Solve 41/2+52/7+83/8+71/4+6frac{4}{5}

$$4 \frac { 1 } { 2 } + 5 \frac { 2 } { 7 } + 8 \frac { 3 } { 8 } + 7 \frac { 1 } { 4 } + 6 \frac { 4 } { 5 }$$

Evaluate

$$\frac{9019}{280}\approx 32.210714286$$

Solution Steps

Multiply 4 and 2 to get 8.

$$\frac{8+1}{2}+\frac{5\times 7+2}{7}+\frac{8\times 8+3}{8}+\frac{7\times 4+1}{4}+\frac{6\times 5+4}{5}$$

Add 8 and 1 to get 9.

$$\frac{9}{2}+\frac{5\times 7+2}{7}+\frac{8\times 8+3}{8}+\frac{7\times 4+1}{4}+\frac{6\times 5+4}{5}$$

Multiply 5 and 7 to get 35.

$$\frac{9}{2}+\frac{35+2}{7}+\frac{8\times 8+3}{8}+\frac{7\times 4+1}{4}+\frac{6\times 5+4}{5}$$

Add 35 and 2 to get 37.

$$\frac{9}{2}+\frac{37}{7}+\frac{8\times 8+3}{8}+\frac{7\times 4+1}{4}+\frac{6\times 5+4}{5}$$

Least common multiple of 2 and 7 is 14. Convert \frac{9}{2} and \frac{37}{7} to fractions with denominator 14.

$$\frac{63}{14}+\frac{74}{14}+\frac{8\times 8+3}{8}+\frac{7\times 4+1}{4}+\frac{6\times 5+4}{5}$$

Since \frac{63}{14} and \frac{74}{14} have the same denominator, add them by adding their numerators.

$$\frac{63+74}{14}+\frac{8\times 8+3}{8}+\frac{7\times 4+1}{4}+\frac{6\times 5+4}{5}$$

Add 63 and 74 to get 137.

$$\frac{137}{14}+\frac{8\times 8+3}{8}+\frac{7\times 4+1}{4}+\frac{6\times 5+4}{5}$$

Multiply 8 and 8 to get 64.

$$\frac{137}{14}+\frac{64+3}{8}+\frac{7\times 4+1}{4}+\frac{6\times 5+4}{5}$$

Add 64 and 3 to get 67.

$$\frac{137}{14}+\frac{67}{8}+\frac{7\times 4+1}{4}+\frac{6\times 5+4}{5}$$

Least common multiple of 14 and 8 is 56. Convert \frac{137}{14} and \frac{67}{8} to fractions with denominator 56.

$$\frac{548}{56}+\frac{469}{56}+\frac{7\times 4+1}{4}+\frac{6\times 5+4}{5}$$

Since \frac{548}{56} and \frac{469}{56} have the same denominator, add them by adding their numerators.

$$\frac{548+469}{56}+\frac{7\times 4+1}{4}+\frac{6\times 5+4}{5}$$

Add 548 and 469 to get 1017.

$$\frac{1017}{56}+\frac{7\times 4+1}{4}+\frac{6\times 5+4}{5}$$

Multiply 7 and 4 to get 28.

$$\frac{1017}{56}+\frac{28+1}{4}+\frac{6\times 5+4}{5}$$

Add 28 and 1 to get 29.

$$\frac{1017}{56}+\frac{29}{4}+\frac{6\times 5+4}{5}$$

Least common multiple of 56 and 4 is 56. Convert \frac{1017}{56} and \frac{29}{4} to fractions with denominator 56.

$$\frac{1017}{56}+\frac{406}{56}+\frac{6\times 5+4}{5}$$

Since \frac{1017}{56} and \frac{406}{56} have the same denominator, add them by adding their numerators.

$$\frac{1017+406}{56}+\frac{6\times 5+4}{5}$$

Add 1017 and 406 to get 1423.

$$\frac{1423}{56}+\frac{6\times 5+4}{5}$$

Multiply 6 and 5 to get 30.

$$\frac{1423}{56}+\frac{30+4}{5}$$

Add 30 and 4 to get 34.

$$\frac{1423}{56}+\frac{34}{5}$$

Least common multiple of 56 and 5 is 280. Convert \frac{1423}{56} and \frac{34}{5} to fractions with denominator 280.

$$\frac{7115}{280}+\frac{1904}{280}$$

Since \frac{7115}{280} and \frac{1904}{280} have the same denominator, add them by adding their numerators.

$$\frac{7115+1904}{280}$$

Add 7115 and 1904 to get 9019.

$$\frac{9019}{280}$$

Factor

$$\frac{29 \cdot 311}{2 ^ {3} \cdot 5 \cdot 7} = 32\frac{59}{280} = 32.21071428571429$$