Solve 1div((1div(100div15+2))+.5)

$$1 \div ((1 \div (100 \div 15+2))+.5)$$

Evaluate

$$1.625$$

Solution Steps

Reduce the fraction \frac{100}{15} to lowest terms by extracting and canceling out 5.

$$\frac{1}{\frac{1}{\frac{20}{3}+2}+0.5}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{1}{\frac{1}{\frac{20}{3}+\frac{6}{3}}+0.5}$$

Since \frac{20}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{1}{\frac{20+6}{3}}+0.5}$$

Add 20 and 6 to get 26.

$$\frac{1}{\frac{1}{\frac{26}{3}}+0.5}$$

Divide 1 by \frac{26}{3} by multiplying 1 by the reciprocal of \frac{26}{3}.

$$\frac{1}{1\times \frac{3}{26}+0.5}$$

Multiply 1 and \frac{3}{26} to get \frac{3}{26}.

$$\frac{1}{\frac{3}{26}+0.5}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{\frac{3}{26}+\frac{1}{2}}$$

Least common multiple of 26 and 2 is 26. Convert \frac{3}{26} and \frac{1}{2} to fractions with denominator 26.

$$\frac{1}{\frac{3}{26}+\frac{13}{26}}$$

Since \frac{3}{26} and \frac{13}{26} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{3+13}{26}}$$

Add 3 and 13 to get 16.

$$\frac{1}{\frac{16}{26}}$$

Reduce the fraction \frac{16}{26} to lowest terms by extracting and canceling out 2.

$$\frac{1}{\frac{8}{13}}$$

Divide 1 by \frac{8}{13} by multiplying 1 by the reciprocal of \frac{8}{13}.

$$1\times \frac{13}{8}$$

Multiply 1 and \frac{13}{8} to get \frac{13}{8}.

$$\frac{13}{8}$$

Factor

$$\frac{13}{2 ^ {3}} = 1\frac{5}{8} = 1.625$$