Solve 2(2/3+5/18)+-7/12

$$2 ( \frac { 2 } { 3 } + \frac { 5 } { 18 } ) + \frac { - 7 } { 12 }$$

Evaluate

$$\frac{47}{36}\approx 1.305555556$$

Solution Steps

Least common multiple of 3 and 18 is 18. Convert \frac{2}{3} and \frac{5}{18} to fractions with denominator 18.

$$2\left(\frac{12}{18}+\frac{5}{18}\right)+\frac{-7}{12}$$

Since \frac{12}{18} and \frac{5}{18} have the same denominator, add them by adding their numerators.

$$2\times \frac{12+5}{18}+\frac{-7}{12}$$

Add 12 and 5 to get 17.

$$2\times \frac{17}{18}+\frac{-7}{12}$$

Express 2\times \frac{17}{18} as a single fraction.

$$\frac{2\times 17}{18}+\frac{-7}{12}$$

Multiply 2 and 17 to get 34.

$$\frac{34}{18}+\frac{-7}{12}$$

Reduce the fraction \frac{34}{18} to lowest terms by extracting and canceling out 2.

$$\frac{17}{9}+\frac{-7}{12}$$

Fraction \frac{-7}{12} can be rewritten as -\frac{7}{12} by extracting the negative sign.

$$\frac{17}{9}-\frac{7}{12}$$

Least common multiple of 9 and 12 is 36. Convert \frac{17}{9} and \frac{7}{12} to fractions with denominator 36.

$$\frac{68}{36}-\frac{21}{36}$$

Since \frac{68}{36} and \frac{21}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{68-21}{36}$$

Subtract 21 from 68 to get 47.

$$\frac{47}{36}$$

Factor

$$\frac{47}{2 ^ {2} \cdot 3 ^ {2}} = 1\frac{11}{36} = 1.3055555555555556$$