Solve 207/12*135/6+183/4-191/2+1frac{3}{10}

$$20 \frac { 7 } { 12 } \cdot 13 \frac { 5 } { 6 } + 18 \frac { 3 } { 4 } - 19 \frac { 1 } { 2 } + 1 \frac { 3 } { 10 }$$

Evaluate

$$\frac{102703}{360}\approx 285.286111111$$

Solution Steps

Multiply 20 and 12 to get 240.

$$\frac{240+7}{12}\times \frac{13\times 6+5}{6}+\frac{18\times 4+3}{4}-\frac{19\times 2+1}{2}+\frac{1\times 10+3}{10}$$

Add 240 and 7 to get 247.

$$\frac{247}{12}\times \frac{13\times 6+5}{6}+\frac{18\times 4+3}{4}-\frac{19\times 2+1}{2}+\frac{1\times 10+3}{10}$$

Multiply 13 and 6 to get 78.

$$\frac{247}{12}\times \frac{78+5}{6}+\frac{18\times 4+3}{4}-\frac{19\times 2+1}{2}+\frac{1\times 10+3}{10}$$

Add 78 and 5 to get 83.

$$\frac{247}{12}\times \frac{83}{6}+\frac{18\times 4+3}{4}-\frac{19\times 2+1}{2}+\frac{1\times 10+3}{10}$$

Multiply \frac{247}{12} times \frac{83}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{247\times 83}{12\times 6}+\frac{18\times 4+3}{4}-\frac{19\times 2+1}{2}+\frac{1\times 10+3}{10}$$

Do the multiplications in the fraction \frac{247\times 83}{12\times 6}.

$$\frac{20501}{72}+\frac{18\times 4+3}{4}-\frac{19\times 2+1}{2}+\frac{1\times 10+3}{10}$$

Multiply 18 and 4 to get 72.

$$\frac{20501}{72}+\frac{72+3}{4}-\frac{19\times 2+1}{2}+\frac{1\times 10+3}{10}$$

Add 72 and 3 to get 75.

$$\frac{20501}{72}+\frac{75}{4}-\frac{19\times 2+1}{2}+\frac{1\times 10+3}{10}$$

Least common multiple of 72 and 4 is 72. Convert \frac{20501}{72} and \frac{75}{4} to fractions with denominator 72.

$$\frac{20501}{72}+\frac{1350}{72}-\frac{19\times 2+1}{2}+\frac{1\times 10+3}{10}$$

Since \frac{20501}{72} and \frac{1350}{72} have the same denominator, add them by adding their numerators.

$$\frac{20501+1350}{72}-\frac{19\times 2+1}{2}+\frac{1\times 10+3}{10}$$

Add 20501 and 1350 to get 21851.

$$\frac{21851}{72}-\frac{19\times 2+1}{2}+\frac{1\times 10+3}{10}$$

Multiply 19 and 2 to get 38.

$$\frac{21851}{72}-\frac{38+1}{2}+\frac{1\times 10+3}{10}$$

Add 38 and 1 to get 39.

$$\frac{21851}{72}-\frac{39}{2}+\frac{1\times 10+3}{10}$$

Least common multiple of 72 and 2 is 72. Convert \frac{21851}{72} and \frac{39}{2} to fractions with denominator 72.

$$\frac{21851}{72}-\frac{1404}{72}+\frac{1\times 10+3}{10}$$

Since \frac{21851}{72} and \frac{1404}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21851-1404}{72}+\frac{1\times 10+3}{10}$$

Subtract 1404 from 21851 to get 20447.

$$\frac{20447}{72}+\frac{1\times 10+3}{10}$$

Multiply 1 and 10 to get 10.

$$\frac{20447}{72}+\frac{10+3}{10}$$

Add 10 and 3 to get 13.

$$\frac{20447}{72}+\frac{13}{10}$$

Least common multiple of 72 and 10 is 360. Convert \frac{20447}{72} and \frac{13}{10} to fractions with denominator 360.

$$\frac{102235}{360}+\frac{468}{360}$$

Since \frac{102235}{360} and \frac{468}{360} have the same denominator, add them by adding their numerators.

$$\frac{102235+468}{360}$$

Add 102235 and 468 to get 102703.

$$\frac{102703}{360}$$

Factor

$$\frac{31 \cdot 3313}{2 ^ {3} \cdot 3 ^ {2} \cdot 5} = 285\frac{103}{360} = 285.2861111111111$$