Solve (3+1/4)-(2+1/6)[1/2div(1/4+frac{1}{3})]

$$( 3 + \frac { 1 } { 4 } ) - ( 2 + \frac { 1 } { 6 } ) [ \frac { 1 } { 2 } \div ( \frac { 1 } { 4 } + \frac { 1 } { 3 } ) ]$$

Evaluate

$$\frac{39}{28}\approx 1.392857143$$

Solution Steps

Convert 3 to fraction \frac{12}{4}.

$$\frac{12}{4}+\frac{1}{4}-\left(2+\frac{1}{6}\right)\times \frac{\frac{1}{2}}{\frac{1}{4}+\frac{1}{3}}$$

Since \frac{12}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{12+1}{4}-\left(2+\frac{1}{6}\right)\times \frac{\frac{1}{2}}{\frac{1}{4}+\frac{1}{3}}$$

Add 12 and 1 to get 13.

$$\frac{13}{4}-\left(2+\frac{1}{6}\right)\times \frac{\frac{1}{2}}{\frac{1}{4}+\frac{1}{3}}$$

Convert 2 to fraction \frac{12}{6}.

$$\frac{13}{4}-\left(\frac{12}{6}+\frac{1}{6}\right)\times \frac{\frac{1}{2}}{\frac{1}{4}+\frac{1}{3}}$$

Since \frac{12}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{13}{4}-\frac{12+1}{6}\times \frac{\frac{1}{2}}{\frac{1}{4}+\frac{1}{3}}$$

Add 12 and 1 to get 13.

$$\frac{13}{4}-\frac{13}{6}\times \frac{\frac{1}{2}}{\frac{1}{4}+\frac{1}{3}}$$

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{1}{3} to fractions with denominator 12.

$$\frac{13}{4}-\frac{13}{6}\times \frac{\frac{1}{2}}{\frac{3}{12}+\frac{4}{12}}$$

Since \frac{3}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

$$\frac{13}{4}-\frac{13}{6}\times \frac{\frac{1}{2}}{\frac{3+4}{12}}$$

Add 3 and 4 to get 7.

$$\frac{13}{4}-\frac{13}{6}\times \frac{\frac{1}{2}}{\frac{7}{12}}$$

Divide \frac{1}{2} by \frac{7}{12} by multiplying \frac{1}{2} by the reciprocal of \frac{7}{12}.

$$\frac{13}{4}-\frac{13}{6}\times \frac{1}{2}\times \frac{12}{7}$$

Multiply \frac{1}{2} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13}{4}-\frac{13}{6}\times \frac{1\times 12}{2\times 7}$$

Do the multiplications in the fraction \frac{1\times 12}{2\times 7}.

$$\frac{13}{4}-\frac{13}{6}\times \frac{12}{14}$$

Reduce the fraction \frac{12}{14} to lowest terms by extracting and canceling out 2.

$$\frac{13}{4}-\frac{13}{6}\times \frac{6}{7}$$

Multiply \frac{13}{6} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13}{4}-\frac{13\times 6}{6\times 7}$$

Cancel out 6 in both numerator and denominator.

$$\frac{13}{4}-\frac{13}{7}$$

Least common multiple of 4 and 7 is 28. Convert \frac{13}{4} and \frac{13}{7} to fractions with denominator 28.

$$\frac{91}{28}-\frac{52}{28}$$

Since \frac{91}{28} and \frac{52}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{91-52}{28}$$

Subtract 52 from 91 to get 39.

$$\frac{39}{28}$$

Factor

$$\frac{3 \cdot 13}{2 ^ {2} \cdot 7} = 1\frac{11}{28} = 1.3928571428571428$$