Solve (5/3)(2/5)-(1/30)/frac{7{3}}-frac{13}{4}

$$\frac { ( \frac { 5 } { 3 } ) ( \frac { 2 } { 5 } ) - ( \frac { 1 } { 30 } ) } { \frac { 7 } { 3 } } - \frac { 13 } { 4 }$$

Evaluate

$$-\frac{417}{140}\approx -2.978571429$$

Solution Steps

Multiply \frac{5}{3} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5\times 2}{3\times 5}-\frac{1}{30}}{\frac{7}{3}}-\frac{13}{4}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\frac{2}{3}-\frac{1}{30}}{\frac{7}{3}}-\frac{13}{4}$$

Least common multiple of 3 and 30 is 30. Convert \frac{2}{3} and \frac{1}{30} to fractions with denominator 30.

$$\frac{\frac{20}{30}-\frac{1}{30}}{\frac{7}{3}}-\frac{13}{4}$$

Since \frac{20}{30} and \frac{1}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{20-1}{30}}{\frac{7}{3}}-\frac{13}{4}$$

Subtract 1 from 20 to get 19.

$$\frac{\frac{19}{30}}{\frac{7}{3}}-\frac{13}{4}$$

Divide \frac{19}{30} by \frac{7}{3} by multiplying \frac{19}{30} by the reciprocal of \frac{7}{3}.

$$\frac{19}{30}\times \frac{3}{7}-\frac{13}{4}$$

Multiply \frac{19}{30} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19\times 3}{30\times 7}-\frac{13}{4}$$

Do the multiplications in the fraction \frac{19\times 3}{30\times 7}.

$$\frac{57}{210}-\frac{13}{4}$$

Reduce the fraction \frac{57}{210} to lowest terms by extracting and canceling out 3.

$$\frac{19}{70}-\frac{13}{4}$$

Least common multiple of 70 and 4 is 140. Convert \frac{19}{70} and \frac{13}{4} to fractions with denominator 140.

$$\frac{38}{140}-\frac{455}{140}$$

Since \frac{38}{140} and \frac{455}{140} have the same denominator, subtract them by subtracting their numerators.

$$\frac{38-455}{140}$$

Subtract 455 from 38 to get -417.

$$-\frac{417}{140}$$

Factor

$$-\frac{417}{140} = -2\frac{137}{140} = -2.9785714285714286$$