Solve 11/2*11/2*11/4*2

$$1 \frac { 1 } { 2 } \times 1 \frac { 1 } { 2 } \times 1 \frac { 1 } { 4 } \times 2$$

Evaluate

$$\frac{45}{8}=5.625$$

Solution Steps

Multiply \frac{1\times 2+1}{2} and \frac{1\times 2+1}{2} to get \left(\frac{1\times 2+1}{2}\right)^{2}.

$$\left(\frac{1\times 2+1}{2}\right)^{2}\times \frac{1\times 4+1}{4}\times 2$$

Multiply 1 and 2 to get 2.

$$\left(\frac{2+1}{2}\right)^{2}\times \frac{1\times 4+1}{4}\times 2$$

Add 2 and 1 to get 3.

$$\left(\frac{3}{2}\right)^{2}\times \frac{1\times 4+1}{4}\times 2$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{9}{4}\times \frac{1\times 4+1}{4}\times 2$$

Multiply 1 and 4 to get 4.

$$\frac{9}{4}\times \frac{4+1}{4}\times 2$$

Add 4 and 1 to get 5.

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

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

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

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

$$\frac{45}{16}\times 2$$

Express \frac{45}{16}\times 2 as a single fraction.

$$\frac{45\times 2}{16}$$

Multiply 45 and 2 to get 90.

$$\frac{90}{16}$$

Reduce the fraction \frac{90}{16} to lowest terms by extracting and canceling out 2.

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

Factor

$$\frac{3 ^ {2} \cdot 5}{2 ^ {3}} = 5\frac{5}{8} = 5.625$$