Solve (-9/4x2/27)+(7/10div49/30)

$$( \frac { - 9 } { 4 } x \frac { 2 } { 27 } ) + ( \frac { 7 } { 10 } \div \frac { 49 } { 30 } )$$

Evaluate

$$-\frac{x}{6}+\frac{3}{7}$$

Solution Steps

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$-\frac{9}{4}x\times \frac{2}{27}+\frac{\frac{7}{10}}{\frac{49}{30}}$$

Multiply -\frac{9}{4} times \frac{2}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-9\times 2}{4\times 27}x+\frac{\frac{7}{10}}{\frac{49}{30}}$$

Do the multiplications in the fraction \frac{-9\times 2}{4\times 27}.

$$\frac{-18}{108}x+\frac{\frac{7}{10}}{\frac{49}{30}}$$

Reduce the fraction \frac{-18}{108} to lowest terms by extracting and canceling out 18.

$$-\frac{1}{6}x+\frac{\frac{7}{10}}{\frac{49}{30}}$$

Divide \frac{7}{10} by \frac{49}{30} by multiplying \frac{7}{10} by the reciprocal of \frac{49}{30}.

$$-\frac{1}{6}x+\frac{7}{10}\times \frac{30}{49}$$

Multiply \frac{7}{10} times \frac{30}{49} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{6}x+\frac{7\times 30}{10\times 49}$$

Do the multiplications in the fraction \frac{7\times 30}{10\times 49}.

$$-\frac{1}{6}x+\frac{210}{490}$$

Reduce the fraction \frac{210}{490} to lowest terms by extracting and canceling out 70.

$$-\frac{1}{6}x+\frac{3}{7}$$

Factor

$$\frac{18-7x}{42}$$

Solution Steps

Factor out \frac{1}{42}.

$$\frac{-7x+18}{42}$$