Solve [(5+1/3)*9/16+1/5div3/10]*frac{6}{11}+3

$$[ ( 5 + \frac { 1 } { 3 } ) \cdot \frac { 9 } { 16 } + \frac { 1 } { 5 } \div \frac { 3 } { 10 } ] \cdot \frac { 6 } { 11 } + 3$$

Evaluate

$$5$$

Solution Steps

Convert 5 to fraction \frac{15}{3}.

$$\left(\left(\frac{15}{3}+\frac{1}{3}\right)\times \frac{9}{16}+\frac{\frac{1}{5}}{\frac{3}{10}}\right)\times \frac{6}{11}+3$$

Since \frac{15}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\left(\frac{15+1}{3}\times \frac{9}{16}+\frac{\frac{1}{5}}{\frac{3}{10}}\right)\times \frac{6}{11}+3$$

Add 15 and 1 to get 16.

$$\left(\frac{16}{3}\times \frac{9}{16}+\frac{\frac{1}{5}}{\frac{3}{10}}\right)\times \frac{6}{11}+3$$

Multiply \frac{16}{3} times \frac{9}{16} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{16\times 9}{3\times 16}+\frac{\frac{1}{5}}{\frac{3}{10}}\right)\times \frac{6}{11}+3$$

Cancel out 16 in both numerator and denominator.

$$\left(\frac{9}{3}+\frac{\frac{1}{5}}{\frac{3}{10}}\right)\times \frac{6}{11}+3$$

Divide 9 by 3 to get 3.

$$\left(3+\frac{\frac{1}{5}}{\frac{3}{10}}\right)\times \frac{6}{11}+3$$

Divide \frac{1}{5} by \frac{3}{10} by multiplying \frac{1}{5} by the reciprocal of \frac{3}{10}.

$$\left(3+\frac{1}{5}\times \frac{10}{3}\right)\times \frac{6}{11}+3$$

Multiply \frac{1}{5} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\left(3+\frac{1\times 10}{5\times 3}\right)\times \frac{6}{11}+3$$

Do the multiplications in the fraction \frac{1\times 10}{5\times 3}.

$$\left(3+\frac{10}{15}\right)\times \frac{6}{11}+3$$

Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.

$$\left(3+\frac{2}{3}\right)\times \frac{6}{11}+3$$

Convert 3 to fraction \frac{9}{3}.

$$\left(\frac{9}{3}+\frac{2}{3}\right)\times \frac{6}{11}+3$$

Since \frac{9}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{9+2}{3}\times \frac{6}{11}+3$$

Add 9 and 2 to get 11.

$$\frac{11}{3}\times \frac{6}{11}+3$$

Multiply \frac{11}{3} times \frac{6}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 6}{3\times 11}+3$$

Cancel out 11 in both numerator and denominator.

$$\frac{6}{3}+3$$

Divide 6 by 3 to get 2.

$$2+3$$

Add 2 and 3 to get 5.

$$5$$

Factor

$$5$$