Solve (-2/3)^1-(-13/4)-(-2/3)+1.75

$$( - \frac { 2 } { 3 } ) ^ { 1 } - ( - 1 \frac { 3 } { 4 } ) - ( - \frac { 2 } { 3 } ) + 1.75$$

Evaluate

$$3.5$$

Solution Steps

Calculate -\frac{2}{3} to the power of 1 and get -\frac{2}{3}.

$$-\frac{2}{3}-\left(-\frac{1\times 4+3}{4}\right)-\left(-\frac{2}{3}\right)+1.75$$

Multiply 1 and 4 to get 4.

$$-\frac{2}{3}-\left(-\frac{4+3}{4}\right)-\left(-\frac{2}{3}\right)+1.75$$

Add 4 and 3 to get 7.

$$-\frac{2}{3}-\left(-\frac{7}{4}\right)-\left(-\frac{2}{3}\right)+1.75$$

The opposite of -\frac{7}{4} is \frac{7}{4}.

$$-\frac{2}{3}+\frac{7}{4}-\left(-\frac{2}{3}\right)+1.75$$

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

$$-\frac{8}{12}+\frac{21}{12}-\left(-\frac{2}{3}\right)+1.75$$

Since -\frac{8}{12} and \frac{21}{12} have the same denominator, add them by adding their numerators.

$$\frac{-8+21}{12}-\left(-\frac{2}{3}\right)+1.75$$

Add -8 and 21 to get 13.

$$\frac{13}{12}-\left(-\frac{2}{3}\right)+1.75$$

The opposite of -\frac{2}{3} is \frac{2}{3}.

$$\frac{13}{12}+\frac{2}{3}+1.75$$

Least common multiple of 12 and 3 is 12. Convert \frac{13}{12} and \frac{2}{3} to fractions with denominator 12.

$$\frac{13}{12}+\frac{8}{12}+1.75$$

Since \frac{13}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{13+8}{12}+1.75$$

Add 13 and 8 to get 21.

$$\frac{21}{12}+1.75$$

Reduce the fraction \frac{21}{12} to lowest terms by extracting and canceling out 3.

$$\frac{7}{4}+1.75$$

Convert decimal number 1.75 to fraction \frac{175}{100}. Reduce the fraction \frac{175}{100} to lowest terms by extracting and canceling out 25.

$$\frac{7}{4}+\frac{7}{4}$$

Since \frac{7}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

$$\frac{7+7}{4}$$

Add 7 and 7 to get 14.

$$\frac{14}{4}$$

Reduce the fraction \frac{14}{4} to lowest terms by extracting and canceling out 2.

$$\frac{7}{2}$$

Factor

$$\frac{7}{2} = 3\frac{1}{2} = 3.5$$