Solve 3/5text{of}[93/5-1/3(11/3+2frac{1}{4})*3frac{2}{5}]

$$\frac { 3 } { 5 } \text { of } [ 9 \frac { 3 } { 5 } - \frac { 1 } { 3 } ( 1 \frac { 1 } { 3 } + 2 \frac { 1 } { 4 } ) \times 3 \frac { 2 } { 5 } ]$$

Evaluate

$$\frac{997}{300}\approx 3.323333333$$

Solution Steps

Multiply 9 and 5 to get 45.

$$\frac{3}{5}\left(\frac{45+3}{5}-\frac{1}{3}\left(\frac{1\times 3+1}{3}+\frac{2\times 4+1}{4}\right)\times \frac{3\times 5+2}{5}\right)$$

Add 45 and 3 to get 48.

$$\frac{3}{5}\left(\frac{48}{5}-\frac{1}{3}\left(\frac{1\times 3+1}{3}+\frac{2\times 4+1}{4}\right)\times \frac{3\times 5+2}{5}\right)$$

Multiply 1 and 3 to get 3.

$$\frac{3}{5}\left(\frac{48}{5}-\frac{1}{3}\left(\frac{3+1}{3}+\frac{2\times 4+1}{4}\right)\times \frac{3\times 5+2}{5}\right)$$

Add 3 and 1 to get 4.

$$\frac{3}{5}\left(\frac{48}{5}-\frac{1}{3}\left(\frac{4}{3}+\frac{2\times 4+1}{4}\right)\times \frac{3\times 5+2}{5}\right)$$

Multiply 2 and 4 to get 8.

$$\frac{3}{5}\left(\frac{48}{5}-\frac{1}{3}\left(\frac{4}{3}+\frac{8+1}{4}\right)\times \frac{3\times 5+2}{5}\right)$$

Add 8 and 1 to get 9.

$$\frac{3}{5}\left(\frac{48}{5}-\frac{1}{3}\left(\frac{4}{3}+\frac{9}{4}\right)\times \frac{3\times 5+2}{5}\right)$$

Least common multiple of 3 and 4 is 12. Convert \frac{4}{3} and \frac{9}{4} to fractions with denominator 12.

$$\frac{3}{5}\left(\frac{48}{5}-\frac{1}{3}\left(\frac{16}{12}+\frac{27}{12}\right)\times \frac{3\times 5+2}{5}\right)$$

Since \frac{16}{12} and \frac{27}{12} have the same denominator, add them by adding their numerators.

$$\frac{3}{5}\left(\frac{48}{5}-\frac{1}{3}\times \frac{16+27}{12}\times \frac{3\times 5+2}{5}\right)$$

Add 16 and 27 to get 43.

$$\frac{3}{5}\left(\frac{48}{5}-\frac{1}{3}\times \frac{43}{12}\times \frac{3\times 5+2}{5}\right)$$

Multiply \frac{1}{3} times \frac{43}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{5}\left(\frac{48}{5}-\frac{1\times 43}{3\times 12}\times \frac{3\times 5+2}{5}\right)$$

Do the multiplications in the fraction \frac{1\times 43}{3\times 12}.

$$\frac{3}{5}\left(\frac{48}{5}-\frac{43}{36}\times \frac{3\times 5+2}{5}\right)$$

Multiply 3 and 5 to get 15.

$$\frac{3}{5}\left(\frac{48}{5}-\frac{43}{36}\times \frac{15+2}{5}\right)$$

Add 15 and 2 to get 17.

$$\frac{3}{5}\left(\frac{48}{5}-\frac{43}{36}\times \frac{17}{5}\right)$$

Multiply \frac{43}{36} times \frac{17}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{5}\left(\frac{48}{5}-\frac{43\times 17}{36\times 5}\right)$$

Do the multiplications in the fraction \frac{43\times 17}{36\times 5}.

$$\frac{3}{5}\left(\frac{48}{5}-\frac{731}{180}\right)$$

Least common multiple of 5 and 180 is 180. Convert \frac{48}{5} and \frac{731}{180} to fractions with denominator 180.

$$\frac{3}{5}\left(\frac{1728}{180}-\frac{731}{180}\right)$$

Since \frac{1728}{180} and \frac{731}{180} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{5}\times \frac{1728-731}{180}$$

Subtract 731 from 1728 to get 997.

$$\frac{3}{5}\times \frac{997}{180}$$

Multiply \frac{3}{5} times \frac{997}{180} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 997}{5\times 180}$$

Do the multiplications in the fraction \frac{3\times 997}{5\times 180}.

$$\frac{2991}{900}$$

Reduce the fraction \frac{2991}{900} to lowest terms by extracting and canceling out 3.

$$\frac{997}{300}$$

Factor

$$\frac{997}{2 ^ {2} \cdot 3 \cdot 5 ^ {2}} = 3\frac{97}{300} = 3.3233333333333333$$