Solve -64/9*(-17/29)-(91/6-33/4):4frac{1}{6}

$$- 6 \frac { 4 } { 9 } \cdot ( - 1 \frac { 7 } { 29 } ) - ( 9 \frac { 1 } { 6 } - 3 \frac { 3 } { 4 } ) : 4 \frac { 1 } { 6 }$$

Evaluate

$$\frac{67}{10}=6.7$$

Solution Steps

Multiply 6 and 9 to get 54.

$$\left(-\frac{54+4}{9}\right)\left(-\frac{1\times 29+7}{29}\right)-\frac{\frac{9\times 6+1}{6}-\frac{3\times 4+3}{4}}{\frac{4\times 6+1}{6}}$$

Add 54 and 4 to get 58.

$$-\frac{58}{9}\left(-\frac{29+7}{29}\right)-\frac{\frac{9\times 6+1}{6}-\frac{3\times 4+3}{4}}{\frac{4\times 6+1}{6}}$$

Add 29 and 7 to get 36.

$$-\frac{58}{9}\left(-\frac{36}{29}\right)-\frac{\frac{9\times 6+1}{6}-\frac{3\times 4+3}{4}}{\frac{4\times 6+1}{6}}$$

Multiply -\frac{58}{9} times -\frac{36}{29} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-58\left(-36\right)}{9\times 29}-\frac{\frac{9\times 6+1}{6}-\frac{3\times 4+3}{4}}{\frac{4\times 6+1}{6}}$$

Do the multiplications in the fraction \frac{-58\left(-36\right)}{9\times 29}.

$$\frac{2088}{261}-\frac{\frac{9\times 6+1}{6}-\frac{3\times 4+3}{4}}{\frac{4\times 6+1}{6}}$$

Divide 2088 by 261 to get 8.

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

Multiply 9 and 6 to get 54.

$$8-\frac{\frac{54+1}{6}-\frac{3\times 4+3}{4}}{\frac{4\times 6+1}{6}}$$

Add 54 and 1 to get 55.

$$8-\frac{\frac{55}{6}-\frac{3\times 4+3}{4}}{\frac{4\times 6+1}{6}}$$

Multiply 3 and 4 to get 12.

$$8-\frac{\frac{55}{6}-\frac{12+3}{4}}{\frac{4\times 6+1}{6}}$$

Add 12 and 3 to get 15.

$$8-\frac{\frac{55}{6}-\frac{15}{4}}{\frac{4\times 6+1}{6}}$$

Least common multiple of 6 and 4 is 12. Convert \frac{55}{6} and \frac{15}{4} to fractions with denominator 12.

$$8-\frac{\frac{110}{12}-\frac{45}{12}}{\frac{4\times 6+1}{6}}$$

Since \frac{110}{12} and \frac{45}{12} have the same denominator, subtract them by subtracting their numerators.

$$8-\frac{\frac{110-45}{12}}{\frac{4\times 6+1}{6}}$$

Subtract 45 from 110 to get 65.

$$8-\frac{\frac{65}{12}}{\frac{4\times 6+1}{6}}$$

Multiply 4 and 6 to get 24.

$$8-\frac{\frac{65}{12}}{\frac{24+1}{6}}$$

Add 24 and 1 to get 25.

$$8-\frac{\frac{65}{12}}{\frac{25}{6}}$$

Divide \frac{65}{12} by \frac{25}{6} by multiplying \frac{65}{12} by the reciprocal of \frac{25}{6}.

$$8-\frac{65}{12}\times \frac{6}{25}$$

Multiply \frac{65}{12} times \frac{6}{25} by multiplying numerator times numerator and denominator times denominator.

$$8-\frac{65\times 6}{12\times 25}$$

Do the multiplications in the fraction \frac{65\times 6}{12\times 25}.

$$8-\frac{390}{300}$$

Reduce the fraction \frac{390}{300} to lowest terms by extracting and canceling out 30.

$$8-\frac{13}{10}$$

Convert 8 to fraction \frac{80}{10}.

$$\frac{80}{10}-\frac{13}{10}$$

Since \frac{80}{10} and \frac{13}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{80-13}{10}$$

Subtract 13 from 80 to get 67.

$$\frac{67}{10}$$

Factor

$$\frac{67}{2 \cdot 5} = 6\frac{7}{10} = 6.7$$