Solve 34/9div(51/3-23/4)+59/10

$$3 \frac { 4 } { 9 } \div ( 5 \frac { 1 } { 3 } - 2 \frac { 3 } { 4 } ) + 5 \frac { 9 } { 10 }$$

Evaluate

$$\frac{217}{30}\approx 7.233333333$$

Solution Steps

Multiply 3 and 9 to get 27.

$$\frac{\frac{27+4}{9}}{\frac{5\times 3+1}{3}-\frac{2\times 4+3}{4}}+\frac{5\times 10+9}{10}$$

Add 27 and 4 to get 31.

$$\frac{\frac{31}{9}}{\frac{5\times 3+1}{3}-\frac{2\times 4+3}{4}}+\frac{5\times 10+9}{10}$$

Multiply 5 and 3 to get 15.

$$\frac{\frac{31}{9}}{\frac{15+1}{3}-\frac{2\times 4+3}{4}}+\frac{5\times 10+9}{10}$$

Add 15 and 1 to get 16.

$$\frac{\frac{31}{9}}{\frac{16}{3}-\frac{2\times 4+3}{4}}+\frac{5\times 10+9}{10}$$

Multiply 2 and 4 to get 8.

$$\frac{\frac{31}{9}}{\frac{16}{3}-\frac{8+3}{4}}+\frac{5\times 10+9}{10}$$

Add 8 and 3 to get 11.

$$\frac{\frac{31}{9}}{\frac{16}{3}-\frac{11}{4}}+\frac{5\times 10+9}{10}$$

Least common multiple of 3 and 4 is 12. Convert \frac{16}{3} and \frac{11}{4} to fractions with denominator 12.

$$\frac{\frac{31}{9}}{\frac{64}{12}-\frac{33}{12}}+\frac{5\times 10+9}{10}$$

Since \frac{64}{12} and \frac{33}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{31}{9}}{\frac{64-33}{12}}+\frac{5\times 10+9}{10}$$

Subtract 33 from 64 to get 31.

$$\frac{\frac{31}{9}}{\frac{31}{12}}+\frac{5\times 10+9}{10}$$

Divide \frac{31}{9} by \frac{31}{12} by multiplying \frac{31}{9} by the reciprocal of \frac{31}{12}.

$$\frac{31}{9}\times \frac{12}{31}+\frac{5\times 10+9}{10}$$

Multiply \frac{31}{9} times \frac{12}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{31\times 12}{9\times 31}+\frac{5\times 10+9}{10}$$

Cancel out 31 in both numerator and denominator.

$$\frac{12}{9}+\frac{5\times 10+9}{10}$$

Reduce the fraction \frac{12}{9} to lowest terms by extracting and canceling out 3.

$$\frac{4}{3}+\frac{5\times 10+9}{10}$$

Multiply 5 and 10 to get 50.

$$\frac{4}{3}+\frac{50+9}{10}$$

Add 50 and 9 to get 59.

$$\frac{4}{3}+\frac{59}{10}$$

Least common multiple of 3 and 10 is 30. Convert \frac{4}{3} and \frac{59}{10} to fractions with denominator 30.

$$\frac{40}{30}+\frac{177}{30}$$

Since \frac{40}{30} and \frac{177}{30} have the same denominator, add them by adding their numerators.

$$\frac{40+177}{30}$$

Add 40 and 177 to get 217.

$$\frac{217}{30}$$

Factor

$$\frac{7 \cdot 31}{2 \cdot 3 \cdot 5} = 7\frac{7}{30} = 7.233333333333333$$