Solve (-2/3)^2+2/7/frac{-4{7}}-3(7/5)+frac{5}{4}=

$$( - \frac { 2 } { 3 } ) ^ { 2 } + \frac { \frac { 2 } { 7 } } { \frac { - 4 } { 7 } } - 3 ( \frac { 7 } { 5 } ) + \frac { 5 } { 4 } =$$

Evaluate

$$-\frac{541}{180}\approx -3.005555556$$

Solution Steps

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{4}{9}+\frac{\frac{2}{7}}{\frac{-4}{7}}-3\times \frac{7}{5}+\frac{5}{4}$$

Divide \frac{2}{7} by \frac{-4}{7} by multiplying \frac{2}{7} by the reciprocal of \frac{-4}{7}.

$$\frac{4}{9}+\frac{2\times 7}{7\left(-4\right)}-3\times \frac{7}{5}+\frac{5}{4}$$

Cancel out 2\times 7 in both numerator and denominator.

$$\frac{4}{9}+\frac{1}{-2}-3\times \frac{7}{5}+\frac{5}{4}$$

Fraction \frac{1}{-2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\frac{4}{9}-\frac{1}{2}-3\times \frac{7}{5}+\frac{5}{4}$$

Least common multiple of 9 and 2 is 18. Convert \frac{4}{9} and \frac{1}{2} to fractions with denominator 18.

$$\frac{8}{18}-\frac{9}{18}-3\times \frac{7}{5}+\frac{5}{4}$$

Since \frac{8}{18} and \frac{9}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-9}{18}-3\times \frac{7}{5}+\frac{5}{4}$$

Subtract 9 from 8 to get -1.

$$-\frac{1}{18}-3\times \frac{7}{5}+\frac{5}{4}$$

Express 3\times \frac{7}{5} as a single fraction.

$$-\frac{1}{18}-\frac{3\times 7}{5}+\frac{5}{4}$$

Multiply 3 and 7 to get 21.

$$-\frac{1}{18}-\frac{21}{5}+\frac{5}{4}$$

Least common multiple of 18 and 5 is 90. Convert -\frac{1}{18} and \frac{21}{5} to fractions with denominator 90.

$$-\frac{5}{90}-\frac{378}{90}+\frac{5}{4}$$

Since -\frac{5}{90} and \frac{378}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-378}{90}+\frac{5}{4}$$

Subtract 378 from -5 to get -383.

$$-\frac{383}{90}+\frac{5}{4}$$

Least common multiple of 90 and 4 is 180. Convert -\frac{383}{90} and \frac{5}{4} to fractions with denominator 180.

$$-\frac{766}{180}+\frac{225}{180}$$

Since -\frac{766}{180} and \frac{225}{180} have the same denominator, add them by adding their numerators.

$$\frac{-766+225}{180}$$

Add -766 and 225 to get -541.

$$-\frac{541}{180}$$

Factor

$$-\frac{541}{180} = -3\frac{1}{180} = -3.0055555555555555$$