Solve (1+2/5):(3/7-1)/3:frac{6{5}}=

$$\frac { ( 1 + \frac { 2 } { 5 } ) : ( \frac { 3 } { 7 } - 1 ) } { 3 : \frac { 6 } { 5 } } =$$

Evaluate

$$-\frac{49}{50}=-0.98$$

Solution Steps

Divide \frac{1+\frac{2}{5}}{\frac{3}{7}-1} by \frac{3}{\frac{6}{5}} by multiplying \frac{1+\frac{2}{5}}{\frac{3}{7}-1} by the reciprocal of \frac{3}{\frac{6}{5}}.

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

Convert 1 to fraction \frac{5}{5}.

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

Since \frac{5}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

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

Add 5 and 2 to get 7.

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

Multiply \frac{7}{5} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{7\times 6}{5\times 5}.

$$\frac{\frac{42}{25}}{\left(\frac{3}{7}-1\right)\times 3}$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{\frac{42}{25}}{\left(\frac{3}{7}-\frac{7}{7}\right)\times 3}$$

Since \frac{3}{7} and \frac{7}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{42}{25}}{\frac{3-7}{7}\times 3}$$

Subtract 7 from 3 to get -4.

$$\frac{\frac{42}{25}}{-\frac{4}{7}\times 3}$$

Express -\frac{4}{7}\times 3 as a single fraction.

$$\frac{\frac{42}{25}}{\frac{-4\times 3}{7}}$$

Multiply -4 and 3 to get -12.

$$\frac{\frac{42}{25}}{\frac{-12}{7}}$$

Fraction \frac{-12}{7} can be rewritten as -\frac{12}{7} by extracting the negative sign.

$$\frac{\frac{42}{25}}{-\frac{12}{7}}$$

Divide \frac{42}{25} by -\frac{12}{7} by multiplying \frac{42}{25} by the reciprocal of -\frac{12}{7}.

$$\frac{42}{25}\left(-\frac{7}{12}\right)$$

Multiply \frac{42}{25} times -\frac{7}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{42\left(-7\right)}{25\times 12}$$

Do the multiplications in the fraction \frac{42\left(-7\right)}{25\times 12}.

$$\frac{-294}{300}$$

Reduce the fraction \frac{-294}{300} to lowest terms by extracting and canceling out 6.

$$-\frac{49}{50}$$

Factor

$$-\frac{49}{50} = -0.98$$