Solve (8/9:8/27):36/7

$$( \frac { 8 } { 9 } : \frac { 8 } { 27 } ) : \frac { 36 } { 7 }$$

Evaluate

$$\frac{7}{12}\approx 0.583333333$$

Solution Steps

Divide \frac{\frac{8}{9}}{\frac{8}{27}} by \frac{36}{7} by multiplying \frac{\frac{8}{9}}{\frac{8}{27}} by the reciprocal of \frac{36}{7}.

$$\frac{\frac{8}{9}\times 7}{\frac{8}{27}\times 36}$$

Express \frac{8}{9}\times 7 as a single fraction.

$$\frac{\frac{8\times 7}{9}}{\frac{8}{27}\times 36}$$

Multiply 8 and 7 to get 56.

$$\frac{\frac{56}{9}}{\frac{8}{27}\times 36}$$

Express \frac{8}{27}\times 36 as a single fraction.

$$\frac{\frac{56}{9}}{\frac{8\times 36}{27}}$$

Multiply 8 and 36 to get 288.

$$\frac{\frac{56}{9}}{\frac{288}{27}}$$

Reduce the fraction \frac{288}{27} to lowest terms by extracting and canceling out 9.

$$\frac{\frac{56}{9}}{\frac{32}{3}}$$

Divide \frac{56}{9} by \frac{32}{3} by multiplying \frac{56}{9} by the reciprocal of \frac{32}{3}.

$$\frac{56}{9}\times \frac{3}{32}$$

Multiply \frac{56}{9} times \frac{3}{32} by multiplying numerator times numerator and denominator times denominator.

$$\frac{56\times 3}{9\times 32}$$

Do the multiplications in the fraction \frac{56\times 3}{9\times 32}.

$$\frac{168}{288}$$

Reduce the fraction \frac{168}{288} to lowest terms by extracting and canceling out 24.

$$\frac{7}{12}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 3} = 0.5833333333333334$$