Solve [31/4-3/8div(35/6-21/3)]div5frac{1}{3}

$$[ 3 \frac { 1 } { 4 } - \frac { 3 } { 8 } \div ( 3 \frac { 5 } { 6 } - 2 \frac { 1 } { 3 } ) ] \div 5 \frac { 1 } { 3 }$$

Evaluate

$$\frac{9}{16}=0.5625$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\frac{\frac{12+1}{4}-\frac{\frac{3}{8}}{\frac{3\times 6+5}{6}-\frac{2\times 3+1}{3}}}{\frac{5\times 3+1}{3}}$$

Add 12 and 1 to get 13.

$$\frac{\frac{13}{4}-\frac{\frac{3}{8}}{\frac{3\times 6+5}{6}-\frac{2\times 3+1}{3}}}{\frac{5\times 3+1}{3}}$$

Multiply 3 and 6 to get 18.

$$\frac{\frac{13}{4}-\frac{\frac{3}{8}}{\frac{18+5}{6}-\frac{2\times 3+1}{3}}}{\frac{5\times 3+1}{3}}$$

Add 18 and 5 to get 23.

$$\frac{\frac{13}{4}-\frac{\frac{3}{8}}{\frac{23}{6}-\frac{2\times 3+1}{3}}}{\frac{5\times 3+1}{3}}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{13}{4}-\frac{\frac{3}{8}}{\frac{23}{6}-\frac{6+1}{3}}}{\frac{5\times 3+1}{3}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{13}{4}-\frac{\frac{3}{8}}{\frac{23}{6}-\frac{7}{3}}}{\frac{5\times 3+1}{3}}$$

Least common multiple of 6 and 3 is 6. Convert \frac{23}{6} and \frac{7}{3} to fractions with denominator 6.

$$\frac{\frac{13}{4}-\frac{\frac{3}{8}}{\frac{23}{6}-\frac{14}{6}}}{\frac{5\times 3+1}{3}}$$

Since \frac{23}{6} and \frac{14}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13}{4}-\frac{\frac{3}{8}}{\frac{23-14}{6}}}{\frac{5\times 3+1}{3}}$$

Subtract 14 from 23 to get 9.

$$\frac{\frac{13}{4}-\frac{\frac{3}{8}}{\frac{9}{6}}}{\frac{5\times 3+1}{3}}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{13}{4}-\frac{\frac{3}{8}}{\frac{3}{2}}}{\frac{5\times 3+1}{3}}$$

Divide \frac{3}{8} by \frac{3}{2} by multiplying \frac{3}{8} by the reciprocal of \frac{3}{2}.

$$\frac{\frac{13}{4}-\frac{3}{8}\times \frac{2}{3}}{\frac{5\times 3+1}{3}}$$

Multiply \frac{3}{8} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13}{4}-\frac{3\times 2}{8\times 3}}{\frac{5\times 3+1}{3}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{13}{4}-\frac{2}{8}}{\frac{5\times 3+1}{3}}$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{13}{4}-\frac{1}{4}}{\frac{5\times 3+1}{3}}$$

Since \frac{13}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13-1}{4}}{\frac{5\times 3+1}{3}}$$

Subtract 1 from 13 to get 12.

$$\frac{\frac{12}{4}}{\frac{5\times 3+1}{3}}$$

Divide 12 by 4 to get 3.

$$\frac{3}{\frac{5\times 3+1}{3}}$$

Multiply 5 and 3 to get 15.

$$\frac{3}{\frac{15+1}{3}}$$

Add 15 and 1 to get 16.

$$\frac{3}{\frac{16}{3}}$$

Divide 3 by \frac{16}{3} by multiplying 3 by the reciprocal of \frac{16}{3}.

$$3\times \frac{3}{16}$$

Express 3\times \frac{3}{16} as a single fraction.

$$\frac{3\times 3}{16}$$

Multiply 3 and 3 to get 9.

$$\frac{9}{16}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {4}} = 0.5625$$