Solve {l}{72/3+83/7}{+12/5}

$$\left. \begin{array} { l } { 7 \frac { 2 } { 3 } + 8 \frac { 3 } { 7 } } \\ { + 1 \frac { 2 } { 5 } } \end{array} \right.$$

Evaluate

$$\frac{1837}{105}\approx 17.495238095$$

Solution Steps

Multiply 7 and 3 to get 21.

$$\frac{21+2}{3}+\frac{8\times 7+3}{7}+\frac{1\times 5+2}{5}$$

Add 21 and 2 to get 23.

$$\frac{23}{3}+\frac{8\times 7+3}{7}+\frac{1\times 5+2}{5}$$

Multiply 8 and 7 to get 56.

$$\frac{23}{3}+\frac{56+3}{7}+\frac{1\times 5+2}{5}$$

Add 56 and 3 to get 59.

$$\frac{23}{3}+\frac{59}{7}+\frac{1\times 5+2}{5}$$

Least common multiple of 3 and 7 is 21. Convert \frac{23}{3} and \frac{59}{7} to fractions with denominator 21.

$$\frac{161}{21}+\frac{177}{21}+\frac{1\times 5+2}{5}$$

Since \frac{161}{21} and \frac{177}{21} have the same denominator, add them by adding their numerators.

$$\frac{161+177}{21}+\frac{1\times 5+2}{5}$$

Add 161 and 177 to get 338.

$$\frac{338}{21}+\frac{1\times 5+2}{5}$$

Multiply 1 and 5 to get 5.

$$\frac{338}{21}+\frac{5+2}{5}$$

Add 5 and 2 to get 7.

$$\frac{338}{21}+\frac{7}{5}$$

Least common multiple of 21 and 5 is 105. Convert \frac{338}{21} and \frac{7}{5} to fractions with denominator 105.

$$\frac{1690}{105}+\frac{147}{105}$$

Since \frac{1690}{105} and \frac{147}{105} have the same denominator, add them by adding their numerators.

$$\frac{1690+147}{105}$$

Add 1690 and 147 to get 1837.

$$\frac{1837}{105}$$

Factor

$$\frac{11 \cdot 167}{3 \cdot 5 \cdot 7} = 17\frac{52}{105} = 17.495238095238093$$