Solve 1div((1div(100div15+2))+.05)

$$1 \div ((1 \div (100 \div 15+2))+.05)$$

Evaluate

$$\frac{260}{43}\approx 6.046511628$$

Solution Steps

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

$$\frac{1}{\frac{1}{\frac{20}{3}+2}+0.05}$$

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

$$\frac{1}{\frac{1}{\frac{20}{3}+\frac{6}{3}}+0.05}$$

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

$$\frac{1}{\frac{1}{\frac{20+6}{3}}+0.05}$$

Add 20 and 6 to get 26.

$$\frac{1}{\frac{1}{\frac{26}{3}}+0.05}$$

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

$$\frac{1}{1\times \frac{3}{26}+0.05}$$

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

$$\frac{1}{\frac{3}{26}+0.05}$$

Convert decimal number 0.05 to fraction \frac{5}{100}. Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$\frac{1}{\frac{3}{26}+\frac{1}{20}}$$

Least common multiple of 26 and 20 is 260. Convert \frac{3}{26} and \frac{1}{20} to fractions with denominator 260.

$$\frac{1}{\frac{30}{260}+\frac{13}{260}}$$

Since \frac{30}{260} and \frac{13}{260} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{30+13}{260}}$$

Add 30 and 13 to get 43.

$$\frac{1}{\frac{43}{260}}$$

Divide 1 by \frac{43}{260} by multiplying 1 by the reciprocal of \frac{43}{260}.

$$1\times \frac{260}{43}$$

Multiply 1 and \frac{260}{43} to get \frac{260}{43}.

$$\frac{260}{43}$$

Factor

$$\frac{5 \cdot 13 \cdot 2 ^ {2}}{43} = 6\frac{2}{43} = 6.046511627906977$$