Solve 1/2+(51/6-33/4+1/2)*frac{10}{23}=

$$\frac { 1 } { 2 } + ( 5 \frac { 1 } { 6 } - 3 \frac { 3 } { 4 } + \frac { 1 } { 2 } ) \cdot \frac { 10 } { 23 } =$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

Multiply 5 and 6 to get 30.

$$\frac{1}{2}+\left(\frac{30+1}{6}-\frac{3\times 4+3}{4}+\frac{1}{2}\right)\times \frac{10}{23}$$

Add 30 and 1 to get 31.

$$\frac{1}{2}+\left(\frac{31}{6}-\frac{3\times 4+3}{4}+\frac{1}{2}\right)\times \frac{10}{23}$$

Multiply 3 and 4 to get 12.

$$\frac{1}{2}+\left(\frac{31}{6}-\frac{12+3}{4}+\frac{1}{2}\right)\times \frac{10}{23}$$

Add 12 and 3 to get 15.

$$\frac{1}{2}+\left(\frac{31}{6}-\frac{15}{4}+\frac{1}{2}\right)\times \frac{10}{23}$$

Least common multiple of 6 and 4 is 12. Convert \frac{31}{6} and \frac{15}{4} to fractions with denominator 12.

$$\frac{1}{2}+\left(\frac{62}{12}-\frac{45}{12}+\frac{1}{2}\right)\times \frac{10}{23}$$

Since \frac{62}{12} and \frac{45}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}+\left(\frac{62-45}{12}+\frac{1}{2}\right)\times \frac{10}{23}$$

Subtract 45 from 62 to get 17.

$$\frac{1}{2}+\left(\frac{17}{12}+\frac{1}{2}\right)\times \frac{10}{23}$$

Least common multiple of 12 and 2 is 12. Convert \frac{17}{12} and \frac{1}{2} to fractions with denominator 12.

$$\frac{1}{2}+\left(\frac{17}{12}+\frac{6}{12}\right)\times \frac{10}{23}$$

Since \frac{17}{12} and \frac{6}{12} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}+\frac{17+6}{12}\times \frac{10}{23}$$

Add 17 and 6 to get 23.

$$\frac{1}{2}+\frac{23}{12}\times \frac{10}{23}$$

Multiply \frac{23}{12} times \frac{10}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{23\times 10}{12\times 23}$$

Cancel out 23 in both numerator and denominator.

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

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

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

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{5}{6} to fractions with denominator 6.

$$\frac{3}{6}+\frac{5}{6}$$

Since \frac{3}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+5}{6}$$

Add 3 and 5 to get 8.

$$\frac{8}{6}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$