Solve 160/19-(2(-7/19)/3

$$\frac { 160 } { 19 } - \frac { ( 2 ( - \frac { 7 } { 19 } ) } { 3 }$$

Evaluate

$$\frac{26}{3}\approx 8.666666667$$

Solution Steps

Express 2\left(-\frac{7}{19}\right) as a single fraction.

$$\frac{160}{19}-\frac{\frac{2\left(-7\right)}{19}}{3}$$

Multiply 2 and -7 to get -14.

$$\frac{160}{19}-\frac{\frac{-14}{19}}{3}$$

Fraction \frac{-14}{19} can be rewritten as -\frac{14}{19} by extracting the negative sign.

$$\frac{160}{19}-\frac{-\frac{14}{19}}{3}$$

Express \frac{-\frac{14}{19}}{3} as a single fraction.

$$\frac{160}{19}-\frac{-14}{19\times 3}$$

Multiply 19 and 3 to get 57.

$$\frac{160}{19}-\frac{-14}{57}$$

Fraction \frac{-14}{57} can be rewritten as -\frac{14}{57} by extracting the negative sign.

$$\frac{160}{19}-\left(-\frac{14}{57}\right)$$

The opposite of -\frac{14}{57} is \frac{14}{57}.

$$\frac{160}{19}+\frac{14}{57}$$

Least common multiple of 19 and 57 is 57. Convert \frac{160}{19} and \frac{14}{57} to fractions with denominator 57.

$$\frac{480}{57}+\frac{14}{57}$$

Since \frac{480}{57} and \frac{14}{57} have the same denominator, add them by adding their numerators.

$$\frac{480+14}{57}$$

Add 480 and 14 to get 494.

$$\frac{494}{57}$$

Reduce the fraction \frac{494}{57} to lowest terms by extracting and canceling out 19.

$$\frac{26}{3}$$

Factor

$$\frac{2 \cdot 13}{3} = 8\frac{2}{3} = 8.666666666666666$$