Solve 2+3/42+2/frac{24{18}}+2/43/frac{72{86}}=

$$2 + \frac { 3 } { 42 } + \frac { 2 } { \frac { 24 } { 18 } } + \frac { \frac { 2 } { 43 } } { \frac { 72 } { 86 } } =$$

Evaluate

$$\frac{457}{126}\approx 3.626984127$$

Solution Steps

Reduce the fraction \frac{3}{42} to lowest terms by extracting and canceling out 3.

$$2+\frac{1}{14}+\frac{2}{\frac{24}{18}}+\frac{\frac{2}{43}}{\frac{72}{86}}$$

Convert 2 to fraction \frac{28}{14}.

$$\frac{28}{14}+\frac{1}{14}+\frac{2}{\frac{24}{18}}+\frac{\frac{2}{43}}{\frac{72}{86}}$$

Since \frac{28}{14} and \frac{1}{14} have the same denominator, add them by adding their numerators.

$$\frac{28+1}{14}+\frac{2}{\frac{24}{18}}+\frac{\frac{2}{43}}{\frac{72}{86}}$$

Add 28 and 1 to get 29.

$$\frac{29}{14}+\frac{2}{\frac{24}{18}}+\frac{\frac{2}{43}}{\frac{72}{86}}$$

Divide 2 by \frac{24}{18} by multiplying 2 by the reciprocal of \frac{24}{18}.

$$\frac{29}{14}+\frac{2\times 18}{24}+\frac{\frac{2}{43}}{\frac{72}{86}}$$

Multiply 2 and 18 to get 36.

$$\frac{29}{14}+\frac{36}{24}+\frac{\frac{2}{43}}{\frac{72}{86}}$$

Reduce the fraction \frac{36}{24} to lowest terms by extracting and canceling out 12.

$$\frac{29}{14}+\frac{3}{2}+\frac{\frac{2}{43}}{\frac{72}{86}}$$

Least common multiple of 14 and 2 is 14. Convert \frac{29}{14} and \frac{3}{2} to fractions with denominator 14.

$$\frac{29}{14}+\frac{21}{14}+\frac{\frac{2}{43}}{\frac{72}{86}}$$

Since \frac{29}{14} and \frac{21}{14} have the same denominator, add them by adding their numerators.

$$\frac{29+21}{14}+\frac{\frac{2}{43}}{\frac{72}{86}}$$

Add 29 and 21 to get 50.

$$\frac{50}{14}+\frac{\frac{2}{43}}{\frac{72}{86}}$$

Reduce the fraction \frac{50}{14} to lowest terms by extracting and canceling out 2.

$$\frac{25}{7}+\frac{\frac{2}{43}}{\frac{72}{86}}$$

Divide \frac{2}{43} by \frac{72}{86} by multiplying \frac{2}{43} by the reciprocal of \frac{72}{86}.

$$\frac{25}{7}+\frac{2\times 86}{43\times 72}$$

Cancel out 2\times 2\times 43 in both numerator and denominator.

$$\frac{25}{7}+\frac{1}{18}$$

Least common multiple of 7 and 18 is 126. Convert \frac{25}{7} and \frac{1}{18} to fractions with denominator 126.

$$\frac{450}{126}+\frac{7}{126}$$

Since \frac{450}{126} and \frac{7}{126} have the same denominator, add them by adding their numerators.

$$\frac{450+7}{126}$$

Add 450 and 7 to get 457.

$$\frac{457}{126}$$

Factor

$$\frac{457}{2 \cdot 3 ^ {2} \cdot 7} = 3\frac{79}{126} = 3.626984126984127$$