Solve -2/9+(2/9+2/3)-7/4+frac{7}{4}

$$- \frac { 2 } { 9 } + ( \frac { 2 } { 9 } + \frac { 2 } { 3 } ) - \frac { 7 } { 4 } + \frac { 7 } { 4 }$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Add -\frac{2}{9} and \frac{2}{9} to get 0.

$$\frac{2}{3}-\frac{7}{4}+\frac{7}{4}$$

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{7}{4} to fractions with denominator 12.

$$\frac{8}{12}-\frac{21}{12}+\frac{7}{4}$$

Since \frac{8}{12} and \frac{21}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-21}{12}+\frac{7}{4}$$

Subtract 21 from 8 to get -13.

$$-\frac{13}{12}+\frac{7}{4}$$

Least common multiple of 12 and 4 is 12. Convert -\frac{13}{12} and \frac{7}{4} to fractions with denominator 12.

$$-\frac{13}{12}+\frac{21}{12}$$

Since -\frac{13}{12} and \frac{21}{12} have the same denominator, add them by adding their numerators.

$$\frac{-13+21}{12}$$

Add -13 and 21 to get 8.

$$\frac{8}{12}$$

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$