Solve -2/5*(7/3)-1/6*5/2+frac{1}{14}*frac{2}{5}

$$- \frac { 2 } { 5 } \times ( \frac { 7 } { 3 } ) - \frac { 1 } { 6 } \times \frac { 5 } { 2 } + \frac { 1 } { 14 } \times \frac { 2 } { 5 }$$

Evaluate

$$-\frac{37}{28}\approx -1.321428571$$

Solution Steps

Multiply -\frac{2}{5} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\times 7}{5\times 3}-\frac{1}{6}\times \frac{5}{2}+\frac{1}{14}\times \frac{2}{5}$$

Do the multiplications in the fraction \frac{-2\times 7}{5\times 3}.

$$\frac{-14}{15}-\frac{1}{6}\times \frac{5}{2}+\frac{1}{14}\times \frac{2}{5}$$

Fraction \frac{-14}{15} can be rewritten as -\frac{14}{15} by extracting the negative sign.

$$-\frac{14}{15}-\frac{1}{6}\times \frac{5}{2}+\frac{1}{14}\times \frac{2}{5}$$

Multiply \frac{1}{6} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{14}{15}-\frac{1\times 5}{6\times 2}+\frac{1}{14}\times \frac{2}{5}$$

Do the multiplications in the fraction \frac{1\times 5}{6\times 2}.

$$-\frac{14}{15}-\frac{5}{12}+\frac{1}{14}\times \frac{2}{5}$$

Least common multiple of 15 and 12 is 60. Convert -\frac{14}{15} and \frac{5}{12} to fractions with denominator 60.

$$-\frac{56}{60}-\frac{25}{60}+\frac{1}{14}\times \frac{2}{5}$$

Since -\frac{56}{60} and \frac{25}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-56-25}{60}+\frac{1}{14}\times \frac{2}{5}$$

Subtract 25 from -56 to get -81.

$$\frac{-81}{60}+\frac{1}{14}\times \frac{2}{5}$$

Reduce the fraction \frac{-81}{60} to lowest terms by extracting and canceling out 3.

$$-\frac{27}{20}+\frac{1}{14}\times \frac{2}{5}$$

Multiply \frac{1}{14} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{27}{20}+\frac{1\times 2}{14\times 5}$$

Do the multiplications in the fraction \frac{1\times 2}{14\times 5}.

$$-\frac{27}{20}+\frac{2}{70}$$

Reduce the fraction \frac{2}{70} to lowest terms by extracting and canceling out 2.

$$-\frac{27}{20}+\frac{1}{35}$$

Least common multiple of 20 and 35 is 140. Convert -\frac{27}{20} and \frac{1}{35} to fractions with denominator 140.

$$-\frac{189}{140}+\frac{4}{140}$$

Since -\frac{189}{140} and \frac{4}{140} have the same denominator, add them by adding their numerators.

$$\frac{-189+4}{140}$$

Add -189 and 4 to get -185.

$$\frac{-185}{140}$$

Reduce the fraction \frac{-185}{140} to lowest terms by extracting and canceling out 5.

$$-\frac{37}{28}$$

Factor

$$-\frac{37}{28} = -1\frac{9}{28} = -1.3214285714285714$$