Solve 4+62/3-21/4*(2/3-2/9)]:4frac{5}{6}+frac{29}{4}

$$4 + 6 \frac { 2 } { 3 } - 2 \frac { 1 } { 4 } \cdot ( \frac { 2 } { 3 } - \frac { 2 } { 9 } ) ] : 4 \frac { 5 } { 6 } + \frac { 29 } { 4 }$$

Evaluate

$$\frac{29}{3}\approx 9.666666667$$

Solution Steps

Multiply 6 and 3 to get 18.

$$4+\frac{18+2}{3}-\frac{2\times 4+1}{4}\left(\frac{2}{3}-\frac{2}{9}\right)$$

Add 18 and 2 to get 20.

$$4+\frac{20}{3}-\frac{2\times 4+1}{4}\left(\frac{2}{3}-\frac{2}{9}\right)$$

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

$$\frac{12}{3}+\frac{20}{3}-\frac{2\times 4+1}{4}\left(\frac{2}{3}-\frac{2}{9}\right)$$

Since \frac{12}{3} and \frac{20}{3} have the same denominator, add them by adding their numerators.

$$\frac{12+20}{3}-\frac{2\times 4+1}{4}\left(\frac{2}{3}-\frac{2}{9}\right)$$

Add 12 and 20 to get 32.

$$\frac{32}{3}-\frac{2\times 4+1}{4}\left(\frac{2}{3}-\frac{2}{9}\right)$$

Multiply 2 and 4 to get 8.

$$\frac{32}{3}-\frac{8+1}{4}\left(\frac{2}{3}-\frac{2}{9}\right)$$

Add 8 and 1 to get 9.

$$\frac{32}{3}-\frac{9}{4}\left(\frac{2}{3}-\frac{2}{9}\right)$$

Least common multiple of 3 and 9 is 9. Convert \frac{2}{3} and \frac{2}{9} to fractions with denominator 9.

$$\frac{32}{3}-\frac{9}{4}\left(\frac{6}{9}-\frac{2}{9}\right)$$

Since \frac{6}{9} and \frac{2}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{32}{3}-\frac{9}{4}\times \frac{6-2}{9}$$

Subtract 2 from 6 to get 4.

$$\frac{32}{3}-\frac{9}{4}\times \frac{4}{9}$$

Cancel out \frac{9}{4} and its reciprocal \frac{4}{9}.

$$\frac{32}{3}-1$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{32}{3}-\frac{3}{3}$$

Since \frac{32}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{32-3}{3}$$

Subtract 3 from 32 to get 29.

$$\frac{29}{3}$$

Factor

$$\frac{29}{3} = 9\frac{2}{3} = 9.666666666666666$$