Solve 83/4+72/3+65/8+51/2

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

Evaluate

$$\frac{685}{24}\approx 28.541666667$$

Solution Steps

Multiply 8 and 4 to get 32.

$$\frac{32+3}{4}+\frac{7\times 3+2}{3}+\frac{6\times 8+5}{8}+\frac{5\times 2+1}{2}$$

Add 32 and 3 to get 35.

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

Multiply 7 and 3 to get 21.

$$\frac{35}{4}+\frac{21+2}{3}+\frac{6\times 8+5}{8}+\frac{5\times 2+1}{2}$$

Add 21 and 2 to get 23.

$$\frac{35}{4}+\frac{23}{3}+\frac{6\times 8+5}{8}+\frac{5\times 2+1}{2}$$

Least common multiple of 4 and 3 is 12. Convert \frac{35}{4} and \frac{23}{3} to fractions with denominator 12.

$$\frac{105}{12}+\frac{92}{12}+\frac{6\times 8+5}{8}+\frac{5\times 2+1}{2}$$

Since \frac{105}{12} and \frac{92}{12} have the same denominator, add them by adding their numerators.

$$\frac{105+92}{12}+\frac{6\times 8+5}{8}+\frac{5\times 2+1}{2}$$

Add 105 and 92 to get 197.

$$\frac{197}{12}+\frac{6\times 8+5}{8}+\frac{5\times 2+1}{2}$$

Multiply 6 and 8 to get 48.

$$\frac{197}{12}+\frac{48+5}{8}+\frac{5\times 2+1}{2}$$

Add 48 and 5 to get 53.

$$\frac{197}{12}+\frac{53}{8}+\frac{5\times 2+1}{2}$$

Least common multiple of 12 and 8 is 24. Convert \frac{197}{12} and \frac{53}{8} to fractions with denominator 24.

$$\frac{394}{24}+\frac{159}{24}+\frac{5\times 2+1}{2}$$

Since \frac{394}{24} and \frac{159}{24} have the same denominator, add them by adding their numerators.

$$\frac{394+159}{24}+\frac{5\times 2+1}{2}$$

Add 394 and 159 to get 553.

$$\frac{553}{24}+\frac{5\times 2+1}{2}$$

Multiply 5 and 2 to get 10.

$$\frac{553}{24}+\frac{10+1}{2}$$

Add 10 and 1 to get 11.

$$\frac{553}{24}+\frac{11}{2}$$

Least common multiple of 24 and 2 is 24. Convert \frac{553}{24} and \frac{11}{2} to fractions with denominator 24.

$$\frac{553}{24}+\frac{132}{24}$$

Since \frac{553}{24} and \frac{132}{24} have the same denominator, add them by adding their numerators.

$$\frac{553+132}{24}$$

Add 553 and 132 to get 685.

$$\frac{685}{24}$$

Factor

$$\frac{5 \cdot 137}{2 ^ {3} \cdot 3} = 28\frac{13}{24} = 28.541666666666668$$