Solve 13/4*(4/9+2/3)*(11/5-frac{1}{2})=

$$1 \frac { 3 } { 4 } \times ( \frac { 4 } { 9 } + \frac { 2 } { 3 } ) \times ( 1 \frac { 1 } { 5 } - \frac { 1 } { 2 } ) =$$

Evaluate

$$\frac{49}{36}\approx 1.361111111$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{4+3}{4}\left(\frac{4}{9}+\frac{2}{3}\right)\left(\frac{1\times 5+1}{5}-\frac{1}{2}\right)$$

Add 4 and 3 to get 7.

$$\frac{7}{4}\left(\frac{4}{9}+\frac{2}{3}\right)\left(\frac{1\times 5+1}{5}-\frac{1}{2}\right)$$

Least common multiple of 9 and 3 is 9. Convert \frac{4}{9} and \frac{2}{3} to fractions with denominator 9.

$$\frac{7}{4}\left(\frac{4}{9}+\frac{6}{9}\right)\left(\frac{1\times 5+1}{5}-\frac{1}{2}\right)$$

Since \frac{4}{9} and \frac{6}{9} have the same denominator, add them by adding their numerators.

$$\frac{7}{4}\times \frac{4+6}{9}\left(\frac{1\times 5+1}{5}-\frac{1}{2}\right)$$

Add 4 and 6 to get 10.

$$\frac{7}{4}\times \frac{10}{9}\left(\frac{1\times 5+1}{5}-\frac{1}{2}\right)$$

Multiply \frac{7}{4} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 10}{4\times 9}\left(\frac{1\times 5+1}{5}-\frac{1}{2}\right)$$

Do the multiplications in the fraction \frac{7\times 10}{4\times 9}.

$$\frac{70}{36}\left(\frac{1\times 5+1}{5}-\frac{1}{2}\right)$$

Reduce the fraction \frac{70}{36} to lowest terms by extracting and canceling out 2.

$$\frac{35}{18}\left(\frac{1\times 5+1}{5}-\frac{1}{2}\right)$$

Multiply 1 and 5 to get 5.

$$\frac{35}{18}\left(\frac{5+1}{5}-\frac{1}{2}\right)$$

Add 5 and 1 to get 6.

$$\frac{35}{18}\left(\frac{6}{5}-\frac{1}{2}\right)$$

Least common multiple of 5 and 2 is 10. Convert \frac{6}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{35}{18}\left(\frac{12}{10}-\frac{5}{10}\right)$$

Since \frac{12}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35}{18}\times \frac{12-5}{10}$$

Subtract 5 from 12 to get 7.

$$\frac{35}{18}\times \frac{7}{10}$$

Multiply \frac{35}{18} times \frac{7}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 7}{18\times 10}$$

Do the multiplications in the fraction \frac{35\times 7}{18\times 10}.

$$\frac{245}{180}$$

Reduce the fraction \frac{245}{180} to lowest terms by extracting and canceling out 5.

$$\frac{49}{36}$$

Factor

$$\frac{7 ^ {2}}{2 ^ {2} \cdot 3 ^ {2}} = 1\frac{13}{36} = 1.3611111111111112$$