Solve (-13/10-24/5):(13/4-35/6)

$$( - 1 \frac { 3 } { 10 } - 2 \frac { 4 } { 5 } ) : ( 1 \frac { 3 } { 4 } - 3 \frac { 5 } { 6 } )$$

Evaluate

$$\frac{246}{125}=1.968$$

Solution Steps

Multiply 1 and 10 to get 10.

$$\frac{-\frac{10+3}{10}-\frac{2\times 5+4}{5}}{\frac{1\times 4+3}{4}-\frac{3\times 6+5}{6}}$$

Add 10 and 3 to get 13.

$$\frac{-\frac{13}{10}-\frac{2\times 5+4}{5}}{\frac{1\times 4+3}{4}-\frac{3\times 6+5}{6}}$$

Multiply 2 and 5 to get 10.

$$\frac{-\frac{13}{10}-\frac{10+4}{5}}{\frac{1\times 4+3}{4}-\frac{3\times 6+5}{6}}$$

Add 10 and 4 to get 14.

$$\frac{-\frac{13}{10}-\frac{14}{5}}{\frac{1\times 4+3}{4}-\frac{3\times 6+5}{6}}$$

Least common multiple of 10 and 5 is 10. Convert -\frac{13}{10} and \frac{14}{5} to fractions with denominator 10.

$$\frac{-\frac{13}{10}-\frac{28}{10}}{\frac{1\times 4+3}{4}-\frac{3\times 6+5}{6}}$$

Since -\frac{13}{10} and \frac{28}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-13-28}{10}}{\frac{1\times 4+3}{4}-\frac{3\times 6+5}{6}}$$

Subtract 28 from -13 to get -41.

$$\frac{-\frac{41}{10}}{\frac{1\times 4+3}{4}-\frac{3\times 6+5}{6}}$$

Multiply 1 and 4 to get 4.

$$\frac{-\frac{41}{10}}{\frac{4+3}{4}-\frac{3\times 6+5}{6}}$$

Add 4 and 3 to get 7.

$$\frac{-\frac{41}{10}}{\frac{7}{4}-\frac{3\times 6+5}{6}}$$

Multiply 3 and 6 to get 18.

$$\frac{-\frac{41}{10}}{\frac{7}{4}-\frac{18+5}{6}}$$

Add 18 and 5 to get 23.

$$\frac{-\frac{41}{10}}{\frac{7}{4}-\frac{23}{6}}$$

Least common multiple of 4 and 6 is 12. Convert \frac{7}{4} and \frac{23}{6} to fractions with denominator 12.

$$\frac{-\frac{41}{10}}{\frac{21}{12}-\frac{46}{12}}$$

Since \frac{21}{12} and \frac{46}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{41}{10}}{\frac{21-46}{12}}$$

Subtract 46 from 21 to get -25.

$$\frac{-\frac{41}{10}}{-\frac{25}{12}}$$

Divide -\frac{41}{10} by -\frac{25}{12} by multiplying -\frac{41}{10} by the reciprocal of -\frac{25}{12}.

$$-\frac{41}{10}\left(-\frac{12}{25}\right)$$

Multiply -\frac{41}{10} times -\frac{12}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-41\left(-12\right)}{10\times 25}$$

Do the multiplications in the fraction \frac{-41\left(-12\right)}{10\times 25}.

$$\frac{492}{250}$$

Reduce the fraction \frac{492}{250} to lowest terms by extracting and canceling out 2.

$$\frac{246}{125}$$

Factor

$$\frac{2 \cdot 3 \cdot 41}{5 ^ {3}} = 1\frac{121}{125} = 1.968$$