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

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

Evaluate

$$-\frac{6x}{35}-\frac{31}{140}$$

Solution Steps

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

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

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

$$\frac{-6}{35}x-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$$

Fraction \frac{-6}{35} can be rewritten as -\frac{6}{35} by extracting the negative sign.

$$-\frac{6}{35}x-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$$

Multiply \frac{1}{6} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{6}{35}x-\frac{1\times 3}{6\times 2}+\frac{1}{14}\times \frac{2}{5}$$

Do the multiplications in the fraction \frac{1\times 3}{6\times 2}.

$$-\frac{6}{35}x-\frac{3}{12}+\frac{1}{14}\times \frac{2}{5}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$-\frac{6}{35}x-\frac{1}{4}+\frac{1}{14}\times \frac{2}{5}$$

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

$$-\frac{6}{35}x-\frac{1}{4}+\frac{1\times 2}{14\times 5}$$

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

$$-\frac{6}{35}x-\frac{1}{4}+\frac{2}{70}$$

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

$$-\frac{6}{35}x-\frac{1}{4}+\frac{1}{35}$$

Least common multiple of 4 and 35 is 140. Convert -\frac{1}{4} and \frac{1}{35} to fractions with denominator 140.

$$-\frac{6}{35}x-\frac{35}{140}+\frac{4}{140}$$

Since -\frac{35}{140} and \frac{4}{140} have the same denominator, add them by adding their numerators.

$$-\frac{6}{35}x+\frac{-35+4}{140}$$

Add -35 and 4 to get -31.

$$-\frac{6}{35}x-\frac{31}{140}$$

Factor

$$\frac{-24x-31}{140}$$

Solution Steps

Factor out \frac{1}{140}.

$$\frac{-24x-31}{140}$$

Consider -24x-35+4. Multiply and combine like terms.

$$-24x-31$$

Rewrite the complete factored expression.

$$\frac{-24x-31}{140}$$