Solve 1+13/19/2+1{3+1/4+frac{1{5-frac{9/2}}}}

$$1 + \frac { 1 \frac { 3 } { 19 } } { 2 + \frac { 1 } { 3 + \frac { 1 } { 4 + \frac { 1 } { 5 - \frac { 9 } { 2 } } } } }$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Multiply 1 and 19 to get 19.

$$1+\frac{\frac{19+3}{19}}{2+\frac{1}{3+\frac{1}{4+\frac{1}{5-\frac{9}{2}}}}}$$

Add 19 and 3 to get 22.

$$1+\frac{\frac{22}{19}}{2+\frac{1}{3+\frac{1}{4+\frac{1}{5-\frac{9}{2}}}}}$$

Convert 5 to fraction \frac{10}{2}.

$$1+\frac{\frac{22}{19}}{2+\frac{1}{3+\frac{1}{4+\frac{1}{\frac{10}{2}-\frac{9}{2}}}}}$$

Since \frac{10}{2} and \frac{9}{2} have the same denominator, subtract them by subtracting their numerators.

$$1+\frac{\frac{22}{19}}{2+\frac{1}{3+\frac{1}{4+\frac{1}{\frac{10-9}{2}}}}}$$

Subtract 9 from 10 to get 1.

$$1+\frac{\frac{22}{19}}{2+\frac{1}{3+\frac{1}{4+\frac{1}{\frac{1}{2}}}}}$$

Divide 1 by \frac{1}{2} by multiplying 1 by the reciprocal of \frac{1}{2}.

$$1+\frac{\frac{22}{19}}{2+\frac{1}{3+\frac{1}{4+1\times 2}}}$$

Multiply 1 and 2 to get 2.

$$1+\frac{\frac{22}{19}}{2+\frac{1}{3+\frac{1}{4+2}}}$$

Add 4 and 2 to get 6.

$$1+\frac{\frac{22}{19}}{2+\frac{1}{3+\frac{1}{6}}}$$

Convert 3 to fraction \frac{18}{6}.

$$1+\frac{\frac{22}{19}}{2+\frac{1}{\frac{18}{6}+\frac{1}{6}}}$$

Since \frac{18}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$1+\frac{\frac{22}{19}}{2+\frac{1}{\frac{18+1}{6}}}$$

Add 18 and 1 to get 19.

$$1+\frac{\frac{22}{19}}{2+\frac{1}{\frac{19}{6}}}$$

Divide 1 by \frac{19}{6} by multiplying 1 by the reciprocal of \frac{19}{6}.

$$1+\frac{\frac{22}{19}}{2+1\times \frac{6}{19}}$$

Multiply 1 and \frac{6}{19} to get \frac{6}{19}.

$$1+\frac{\frac{22}{19}}{2+\frac{6}{19}}$$

Convert 2 to fraction \frac{38}{19}.

$$1+\frac{\frac{22}{19}}{\frac{38}{19}+\frac{6}{19}}$$

Since \frac{38}{19} and \frac{6}{19} have the same denominator, add them by adding their numerators.

$$1+\frac{\frac{22}{19}}{\frac{38+6}{19}}$$

Add 38 and 6 to get 44.

$$1+\frac{\frac{22}{19}}{\frac{44}{19}}$$

Divide \frac{22}{19} by \frac{44}{19} by multiplying \frac{22}{19} by the reciprocal of \frac{44}{19}.

$$1+\frac{22}{19}\times \frac{19}{44}$$

Multiply \frac{22}{19} times \frac{19}{44} by multiplying numerator times numerator and denominator times denominator.

$$1+\frac{22\times 19}{19\times 44}$$

Cancel out 19 in both numerator and denominator.

$$1+\frac{22}{44}$$

Reduce the fraction \frac{22}{44} to lowest terms by extracting and canceling out 22.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 2 and 1 to get 3.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$