Solve 42*1/3+1{3+frac{1/frac{3{4}}}}

$$42 \times \frac { 1 } { 3 + \frac { 1 } { 3 + \frac { 1 } { \frac { 3 } { 4 } } } }$$

Evaluate

$$13$$

Solution Steps

Divide 1 by \frac{3}{4} by multiplying 1 by the reciprocal of \frac{3}{4}.

$$42\times \frac{1}{3+\frac{1}{3+1\times \frac{4}{3}}}$$

Multiply 1 and \frac{4}{3} to get \frac{4}{3}.

$$42\times \frac{1}{3+\frac{1}{3+\frac{4}{3}}}$$

Convert 3 to fraction \frac{9}{3}.

$$42\times \frac{1}{3+\frac{1}{\frac{9}{3}+\frac{4}{3}}}$$

Since \frac{9}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$42\times \frac{1}{3+\frac{1}{\frac{9+4}{3}}}$$

Add 9 and 4 to get 13.

$$42\times \frac{1}{3+\frac{1}{\frac{13}{3}}}$$

Divide 1 by \frac{13}{3} by multiplying 1 by the reciprocal of \frac{13}{3}.

$$42\times \frac{1}{3+1\times \frac{3}{13}}$$

Multiply 1 and \frac{3}{13} to get \frac{3}{13}.

$$42\times \frac{1}{3+\frac{3}{13}}$$

Convert 3 to fraction \frac{39}{13}.

$$42\times \frac{1}{\frac{39}{13}+\frac{3}{13}}$$

Since \frac{39}{13} and \frac{3}{13} have the same denominator, add them by adding their numerators.

$$42\times \frac{1}{\frac{39+3}{13}}$$

Add 39 and 3 to get 42.

$$42\times \frac{1}{\frac{42}{13}}$$

Divide 1 by \frac{42}{13} by multiplying 1 by the reciprocal of \frac{42}{13}.

$$42\times 1\times \frac{13}{42}$$

Multiply 1 and \frac{13}{42} to get \frac{13}{42}.

$$42\times \frac{13}{42}$$

Cancel out 42 and 42.

$$13$$

Factor

$$13$$