Solve 1/3+1/4:(1/3-1/2+frac{3}{4})-frac{3}{6}=

$$\frac { 1 } { 3 } + \frac { 1 } { 4 } : ( \frac { 1 } { 3 } - \frac { 1 } { 2 } + \frac { 3 } { 4 } ) - \frac { 3 } { 6 } =$$

Evaluate

$$\frac{11}{42}\approx 0.261904762$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.

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

Since \frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 2 to get -1.

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

Least common multiple of 6 and 4 is 12. Convert -\frac{1}{6} and \frac{3}{4} to fractions with denominator 12.

$$\frac{1}{3}+\frac{\frac{1}{4}}{-\frac{2}{12}+\frac{9}{12}}-\frac{3}{6}$$

Since -\frac{2}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}+\frac{\frac{1}{4}}{\frac{-2+9}{12}}-\frac{3}{6}$$

Add -2 and 9 to get 7.

$$\frac{1}{3}+\frac{\frac{1}{4}}{\frac{7}{12}}-\frac{3}{6}$$

Divide \frac{1}{4} by \frac{7}{12} by multiplying \frac{1}{4} by the reciprocal of \frac{7}{12}.

$$\frac{1}{3}+\frac{1}{4}\times \frac{12}{7}-\frac{3}{6}$$

Multiply \frac{1}{4} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}+\frac{1\times 12}{4\times 7}-\frac{3}{6}$$

Do the multiplications in the fraction \frac{1\times 12}{4\times 7}.

$$\frac{1}{3}+\frac{12}{28}-\frac{3}{6}$$

Reduce the fraction \frac{12}{28} to lowest terms by extracting and canceling out 4.

$$\frac{1}{3}+\frac{3}{7}-\frac{3}{6}$$

Least common multiple of 3 and 7 is 21. Convert \frac{1}{3} and \frac{3}{7} to fractions with denominator 21.

$$\frac{7}{21}+\frac{9}{21}-\frac{3}{6}$$

Since \frac{7}{21} and \frac{9}{21} have the same denominator, add them by adding their numerators.

$$\frac{7+9}{21}-\frac{3}{6}$$

Add 7 and 9 to get 16.

$$\frac{16}{21}-\frac{3}{6}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{16}{21}-\frac{1}{2}$$

Least common multiple of 21 and 2 is 42. Convert \frac{16}{21} and \frac{1}{2} to fractions with denominator 42.

$$\frac{32}{42}-\frac{21}{42}$$

Since \frac{32}{42} and \frac{21}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{32-21}{42}$$

Subtract 21 from 32 to get 11.

$$\frac{11}{42}$$

Factor

$$\frac{11}{2 \cdot 3 \cdot 7} = 0.2619047619047619$$