Solve (3/8-5/4)+2/7div5/4

$$( \frac { 3 } { 8 } - \frac { 5 } { 4 } ) + \frac { 2 } { 7 } \div \frac { 5 } { 4 }$$

Evaluate

$$-\frac{181}{280}\approx -0.646428571$$

Solution Steps

Least common multiple of 8 and 4 is 8. Convert \frac{3}{8} and \frac{5}{4} to fractions with denominator 8.

$$\frac{3}{8}-\frac{10}{8}+\frac{\frac{2}{7}}{\frac{5}{4}}$$

Since \frac{3}{8} and \frac{10}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-10}{8}+\frac{\frac{2}{7}}{\frac{5}{4}}$$

Subtract 10 from 3 to get -7.

$$-\frac{7}{8}+\frac{\frac{2}{7}}{\frac{5}{4}}$$

Divide \frac{2}{7} by \frac{5}{4} by multiplying \frac{2}{7} by the reciprocal of \frac{5}{4}.

$$-\frac{7}{8}+\frac{2}{7}\times \frac{4}{5}$$

Multiply \frac{2}{7} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{7}{8}+\frac{2\times 4}{7\times 5}$$

Do the multiplications in the fraction \frac{2\times 4}{7\times 5}.

$$-\frac{7}{8}+\frac{8}{35}$$

Least common multiple of 8 and 35 is 280. Convert -\frac{7}{8} and \frac{8}{35} to fractions with denominator 280.

$$-\frac{245}{280}+\frac{64}{280}$$

Since -\frac{245}{280} and \frac{64}{280} have the same denominator, add them by adding their numerators.

$$\frac{-245+64}{280}$$

Add -245 and 64 to get -181.

$$-\frac{181}{280}$$

Factor

$$-\frac{181}{280} = -0.6464285714285715$$