Solve -(2/3+7/5)-(-5/2-1/4)div2frac{3}{5}

$$-( \frac{ 2 }{ 3 } + \frac{ 7 }{ 5 } )-(- \frac{ 5 }{ 2 } - \frac{ 1 }{ 4 } ) \div 2 \frac{ 3 }{ 5 }$$

Evaluate

$$-\frac{787}{780}\approx -1.008974359$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{7}{5} to fractions with denominator 15.

$$-\left(\frac{10}{15}+\frac{21}{15}\right)-\frac{-\frac{5}{2}-\frac{1}{4}}{\frac{2\times 5+3}{5}}$$

Since \frac{10}{15} and \frac{21}{15} have the same denominator, add them by adding their numerators.

$$-\frac{10+21}{15}-\frac{-\frac{5}{2}-\frac{1}{4}}{\frac{2\times 5+3}{5}}$$

Add 10 and 21 to get 31.

$$-\frac{31}{15}-\frac{-\frac{5}{2}-\frac{1}{4}}{\frac{2\times 5+3}{5}}$$

Least common multiple of 2 and 4 is 4. Convert -\frac{5}{2} and \frac{1}{4} to fractions with denominator 4.

$$-\frac{31}{15}-\frac{-\frac{10}{4}-\frac{1}{4}}{\frac{2\times 5+3}{5}}$$

Since -\frac{10}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{31}{15}-\frac{\frac{-10-1}{4}}{\frac{2\times 5+3}{5}}$$

Subtract 1 from -10 to get -11.

$$-\frac{31}{15}-\frac{-\frac{11}{4}}{\frac{2\times 5+3}{5}}$$

Multiply 2 and 5 to get 10.

$$-\frac{31}{15}-\frac{-\frac{11}{4}}{\frac{10+3}{5}}$$

Add 10 and 3 to get 13.

$$-\frac{31}{15}-\frac{-\frac{11}{4}}{\frac{13}{5}}$$

Divide -\frac{11}{4} by \frac{13}{5} by multiplying -\frac{11}{4} by the reciprocal of \frac{13}{5}.

$$-\frac{31}{15}-\left(-\frac{11}{4}\times \frac{5}{13}\right)$$

Multiply -\frac{11}{4} times \frac{5}{13} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{31}{15}-\frac{-11\times 5}{4\times 13}$$

Do the multiplications in the fraction \frac{-11\times 5}{4\times 13}.

$$-\frac{31}{15}-\frac{-55}{52}$$

Fraction \frac{-55}{52} can be rewritten as -\frac{55}{52} by extracting the negative sign.

$$-\frac{31}{15}-\left(-\frac{55}{52}\right)$$

The opposite of -\frac{55}{52} is \frac{55}{52}.

$$-\frac{31}{15}+\frac{55}{52}$$

Least common multiple of 15 and 52 is 780. Convert -\frac{31}{15} and \frac{55}{52} to fractions with denominator 780.

$$-\frac{1612}{780}+\frac{825}{780}$$

Since -\frac{1612}{780} and \frac{825}{780} have the same denominator, add them by adding their numerators.

$$\frac{-1612+825}{780}$$

Add -1612 and 825 to get -787.

$$-\frac{787}{780}$$

Factor

$$-\frac{787}{780} = -1\frac{7}{780} = -1.008974358974359$$