Solve (3+13/4-21/3)div(2/3*13/4)

$$( 3 + 1 \frac { 3 } { 4 } - 2 \frac { 1 } { 3 } ) \div ( \frac { 2 } { 3 } \times 1 \frac { 3 } { 4 } )$$

Evaluate

$$\frac{29}{14}\approx 2.071428571$$

Solution Steps

Multiply 1 and 4 to get 4.

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

Add 4 and 3 to get 7.

$$\frac{3+\frac{7}{4}-\frac{2\times 3+1}{3}}{\frac{2}{3}\times \frac{1\times 4+3}{4}}$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{\frac{12}{4}+\frac{7}{4}-\frac{2\times 3+1}{3}}{\frac{2}{3}\times \frac{1\times 4+3}{4}}$$

Since \frac{12}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{12+7}{4}-\frac{2\times 3+1}{3}}{\frac{2}{3}\times \frac{1\times 4+3}{4}}$$

Add 12 and 7 to get 19.

$$\frac{\frac{19}{4}-\frac{2\times 3+1}{3}}{\frac{2}{3}\times \frac{1\times 4+3}{4}}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{19}{4}-\frac{6+1}{3}}{\frac{2}{3}\times \frac{1\times 4+3}{4}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{19}{4}-\frac{7}{3}}{\frac{2}{3}\times \frac{1\times 4+3}{4}}$$

Least common multiple of 4 and 3 is 12. Convert \frac{19}{4} and \frac{7}{3} to fractions with denominator 12.

$$\frac{\frac{57}{12}-\frac{28}{12}}{\frac{2}{3}\times \frac{1\times 4+3}{4}}$$

Since \frac{57}{12} and \frac{28}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{57-28}{12}}{\frac{2}{3}\times \frac{1\times 4+3}{4}}$$

Subtract 28 from 57 to get 29.

$$\frac{\frac{29}{12}}{\frac{2}{3}\times \frac{1\times 4+3}{4}}$$

Multiply 1 and 4 to get 4.

$$\frac{\frac{29}{12}}{\frac{2}{3}\times \frac{4+3}{4}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{29}{12}}{\frac{2}{3}\times \frac{7}{4}}$$

Multiply \frac{2}{3} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{29}{12}}{\frac{2\times 7}{3\times 4}}$$

Do the multiplications in the fraction \frac{2\times 7}{3\times 4}.

$$\frac{\frac{29}{12}}{\frac{14}{12}}$$

Reduce the fraction \frac{14}{12} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{29}{12}}{\frac{7}{6}}$$

Divide \frac{29}{12} by \frac{7}{6} by multiplying \frac{29}{12} by the reciprocal of \frac{7}{6}.

$$\frac{29}{12}\times \frac{6}{7}$$

Multiply \frac{29}{12} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{29\times 6}{12\times 7}$$

Do the multiplications in the fraction \frac{29\times 6}{12\times 7}.

$$\frac{174}{84}$$

Reduce the fraction \frac{174}{84} to lowest terms by extracting and canceling out 6.

$$\frac{29}{14}$$

Factor

$$\frac{29}{2 \cdot 7} = 2\frac{1}{14} = 2.0714285714285716$$