1999}$$

Least common multiple of 1330649 and 1999 is 2659967351. Convert \frac{1330002}{1330649} and \frac{1}{1999} to fractions with denominator 2659967351.

$$\frac{2658673998}{2659967351}+\frac{1330649}{2659967351}$$

Since \frac{2658673998}{2659967351} and \frac{1330649}{2659967351} have the same denominator, add them by adding their numerators.

$$\frac{2658673998+1330649}{2659967351}$$

Add 2658673998 and 1330649 to get 2660004647.

$$\frac{2660004647}{2659967351}$$

Factor

$$\frac{2660004647}{1999 \cdot 1330649} = 1\frac{37296}{2659967351} = 1.000014021224729$$