Solve {r}{1+71/77}{+103/114}

$$\left. \begin{array} { r } { 1 + \frac { 71 } { 77 } } \\ { + \frac { 103 } { 114 } } \end{array} \right.$$

Evaluate

$$\frac{24803}{8778}\approx 2.825586694$$

Solution Steps

Convert 1 to fraction \frac{77}{77}.

$$\frac{77}{77}+\frac{71}{77}+\frac{103}{114}$$

Since \frac{77}{77} and \frac{71}{77} have the same denominator, add them by adding their numerators.

$$\frac{77+71}{77}+\frac{103}{114}$$

Add 77 and 71 to get 148.

$$\frac{148}{77}+\frac{103}{114}$$

Least common multiple of 77 and 114 is 8778. Convert \frac{148}{77} and \frac{103}{114} to fractions with denominator 8778.

$$\frac{16872}{8778}+\frac{7931}{8778}$$

Since \frac{16872}{8778} and \frac{7931}{8778} have the same denominator, add them by adding their numerators.

$$\frac{16872+7931}{8778}$$

Add 16872 and 7931 to get 24803.

$$\frac{24803}{8778}$$

Factor

$$\frac{17 \cdot 1459}{2 \cdot 3 \cdot 7 \cdot 11 \cdot 19} = 2\frac{7247}{8778} = 2.8255866940077468$$