Solve 9/17*(41/5-34/9)

$$\frac { 9 } { 17 } \times ( 4 \frac { 1 } { 5 } - 3 \frac { 4 } { 9 } )$$

Evaluate

$$\frac{2}{5}=0.4$$

Solution Steps

Multiply 4 and 5 to get 20.

$$\frac{9}{17}\left(\frac{20+1}{5}-\frac{3\times 9+4}{9}\right)$$

Add 20 and 1 to get 21.

$$\frac{9}{17}\left(\frac{21}{5}-\frac{3\times 9+4}{9}\right)$$

Multiply 3 and 9 to get 27.

$$\frac{9}{17}\left(\frac{21}{5}-\frac{27+4}{9}\right)$$

Add 27 and 4 to get 31.

$$\frac{9}{17}\left(\frac{21}{5}-\frac{31}{9}\right)$$

Least common multiple of 5 and 9 is 45. Convert \frac{21}{5} and \frac{31}{9} to fractions with denominator 45.

$$\frac{9}{17}\left(\frac{189}{45}-\frac{155}{45}\right)$$

Since \frac{189}{45} and \frac{155}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{17}\times \frac{189-155}{45}$$

Subtract 155 from 189 to get 34.

$$\frac{9}{17}\times \frac{34}{45}$$

Multiply \frac{9}{17} times \frac{34}{45} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 34}{17\times 45}$$

Do the multiplications in the fraction \frac{9\times 34}{17\times 45}.

$$\frac{306}{765}$$

Reduce the fraction \frac{306}{765} to lowest terms by extracting and canceling out 153.

$$\frac{2}{5}$$

Factor

$$\frac{2}{5} = 0.4$$