Solve 43/7-27/14+37/2/6frac{2{3}+5frac{5}{9}-10frac{2}{15}}

$$\frac { 4 \frac { 3 } { 7 } - 2 \frac { 7 } { 14 } + 3 \frac { 7 } { 2 } } { 6 \frac { 2 } { 3 } + 5 \frac { 5 } { 9 } - 10 \frac { 2 } { 15 } }$$

Evaluate

$$\frac{2655}{658}\approx 4.034954407$$

Solution Steps

Multiply 4 and 7 to get 28.

$$\frac{\frac{28+3}{7}-\frac{2\times 14+7}{14}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Add 28 and 3 to get 31.

$$\frac{\frac{31}{7}-\frac{2\times 14+7}{14}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Multiply 2 and 14 to get 28.

$$\frac{\frac{31}{7}-\frac{28+7}{14}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Add 28 and 7 to get 35.

$$\frac{\frac{31}{7}-\frac{35}{14}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Reduce the fraction \frac{35}{14} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{31}{7}-\frac{5}{2}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Least common multiple of 7 and 2 is 14. Convert \frac{31}{7} and \frac{5}{2} to fractions with denominator 14.

$$\frac{\frac{62}{14}-\frac{35}{14}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Since \frac{62}{14} and \frac{35}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{62-35}{14}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Subtract 35 from 62 to get 27.

$$\frac{\frac{27}{14}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Multiply 3 and 2 to get 6.

$$\frac{\frac{27}{14}+\frac{6+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Add 6 and 7 to get 13.

$$\frac{\frac{27}{14}+\frac{13}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Least common multiple of 14 and 2 is 14. Convert \frac{27}{14} and \frac{13}{2} to fractions with denominator 14.

$$\frac{\frac{27}{14}+\frac{91}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Since \frac{27}{14} and \frac{91}{14} have the same denominator, add them by adding their numerators.

$$\frac{\frac{27+91}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Add 27 and 91 to get 118.

$$\frac{\frac{118}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Reduce the fraction \frac{118}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{59}{7}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Multiply 6 and 3 to get 18.

$$\frac{\frac{59}{7}}{\frac{18+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Add 18 and 2 to get 20.

$$\frac{\frac{59}{7}}{\frac{20}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Multiply 5 and 9 to get 45.

$$\frac{\frac{59}{7}}{\frac{20}{3}+\frac{45+5}{9}-\frac{10\times 15+2}{15}}$$

Add 45 and 5 to get 50.

$$\frac{\frac{59}{7}}{\frac{20}{3}+\frac{50}{9}-\frac{10\times 15+2}{15}}$$

Least common multiple of 3 and 9 is 9. Convert \frac{20}{3} and \frac{50}{9} to fractions with denominator 9.

$$\frac{\frac{59}{7}}{\frac{60}{9}+\frac{50}{9}-\frac{10\times 15+2}{15}}$$

Since \frac{60}{9} and \frac{50}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{59}{7}}{\frac{60+50}{9}-\frac{10\times 15+2}{15}}$$

Add 60 and 50 to get 110.

$$\frac{\frac{59}{7}}{\frac{110}{9}-\frac{10\times 15+2}{15}}$$

Multiply 10 and 15 to get 150.

$$\frac{\frac{59}{7}}{\frac{110}{9}-\frac{150+2}{15}}$$

Add 150 and 2 to get 152.

$$\frac{\frac{59}{7}}{\frac{110}{9}-\frac{152}{15}}$$

Least common multiple of 9 and 15 is 45. Convert \frac{110}{9} and \frac{152}{15} to fractions with denominator 45.

$$\frac{\frac{59}{7}}{\frac{550}{45}-\frac{456}{45}}$$

Since \frac{550}{45} and \frac{456}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{59}{7}}{\frac{550-456}{45}}$$

Subtract 456 from 550 to get 94.

$$\frac{\frac{59}{7}}{\frac{94}{45}}$$

Divide \frac{59}{7} by \frac{94}{45} by multiplying \frac{59}{7} by the reciprocal of \frac{94}{45}.

$$\frac{59}{7}\times \frac{45}{94}$$

Multiply \frac{59}{7} times \frac{45}{94} by multiplying numerator times numerator and denominator times denominator.

$$\frac{59\times 45}{7\times 94}$$

Do the multiplications in the fraction \frac{59\times 45}{7\times 94}.

$$\frac{2655}{658}$$

Factor

$$\frac{3 ^ {2} \cdot 5 \cdot 59}{2 \cdot 7 \cdot 47} = 4\frac{23}{658} = 4.0349544072948325$$