Solve 2^2/4-2^2/2^3+(11/2+3/2^3)=

$$\frac { 2 ^ { 2 } } { 4 } - \frac { 2 ^ { 2 } } { 2 ^ { 3 } } + ( 1 \frac { 1 } { 2 } + \frac { 3 } { 2 ^ { 3 } } ) =$$

Evaluate

$$\frac{19}{8}=2.375$$

Solution Steps

Rewrite 2^{3} as 2\times 2^{2}. Cancel out 2^{2} in both numerator and denominator.

$$\frac{2^{2}}{4}-\frac{1}{2}+\frac{1\times 2+1}{2}+\frac{3}{2^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4}{4}-\frac{1}{2}+\frac{1\times 2+1}{2}+\frac{3}{2^{3}}$$

Divide 4 by 4 to get 1.

$$1-\frac{1}{2}+\frac{1\times 2+1}{2}+\frac{3}{2^{3}}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{2}{2}-\frac{1}{2}+\frac{1\times 2+1}{2}+\frac{3}{2^{3}}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-1}{2}+\frac{1\times 2+1}{2}+\frac{3}{2^{3}}$$

Subtract 1 from 2 to get 1.

$$\frac{1}{2}+\frac{1\times 2+1}{2}+\frac{3}{2^{3}}$$

Multiply 1 and 2 to get 2.

$$\frac{1}{2}+\frac{2+1}{2}+\frac{3}{2^{3}}$$

Add 2 and 1 to get 3.

$$\frac{1}{2}+\frac{3}{2}+\frac{3}{2^{3}}$$

Since \frac{1}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\frac{1+3}{2}+\frac{3}{2^{3}}$$

Add 1 and 3 to get 4.

$$\frac{4}{2}+\frac{3}{2^{3}}$$

Divide 4 by 2 to get 2.

$$2+\frac{3}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$2+\frac{3}{8}$$

Convert 2 to fraction \frac{16}{8}.

$$\frac{16}{8}+\frac{3}{8}$$

Since \frac{16}{8} and \frac{3}{8} have the same denominator, add them by adding their numerators.

$$\frac{16+3}{8}$$

Add 16 and 3 to get 19.

$$\frac{19}{8}$$

Factor

$$\frac{19}{2 ^ {3}} = 2\frac{3}{8} = 2.375$$