Solve 5/6--3/2--4/7=

$$\frac { 5 } { 6 } - \frac { - 3 } { 2 } - \frac { - 4 } { 7 } =$$

Evaluate

$$\frac{61}{21}\approx 2.904761905$$

Solution Steps

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$\frac{5}{6}-\left(-\frac{3}{2}\right)-\frac{-4}{7}$$

The opposite of -\frac{3}{2} is \frac{3}{2}.

$$\frac{5}{6}+\frac{3}{2}-\frac{-4}{7}$$

Least common multiple of 6 and 2 is 6. Convert \frac{5}{6} and \frac{3}{2} to fractions with denominator 6.

$$\frac{5}{6}+\frac{9}{6}-\frac{-4}{7}$$

Since \frac{5}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$\frac{5+9}{6}-\frac{-4}{7}$$

Add 5 and 9 to get 14.

$$\frac{14}{6}-\frac{-4}{7}$$

Reduce the fraction \frac{14}{6} to lowest terms by extracting and canceling out 2.

$$\frac{7}{3}-\frac{-4}{7}$$

Fraction \frac{-4}{7} can be rewritten as -\frac{4}{7} by extracting the negative sign.

$$\frac{7}{3}-\left(-\frac{4}{7}\right)$$

The opposite of -\frac{4}{7} is \frac{4}{7}.

$$\frac{7}{3}+\frac{4}{7}$$

Least common multiple of 3 and 7 is 21. Convert \frac{7}{3} and \frac{4}{7} to fractions with denominator 21.

$$\frac{49}{21}+\frac{12}{21}$$

Since \frac{49}{21} and \frac{12}{21} have the same denominator, add them by adding their numerators.

$$\frac{49+12}{21}$$

Add 49 and 12 to get 61.

$$\frac{61}{21}$$

Factor

$$\frac{61}{3 \cdot 7} = 2\frac{19}{21} = 2.9047619047619047$$