Solve 32/5*(34/11+5/17)+3.4*7/11

$$3 \frac { 2 } { 5 } \times ( 3 \frac { 4 } { 11 } + \frac { 5 } { 17 } ) + 3.4 \times \frac { 7 } { 11 }$$

Evaluate

$$14.6$$

Solution Steps

Multiply 3 and 5 to get 15.

$$\frac{15+2}{5}\left(\frac{3\times 11+4}{11}+\frac{5}{17}\right)+3.4\times \frac{7}{11}$$

Add 15 and 2 to get 17.

$$\frac{17}{5}\left(\frac{3\times 11+4}{11}+\frac{5}{17}\right)+3.4\times \frac{7}{11}$$

Multiply 3 and 11 to get 33.

$$\frac{17}{5}\left(\frac{33+4}{11}+\frac{5}{17}\right)+3.4\times \frac{7}{11}$$

Add 33 and 4 to get 37.

$$\frac{17}{5}\left(\frac{37}{11}+\frac{5}{17}\right)+3.4\times \frac{7}{11}$$

Least common multiple of 11 and 17 is 187. Convert \frac{37}{11} and \frac{5}{17} to fractions with denominator 187.

$$\frac{17}{5}\left(\frac{629}{187}+\frac{55}{187}\right)+3.4\times \frac{7}{11}$$

Since \frac{629}{187} and \frac{55}{187} have the same denominator, add them by adding their numerators.

$$\frac{17}{5}\times \frac{629+55}{187}+3.4\times \frac{7}{11}$$

Add 629 and 55 to get 684.

$$\frac{17}{5}\times \frac{684}{187}+3.4\times \frac{7}{11}$$

Multiply \frac{17}{5} times \frac{684}{187} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 684}{5\times 187}+3.4\times \frac{7}{11}$$

Do the multiplications in the fraction \frac{17\times 684}{5\times 187}.

$$\frac{11628}{935}+3.4\times \frac{7}{11}$$

Reduce the fraction \frac{11628}{935} to lowest terms by extracting and canceling out 17.

$$\frac{684}{55}+3.4\times \frac{7}{11}$$

Convert decimal number 3.4 to fraction \frac{34}{10}. Reduce the fraction \frac{34}{10} to lowest terms by extracting and canceling out 2.

$$\frac{684}{55}+\frac{17}{5}\times \frac{7}{11}$$

Multiply \frac{17}{5} times \frac{7}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{684}{55}+\frac{17\times 7}{5\times 11}$$

Do the multiplications in the fraction \frac{17\times 7}{5\times 11}.

$$\frac{684}{55}+\frac{119}{55}$$

Since \frac{684}{55} and \frac{119}{55} have the same denominator, add them by adding their numerators.

$$\frac{684+119}{55}$$

Add 684 and 119 to get 803.

$$\frac{803}{55}$$

Reduce the fraction \frac{803}{55} to lowest terms by extracting and canceling out 11.

$$\frac{73}{5}$$

Factor

$$\frac{73}{5} = 14\frac{3}{5} = 14.6$$