Solve 11/3+12/23*[1/3+1:(1/7+frac{1}{2}:3frac{1}{2})]

$$1 \frac { 1 } { 3 } + \frac { 12 } { 23 } \cdot [ \frac { 1 } { 3 } + 1 : ( \frac { 1 } { 7 } + \frac { 1 } { 2 } : 3 \frac { 1 } { 2 } ) ]$$

Evaluate

$$\frac{10}{3}\approx 3.333333333$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{3+1}{3}+\frac{12}{23}\left(\frac{1}{3}+\frac{1}{\frac{1}{7}+\frac{\frac{1}{2}}{\frac{3\times 2+1}{2}}}\right)$$

Add 3 and 1 to get 4.

$$\frac{4}{3}+\frac{12}{23}\left(\frac{1}{3}+\frac{1}{\frac{1}{7}+\frac{\frac{1}{2}}{\frac{3\times 2+1}{2}}}\right)$$

Divide \frac{1}{2} by \frac{3\times 2+1}{2} by multiplying \frac{1}{2} by the reciprocal of \frac{3\times 2+1}{2}.

$$\frac{4}{3}+\frac{12}{23}\left(\frac{1}{3}+\frac{1}{\frac{1}{7}+\frac{2}{2\left(3\times 2+1\right)}}\right)$$

Multiply 3 and 2 to get 6.

$$\frac{4}{3}+\frac{12}{23}\left(\frac{1}{3}+\frac{1}{\frac{1}{7}+\frac{2}{2\left(6+1\right)}}\right)$$

Add 6 and 1 to get 7.

$$\frac{4}{3}+\frac{12}{23}\left(\frac{1}{3}+\frac{1}{\frac{1}{7}+\frac{2}{2\times 7}}\right)$$

Multiply 2 and 7 to get 14.

$$\frac{4}{3}+\frac{12}{23}\left(\frac{1}{3}+\frac{1}{\frac{1}{7}+\frac{2}{14}}\right)$$

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

$$\frac{4}{3}+\frac{12}{23}\left(\frac{1}{3}+\frac{1}{\frac{1}{7}+\frac{1}{7}}\right)$$

Since \frac{1}{7} and \frac{1}{7} have the same denominator, add them by adding their numerators.

$$\frac{4}{3}+\frac{12}{23}\left(\frac{1}{3}+\frac{1}{\frac{1+1}{7}}\right)$$

Add 1 and 1 to get 2.

$$\frac{4}{3}+\frac{12}{23}\left(\frac{1}{3}+\frac{1}{\frac{2}{7}}\right)$$

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

$$\frac{4}{3}+\frac{12}{23}\left(\frac{1}{3}+1\times \frac{7}{2}\right)$$

Multiply 1 and \frac{7}{2} to get \frac{7}{2}.

$$\frac{4}{3}+\frac{12}{23}\left(\frac{1}{3}+\frac{7}{2}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{7}{2} to fractions with denominator 6.

$$\frac{4}{3}+\frac{12}{23}\left(\frac{2}{6}+\frac{21}{6}\right)$$

Since \frac{2}{6} and \frac{21}{6} have the same denominator, add them by adding their numerators.

$$\frac{4}{3}+\frac{12}{23}\times \frac{2+21}{6}$$

Add 2 and 21 to get 23.

$$\frac{4}{3}+\frac{12}{23}\times \frac{23}{6}$$

Multiply \frac{12}{23} times \frac{23}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{3}+\frac{12\times 23}{23\times 6}$$

Cancel out 23 in both numerator and denominator.

$$\frac{4}{3}+\frac{12}{6}$$

Divide 12 by 6 to get 2.

$$\frac{4}{3}+2$$

Convert 2 to fraction \frac{6}{3}.

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

Since \frac{4}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

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

Add 4 and 6 to get 10.

$$\frac{10}{3}$$

Factor

$$\frac{2 \cdot 5}{3} = 3\frac{1}{3} = 3.3333333333333335$$