Solve 6/9div21/4-28/9*4/9

$$\frac { 6 } { 9 } \div 2 \frac { 1 } { 4 } - \frac { 28 } { 9 } \times \frac { 4 } { 9 }$$

Evaluate

$$-\frac{88}{81}\approx -1.086419753$$

Solution Steps

Divide \frac{6}{9} by \frac{2\times 4+1}{4} by multiplying \frac{6}{9} by the reciprocal of \frac{2\times 4+1}{4}.

$$\frac{6\times 4}{9\left(2\times 4+1\right)}-\frac{28}{9}\times \frac{4}{9}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\times 4}{3\left(1+2\times 4\right)}-\frac{28}{9}\times \frac{4}{9}$$

Multiply 2 and 4 to get 8.

$$\frac{8}{3\left(1+2\times 4\right)}-\frac{28}{9}\times \frac{4}{9}$$

Multiply 2 and 4 to get 8.

$$\frac{8}{3\left(1+8\right)}-\frac{28}{9}\times \frac{4}{9}$$

Add 1 and 8 to get 9.

$$\frac{8}{3\times 9}-\frac{28}{9}\times \frac{4}{9}$$

Multiply 3 and 9 to get 27.

$$\frac{8}{27}-\frac{28}{9}\times \frac{4}{9}$$

Multiply \frac{28}{9} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{27}-\frac{28\times 4}{9\times 9}$$

Do the multiplications in the fraction \frac{28\times 4}{9\times 9}.

$$\frac{8}{27}-\frac{112}{81}$$

Least common multiple of 27 and 81 is 81. Convert \frac{8}{27} and \frac{112}{81} to fractions with denominator 81.

$$\frac{24}{81}-\frac{112}{81}$$

Since \frac{24}{81} and \frac{112}{81} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-112}{81}$$

Subtract 112 from 24 to get -88.

$$-\frac{88}{81}$$

Factor

$$-\frac{88}{81} = -1\frac{7}{81} = -1.0864197530864197$$