Solve f(1/2)=a/2+b/1+frac{1{4}}

$$f ( \frac { 1 } { 2 } ) = \frac { \frac { a } { 2 } + b } { 1 + \frac { 1 } { 4 } }$$

Evaluate

$$\frac{2\left(a+2b\right)}{5}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply b times \frac{2}{2}.

$$\frac{\frac{a}{2}+\frac{2b}{2}}{1+\frac{1}{4}}$$

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

$$\frac{\frac{a+2b}{2}}{1+\frac{1}{4}}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{\frac{a+2b}{2}}{\frac{4}{4}+\frac{1}{4}}$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{a+2b}{2}}{\frac{4+1}{4}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{a+2b}{2}}{\frac{5}{4}}$$

Divide \frac{a+2b}{2} by \frac{5}{4} by multiplying \frac{a+2b}{2} by the reciprocal of \frac{5}{4}.

$$\frac{\left(a+2b\right)\times 4}{2\times 5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\left(a+2b\right)}{5}$$

Use the distributive property to multiply 2 by a+2b.

$$\frac{2a+4b}{5}$$

Expand

$$\frac{2a+4b}{5}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply b times \frac{2}{2}.

$$\frac{\frac{a}{2}+\frac{2b}{2}}{1+\frac{1}{4}}$$

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

$$\frac{\frac{a+2b}{2}}{1+\frac{1}{4}}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{\frac{a+2b}{2}}{\frac{4}{4}+\frac{1}{4}}$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{a+2b}{2}}{\frac{4+1}{4}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{a+2b}{2}}{\frac{5}{4}}$$

Divide \frac{a+2b}{2} by \frac{5}{4} by multiplying \frac{a+2b}{2} by the reciprocal of \frac{5}{4}.

$$\frac{\left(a+2b\right)\times 4}{2\times 5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\left(a+2b\right)}{5}$$

Use the distributive property to multiply 2 by a+2b.

$$\frac{2a+4b}{5}$$