Solve (1/4+1/frac{1{2}+1})(1/4+frac{1/2}{2})

$$( \frac { \frac { 1 } { 4 } + 1 } { \frac { 1 } { 2 } + 1 } ) ( \frac { \frac { 1 } { 4 } + \frac { 1 } { 2 } } { 2 } )$$

Evaluate

$$\frac{5}{16}=0.3125$$

Solution Steps

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

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

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

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

Add 1 and 4 to get 5.

$$\frac{\frac{5}{4}}{\frac{1}{2}+1}\times \frac{\frac{1}{4}+\frac{1}{2}}{2}$$

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

$$\frac{\frac{5}{4}}{\frac{1}{2}+\frac{2}{2}}\times \frac{\frac{1}{4}+\frac{1}{2}}{2}$$

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

$$\frac{\frac{5}{4}}{\frac{1+2}{2}}\times \frac{\frac{1}{4}+\frac{1}{2}}{2}$$

Add 1 and 2 to get 3.

$$\frac{\frac{5}{4}}{\frac{3}{2}}\times \frac{\frac{1}{4}+\frac{1}{2}}{2}$$

Divide \frac{5}{4} by \frac{3}{2} by multiplying \frac{5}{4} by the reciprocal of \frac{3}{2}.

$$\frac{5}{4}\times \frac{2}{3}\times \frac{\frac{1}{4}+\frac{1}{2}}{2}$$

Multiply \frac{5}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 2}{4\times 3}\times \frac{\frac{1}{4}+\frac{1}{2}}{2}$$

Do the multiplications in the fraction \frac{5\times 2}{4\times 3}.

$$\frac{10}{12}\times \frac{\frac{1}{4}+\frac{1}{2}}{2}$$

Reduce the fraction \frac{10}{12} to lowest terms by extracting and canceling out 2.

$$\frac{5}{6}\times \frac{\frac{1}{4}+\frac{1}{2}}{2}$$

Least common multiple of 4 and 2 is 4. Convert \frac{1}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{5}{6}\times \frac{\frac{1}{4}+\frac{2}{4}}{2}$$

Since \frac{1}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}\times \frac{\frac{1+2}{4}}{2}$$

Add 1 and 2 to get 3.

$$\frac{5}{6}\times \frac{\frac{3}{4}}{2}$$

Express \frac{\frac{3}{4}}{2} as a single fraction.

$$\frac{5}{6}\times \frac{3}{4\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{5}{6}\times \frac{3}{8}$$

Multiply \frac{5}{6} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 3}{6\times 8}$$

Do the multiplications in the fraction \frac{5\times 3}{6\times 8}.

$$\frac{15}{48}$$

Reduce the fraction \frac{15}{48} to lowest terms by extracting and canceling out 3.

$$\frac{5}{16}$$

Factor

$$\frac{5}{2 ^ {4}} = 0.3125$$