Solve 11/2div11/4-21/2*frac{1/4}{frac{1}{3}*frac{1}{2}+frac{1}{6}*frac{1}{2}}

$$\frac { 1 \frac { 1 } { 2 } \div 1 \frac { 1 } { 4 } - 2 \frac { 1 } { 2 } \times \frac { 1 } { 4 } } { \frac { 1 } { 3 } \times \frac { 1 } { 2 } + \frac { 1 } { 6 } \times \frac { 1 } { 2 } }$$

Evaluate

$$\frac{23}{10}=2.3$$

Solution Steps

Divide \frac{1\times 2+1}{2} by \frac{1\times 4+1}{4} by multiplying \frac{1\times 2+1}{2} by the reciprocal of \frac{1\times 4+1}{4}.

$$\frac{\frac{\left(1\times 2+1\right)\times 4}{2\left(1\times 4+1\right)}-\frac{2\times 2+1}{2}\times \frac{1}{4}}{\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{2\left(1+2\right)}{1+4}-\frac{2\times 2+1}{2}\times \frac{1}{4}}{\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}}$$

Add 1 and 2 to get 3.

$$\frac{\frac{2\times 3}{1+4}-\frac{2\times 2+1}{2}\times \frac{1}{4}}{\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{6}{1+4}-\frac{2\times 2+1}{2}\times \frac{1}{4}}{\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}}$$

Add 1 and 4 to get 5.

$$\frac{\frac{6}{5}-\frac{2\times 2+1}{2}\times \frac{1}{4}}{\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{6}{5}-\frac{4+1}{2}\times \frac{1}{4}}{\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{6}{5}-\frac{5}{2}\times \frac{1}{4}}{\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}}$$

Multiply \frac{5}{2} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{6}{5}-\frac{5\times 1}{2\times 4}}{\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}}$$

Do the multiplications in the fraction \frac{5\times 1}{2\times 4}.

$$\frac{\frac{6}{5}-\frac{5}{8}}{\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}}$$

Least common multiple of 5 and 8 is 40. Convert \frac{6}{5} and \frac{5}{8} to fractions with denominator 40.

$$\frac{\frac{48}{40}-\frac{25}{40}}{\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}}$$

Since \frac{48}{40} and \frac{25}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{48-25}{40}}{\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}}$$

Subtract 25 from 48 to get 23.

$$\frac{\frac{23}{40}}{\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}}$$

Multiply \frac{1}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{23}{40}}{\frac{1\times 1}{3\times 2}+\frac{1}{6}\times \frac{1}{2}}$$

Do the multiplications in the fraction \frac{1\times 1}{3\times 2}.

$$\frac{\frac{23}{40}}{\frac{1}{6}+\frac{1}{6}\times \frac{1}{2}}$$

Multiply \frac{1}{6} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{23}{40}}{\frac{1}{6}+\frac{1\times 1}{6\times 2}}$$

Do the multiplications in the fraction \frac{1\times 1}{6\times 2}.

$$\frac{\frac{23}{40}}{\frac{1}{6}+\frac{1}{12}}$$

Least common multiple of 6 and 12 is 12. Convert \frac{1}{6} and \frac{1}{12} to fractions with denominator 12.

$$\frac{\frac{23}{40}}{\frac{2}{12}+\frac{1}{12}}$$

Since \frac{2}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{23}{40}}{\frac{2+1}{12}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{23}{40}}{\frac{3}{12}}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{23}{40}}{\frac{1}{4}}$$

Divide \frac{23}{40} by \frac{1}{4} by multiplying \frac{23}{40} by the reciprocal of \frac{1}{4}.

$$\frac{23}{40}\times 4$$

Express \frac{23}{40}\times 4 as a single fraction.

$$\frac{23\times 4}{40}$$

Multiply 23 and 4 to get 92.

$$\frac{92}{40}$$

Reduce the fraction \frac{92}{40} to lowest terms by extracting and canceling out 4.

$$\frac{23}{10}$$

Factor

$$\frac{23}{2 \cdot 5} = 2\frac{3}{10} = 2.3$$