Solve 5a-7/10-3a+8/6

$$\frac { 5 a - 7 } { 10 } - \frac { 3 a + 8 } { 6 }$$

Evaluate

$$-\frac{61}{30}\approx -2.033333333$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 6 is 30. Multiply \frac{5a-7}{10} times \frac{3}{3}. Multiply \frac{3a+8}{6} times \frac{5}{5}.

$$\frac{3\left(5a-7\right)}{30}-\frac{5\left(3a+8\right)}{30}$$

Since \frac{3\left(5a-7\right)}{30} and \frac{5\left(3a+8\right)}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(5a-7\right)-5\left(3a+8\right)}{30}$$

Do the multiplications in 3\left(5a-7\right)-5\left(3a+8\right).

$$\frac{15a-21-15a-40}{30}$$

Combine like terms in 15a-21-15a-40.

$$\frac{-61}{30}$$

Fraction \frac{-61}{30} can be rewritten as -\frac{61}{30} by extracting the negative sign.

$$-\frac{61}{30}$$

Factor

$$-\frac{61}{30} = -2\frac{1}{30} = -2.033333333333333$$

Solution Steps

Factor out \frac{1}{30}.

$$\frac{3\left(5a-7\right)-5\left(3a+8\right)}{30}$$

Simplify.

$$-\frac{61}{30}$$