Solve 5+71/2div92/7*7/3-3/5(frac{5}{3})

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

Evaluate

$$\frac{153}{26}\approx 5.884615385$$

Solution Steps

Divide \frac{7\times 2+1}{2} by \frac{9\times 7+2}{7} by multiplying \frac{7\times 2+1}{2} by the reciprocal of \frac{9\times 7+2}{7}.

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

Multiply 7 and 2 to get 14.

$$5+\frac{\left(14+1\right)\times 7}{2\left(9\times 7+2\right)}\times \frac{7}{3}-\frac{3}{5}\times \frac{5}{3}$$

Add 14 and 1 to get 15.

$$5+\frac{15\times 7}{2\left(9\times 7+2\right)}\times \frac{7}{3}-\frac{3}{5}\times \frac{5}{3}$$

Multiply 15 and 7 to get 105.

$$5+\frac{105}{2\left(9\times 7+2\right)}\times \frac{7}{3}-\frac{3}{5}\times \frac{5}{3}$$

Multiply 9 and 7 to get 63.

$$5+\frac{105}{2\left(63+2\right)}\times \frac{7}{3}-\frac{3}{5}\times \frac{5}{3}$$

Add 63 and 2 to get 65.

$$5+\frac{105}{2\times 65}\times \frac{7}{3}-\frac{3}{5}\times \frac{5}{3}$$

Multiply 2 and 65 to get 130.

$$5+\frac{105}{130}\times \frac{7}{3}-\frac{3}{5}\times \frac{5}{3}$$

Reduce the fraction \frac{105}{130} to lowest terms by extracting and canceling out 5.

$$5+\frac{21}{26}\times \frac{7}{3}-\frac{3}{5}\times \frac{5}{3}$$

Multiply \frac{21}{26} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$5+\frac{21\times 7}{26\times 3}-\frac{3}{5}\times \frac{5}{3}$$

Do the multiplications in the fraction \frac{21\times 7}{26\times 3}.

$$5+\frac{147}{78}-\frac{3}{5}\times \frac{5}{3}$$

Reduce the fraction \frac{147}{78} to lowest terms by extracting and canceling out 3.

$$5+\frac{49}{26}-\frac{3}{5}\times \frac{5}{3}$$

Convert 5 to fraction \frac{130}{26}.

$$\frac{130}{26}+\frac{49}{26}-\frac{3}{5}\times \frac{5}{3}$$

Since \frac{130}{26} and \frac{49}{26} have the same denominator, add them by adding their numerators.

$$\frac{130+49}{26}-\frac{3}{5}\times \frac{5}{3}$$

Add 130 and 49 to get 179.

$$\frac{179}{26}-\frac{3}{5}\times \frac{5}{3}$$

Cancel out \frac{3}{5} and its reciprocal \frac{5}{3}.

$$\frac{179}{26}-1$$

Convert 1 to fraction \frac{26}{26}.

$$\frac{179}{26}-\frac{26}{26}$$

Since \frac{179}{26} and \frac{26}{26} have the same denominator, subtract them by subtracting their numerators.

$$\frac{179-26}{26}$$

Subtract 26 from 179 to get 153.

$$\frac{153}{26}$$

Factor

$$\frac{3 ^ {2} \cdot 17}{2 \cdot 13} = 5\frac{23}{26} = 5.884615384615385$$