Solve 2*29/5/2+frac{29{5}}+3*29/4/3+frac{29{4}}

$$\frac { 2 \times \frac { 29 } { 5 } } { 2 + \frac { 29 } { 5 } } + \frac { 3 \times \frac { 29 } { 4 } } { 3 + \frac { 29 } { 4 } }$$

Evaluate

$$\frac{5771}{1599}\approx 3.609130707$$

Solution Steps

Express 2\times \frac{29}{5} as a single fraction.

$$\frac{\frac{2\times 29}{5}}{2+\frac{29}{5}}+\frac{3\times \frac{29}{4}}{3+\frac{29}{4}}$$

Multiply 2 and 29 to get 58.

$$\frac{\frac{58}{5}}{2+\frac{29}{5}}+\frac{3\times \frac{29}{4}}{3+\frac{29}{4}}$$

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

$$\frac{\frac{58}{5}}{\frac{10}{5}+\frac{29}{5}}+\frac{3\times \frac{29}{4}}{3+\frac{29}{4}}$$

Since \frac{10}{5} and \frac{29}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{58}{5}}{\frac{10+29}{5}}+\frac{3\times \frac{29}{4}}{3+\frac{29}{4}}$$

Add 10 and 29 to get 39.

$$\frac{\frac{58}{5}}{\frac{39}{5}}+\frac{3\times \frac{29}{4}}{3+\frac{29}{4}}$$

Divide \frac{58}{5} by \frac{39}{5} by multiplying \frac{58}{5} by the reciprocal of \frac{39}{5}.

$$\frac{58}{5}\times \frac{5}{39}+\frac{3\times \frac{29}{4}}{3+\frac{29}{4}}$$

Multiply \frac{58}{5} times \frac{5}{39} by multiplying numerator times numerator and denominator times denominator.

$$\frac{58\times 5}{5\times 39}+\frac{3\times \frac{29}{4}}{3+\frac{29}{4}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{58}{39}+\frac{3\times \frac{29}{4}}{3+\frac{29}{4}}$$

Express 3\times \frac{29}{4} as a single fraction.

$$\frac{58}{39}+\frac{\frac{3\times 29}{4}}{3+\frac{29}{4}}$$

Multiply 3 and 29 to get 87.

$$\frac{58}{39}+\frac{\frac{87}{4}}{3+\frac{29}{4}}$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{58}{39}+\frac{\frac{87}{4}}{\frac{12}{4}+\frac{29}{4}}$$

Since \frac{12}{4} and \frac{29}{4} have the same denominator, add them by adding their numerators.

$$\frac{58}{39}+\frac{\frac{87}{4}}{\frac{12+29}{4}}$$

Add 12 and 29 to get 41.

$$\frac{58}{39}+\frac{\frac{87}{4}}{\frac{41}{4}}$$

Divide \frac{87}{4} by \frac{41}{4} by multiplying \frac{87}{4} by the reciprocal of \frac{41}{4}.

$$\frac{58}{39}+\frac{87}{4}\times \frac{4}{41}$$

Multiply \frac{87}{4} times \frac{4}{41} by multiplying numerator times numerator and denominator times denominator.

$$\frac{58}{39}+\frac{87\times 4}{4\times 41}$$

Cancel out 4 in both numerator and denominator.

$$\frac{58}{39}+\frac{87}{41}$$

Least common multiple of 39 and 41 is 1599. Convert \frac{58}{39} and \frac{87}{41} to fractions with denominator 1599.

$$\frac{2378}{1599}+\frac{3393}{1599}$$

Since \frac{2378}{1599} and \frac{3393}{1599} have the same denominator, add them by adding their numerators.

$$\frac{2378+3393}{1599}$$

Add 2378 and 3393 to get 5771.

$$\frac{5771}{1599}$$

Factor

$$\frac{29 \cdot 199}{3 \cdot 13 \cdot 41} = 3\frac{974}{1599} = 3.6091307066916825$$