Solve (7/9+5/6-1/4)*2

$$( \frac { 7 } { 9 } + \frac { 5 } { 6 } - \frac { 1 } { 4 } ) \times 2$$

Evaluate

$$\frac{49}{18}\approx 2.722222222$$

Solution Steps

Least common multiple of 9 and 6 is 18. Convert \frac{7}{9} and \frac{5}{6} to fractions with denominator 18.

$$\left(\frac{14}{18}+\frac{15}{18}-\frac{1}{4}\right)\times 2$$

Since \frac{14}{18} and \frac{15}{18} have the same denominator, add them by adding their numerators.

$$\left(\frac{14+15}{18}-\frac{1}{4}\right)\times 2$$

Add 14 and 15 to get 29.

$$\left(\frac{29}{18}-\frac{1}{4}\right)\times 2$$

Least common multiple of 18 and 4 is 36. Convert \frac{29}{18} and \frac{1}{4} to fractions with denominator 36.

$$\left(\frac{58}{36}-\frac{9}{36}\right)\times 2$$

Since \frac{58}{36} and \frac{9}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{58-9}{36}\times 2$$

Subtract 9 from 58 to get 49.

$$\frac{49}{36}\times 2$$

Express \frac{49}{36}\times 2 as a single fraction.

$$\frac{49\times 2}{36}$$

Multiply 49 and 2 to get 98.

$$\frac{98}{36}$$

Reduce the fraction \frac{98}{36} to lowest terms by extracting and canceling out 2.

$$\frac{49}{18}$$

Factor

$$\frac{7 ^ {2}}{2 \cdot 3 ^ {2}} = 2\frac{13}{18} = 2.7222222222222223$$