Solve 6-(4*8/9-1/2*5/2*64/81-frac{64}{81})

$$6 - ( 4 \times \frac { 8 } { 9 } - \frac { 1 } { 2 } \times \frac { 5 } { 2 } \times \frac { 64 } { 81 } - \frac { 64 } { 81 } )$$

Evaluate

$$\frac{38}{9}\approx 4.222222222$$

Solution Steps

Express 4\times \frac{8}{9} as a single fraction.

$$6-\left(\frac{4\times 8}{9}-\frac{1}{2}\times \frac{5}{2}\times \frac{64}{81}-\frac{64}{81}\right)$$

Multiply 4 and 8 to get 32.

$$6-\left(\frac{32}{9}-\frac{1}{2}\times \frac{5}{2}\times \frac{64}{81}-\frac{64}{81}\right)$$

Multiply \frac{1}{2} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$6-\left(\frac{32}{9}-\frac{1\times 5}{2\times 2}\times \frac{64}{81}-\frac{64}{81}\right)$$

Do the multiplications in the fraction \frac{1\times 5}{2\times 2}.

$$6-\left(\frac{32}{9}-\frac{5}{4}\times \frac{64}{81}-\frac{64}{81}\right)$$

Multiply \frac{5}{4} times \frac{64}{81} by multiplying numerator times numerator and denominator times denominator.

$$6-\left(\frac{32}{9}-\frac{5\times 64}{4\times 81}-\frac{64}{81}\right)$$

Do the multiplications in the fraction \frac{5\times 64}{4\times 81}.

$$6-\left(\frac{32}{9}-\frac{320}{324}-\frac{64}{81}\right)$$

Reduce the fraction \frac{320}{324} to lowest terms by extracting and canceling out 4.

$$6-\left(\frac{32}{9}-\frac{80}{81}-\frac{64}{81}\right)$$

Least common multiple of 9 and 81 is 81. Convert \frac{32}{9} and \frac{80}{81} to fractions with denominator 81.

$$6-\left(\frac{288}{81}-\frac{80}{81}-\frac{64}{81}\right)$$

Since \frac{288}{81} and \frac{80}{81} have the same denominator, subtract them by subtracting their numerators.

$$6-\left(\frac{288-80}{81}-\frac{64}{81}\right)$$

Subtract 80 from 288 to get 208.

$$6-\left(\frac{208}{81}-\frac{64}{81}\right)$$

Since \frac{208}{81} and \frac{64}{81} have the same denominator, subtract them by subtracting their numerators.

$$6-\frac{208-64}{81}$$

Subtract 64 from 208 to get 144.

$$6-\frac{144}{81}$$

Reduce the fraction \frac{144}{81} to lowest terms by extracting and canceling out 9.

$$6-\frac{16}{9}$$

Convert 6 to fraction \frac{54}{9}.

$$\frac{54}{9}-\frac{16}{9}$$

Since \frac{54}{9} and \frac{16}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{54-16}{9}$$

Subtract 16 from 54 to get 38.

$$\frac{38}{9}$$

Factor

$$\frac{2 \cdot 19}{3 ^ {2}} = 4\frac{2}{9} = 4.222222222222222$$