Solve (2/7-4/5+2/8)*3/2-frac{7}{5}:frac{4}{7}=

$$( \frac { 2 } { 7 } - \frac { 4 } { 5 } + \frac { 2 } { 8 } ) \cdot \frac { 3 } { 2 } - \frac { 7 } { 5 } : \frac { 4 } { 7 } =$$

Evaluate

$$-\frac{797}{280}\approx -2.846428571$$

Solution Steps

Least common multiple of 7 and 5 is 35. Convert \frac{2}{7} and \frac{4}{5} to fractions with denominator 35.

$$\left(\frac{10}{35}-\frac{28}{35}+\frac{2}{8}\right)\times \frac{3}{2}-\frac{\frac{7}{5}}{\frac{4}{7}}$$

Since \frac{10}{35} and \frac{28}{35} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{10-28}{35}+\frac{2}{8}\right)\times \frac{3}{2}-\frac{\frac{7}{5}}{\frac{4}{7}}$$

Subtract 28 from 10 to get -18.

$$\left(-\frac{18}{35}+\frac{2}{8}\right)\times \frac{3}{2}-\frac{\frac{7}{5}}{\frac{4}{7}}$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\left(-\frac{18}{35}+\frac{1}{4}\right)\times \frac{3}{2}-\frac{\frac{7}{5}}{\frac{4}{7}}$$

Least common multiple of 35 and 4 is 140. Convert -\frac{18}{35} and \frac{1}{4} to fractions with denominator 140.

$$\left(-\frac{72}{140}+\frac{35}{140}\right)\times \frac{3}{2}-\frac{\frac{7}{5}}{\frac{4}{7}}$$

Since -\frac{72}{140} and \frac{35}{140} have the same denominator, add them by adding their numerators.

$$\frac{-72+35}{140}\times \frac{3}{2}-\frac{\frac{7}{5}}{\frac{4}{7}}$$

Add -72 and 35 to get -37.

$$-\frac{37}{140}\times \frac{3}{2}-\frac{\frac{7}{5}}{\frac{4}{7}}$$

Multiply -\frac{37}{140} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-37\times 3}{140\times 2}-\frac{\frac{7}{5}}{\frac{4}{7}}$$

Do the multiplications in the fraction \frac{-37\times 3}{140\times 2}.

$$\frac{-111}{280}-\frac{\frac{7}{5}}{\frac{4}{7}}$$

Fraction \frac{-111}{280} can be rewritten as -\frac{111}{280} by extracting the negative sign.

$$-\frac{111}{280}-\frac{\frac{7}{5}}{\frac{4}{7}}$$

Divide \frac{7}{5} by \frac{4}{7} by multiplying \frac{7}{5} by the reciprocal of \frac{4}{7}.

$$-\frac{111}{280}-\frac{7}{5}\times \frac{7}{4}$$

Multiply \frac{7}{5} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{111}{280}-\frac{7\times 7}{5\times 4}$$

Do the multiplications in the fraction \frac{7\times 7}{5\times 4}.

$$-\frac{111}{280}-\frac{49}{20}$$

Least common multiple of 280 and 20 is 280. Convert -\frac{111}{280} and \frac{49}{20} to fractions with denominator 280.

$$-\frac{111}{280}-\frac{686}{280}$$

Since -\frac{111}{280} and \frac{686}{280} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-111-686}{280}$$

Subtract 686 from -111 to get -797.

$$-\frac{797}{280}$$

Factor

$$-\frac{797}{280} = -2\frac{237}{280} = -2.8464285714285715$$