Solve (9/2*5/4)div(1/4*11/2)

$$( \frac { 9 } { 2 } \cdot \frac { 5 } { 4 } ) \div ( \frac { 1 } { 4 } \cdot \frac { 11 } { 2 } )$$

Evaluate

$$\frac{45}{11}\approx 4.090909091$$

Solution Steps

Multiply \frac{9}{2} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9\times 5}{2\times 4}}{\frac{1}{4}\times \frac{11}{2}}$$

Do the multiplications in the fraction \frac{9\times 5}{2\times 4}.

$$\frac{\frac{45}{8}}{\frac{1}{4}\times \frac{11}{2}}$$

Multiply \frac{1}{4} times \frac{11}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{45}{8}}{\frac{1\times 11}{4\times 2}}$$

Do the multiplications in the fraction \frac{1\times 11}{4\times 2}.

$$\frac{\frac{45}{8}}{\frac{11}{8}}$$

Divide \frac{45}{8} by \frac{11}{8} by multiplying \frac{45}{8} by the reciprocal of \frac{11}{8}.

$$\frac{45}{8}\times \frac{8}{11}$$

Multiply \frac{45}{8} times \frac{8}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{45\times 8}{8\times 11}$$

Cancel out 8 in both numerator and denominator.

$$\frac{45}{11}$$

Factor

$$\frac{3 ^ {2} \cdot 5}{11} = 4\frac{1}{11} = 4.090909090909091$$