Solve (22/5+11/3*5)div32/5+3423/7*frac{7}{9}

$$( 2 \frac { 2 } { 5 } + 1 \frac { 1 } { 3 } \times 5 ) \div 3 \frac { 2 } { 5 } + 342 \frac { 3 } { 7 } \times \frac { 7 } { 9 }$$

Evaluate

$$269$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{\frac{10+2}{5}+\frac{1\times 3+1}{3}\times 5}{\frac{3\times 5+2}{5}}+\frac{342\times 7+3}{7}\times \frac{7}{9}$$

Add 10 and 2 to get 12.

$$\frac{\frac{12}{5}+\frac{1\times 3+1}{3}\times 5}{\frac{3\times 5+2}{5}}+\frac{342\times 7+3}{7}\times \frac{7}{9}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{12}{5}+\frac{3+1}{3}\times 5}{\frac{3\times 5+2}{5}}+\frac{342\times 7+3}{7}\times \frac{7}{9}$$

Add 3 and 1 to get 4.

$$\frac{\frac{12}{5}+\frac{4}{3}\times 5}{\frac{3\times 5+2}{5}}+\frac{342\times 7+3}{7}\times \frac{7}{9}$$

Express \frac{4}{3}\times 5 as a single fraction.

$$\frac{\frac{12}{5}+\frac{4\times 5}{3}}{\frac{3\times 5+2}{5}}+\frac{342\times 7+3}{7}\times \frac{7}{9}$$

Multiply 4 and 5 to get 20.

$$\frac{\frac{12}{5}+\frac{20}{3}}{\frac{3\times 5+2}{5}}+\frac{342\times 7+3}{7}\times \frac{7}{9}$$

Least common multiple of 5 and 3 is 15. Convert \frac{12}{5} and \frac{20}{3} to fractions with denominator 15.

$$\frac{\frac{36}{15}+\frac{100}{15}}{\frac{3\times 5+2}{5}}+\frac{342\times 7+3}{7}\times \frac{7}{9}$$

Since \frac{36}{15} and \frac{100}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{36+100}{15}}{\frac{3\times 5+2}{5}}+\frac{342\times 7+3}{7}\times \frac{7}{9}$$

Add 36 and 100 to get 136.

$$\frac{\frac{136}{15}}{\frac{3\times 5+2}{5}}+\frac{342\times 7+3}{7}\times \frac{7}{9}$$

Multiply 3 and 5 to get 15.

$$\frac{\frac{136}{15}}{\frac{15+2}{5}}+\frac{342\times 7+3}{7}\times \frac{7}{9}$$

Add 15 and 2 to get 17.

$$\frac{\frac{136}{15}}{\frac{17}{5}}+\frac{342\times 7+3}{7}\times \frac{7}{9}$$

Divide \frac{136}{15} by \frac{17}{5} by multiplying \frac{136}{15} by the reciprocal of \frac{17}{5}.

$$\frac{136}{15}\times \frac{5}{17}+\frac{342\times 7+3}{7}\times \frac{7}{9}$$

Multiply \frac{136}{15} times \frac{5}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{136\times 5}{15\times 17}+\frac{342\times 7+3}{7}\times \frac{7}{9}$$

Do the multiplications in the fraction \frac{136\times 5}{15\times 17}.

$$\frac{680}{255}+\frac{342\times 7+3}{7}\times \frac{7}{9}$$

Reduce the fraction \frac{680}{255} to lowest terms by extracting and canceling out 85.

$$\frac{8}{3}+\frac{342\times 7+3}{7}\times \frac{7}{9}$$

Multiply 342 and 7 to get 2394.

$$\frac{8}{3}+\frac{2394+3}{7}\times \frac{7}{9}$$

Add 2394 and 3 to get 2397.

$$\frac{8}{3}+\frac{2397}{7}\times \frac{7}{9}$$

Multiply \frac{2397}{7} times \frac{7}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{3}+\frac{2397\times 7}{7\times 9}$$

Cancel out 7 in both numerator and denominator.

$$\frac{8}{3}+\frac{2397}{9}$$

Reduce the fraction \frac{2397}{9} to lowest terms by extracting and canceling out 3.

$$\frac{8}{3}+\frac{799}{3}$$

Since \frac{8}{3} and \frac{799}{3} have the same denominator, add them by adding their numerators.

$$\frac{8+799}{3}$$

Add 8 and 799 to get 807.

$$\frac{807}{3}$$

Divide 807 by 3 to get 269.

$$269$$

Factor

$$269$$