Solve 5a-7/25-2a+9/10

$$\frac { 5 a - 7 } { 25 } - \frac { 2 a + 9 } { 10 }$$

Evaluate

$$-\frac{59}{50}=-1.18$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and 10 is 50. Multiply \frac{5a-7}{25} times \frac{2}{2}. Multiply \frac{2a+9}{10} times \frac{5}{5}.

$$\frac{2\left(5a-7\right)}{50}-\frac{5\left(2a+9\right)}{50}$$

Since \frac{2\left(5a-7\right)}{50} and \frac{5\left(2a+9\right)}{50} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(5a-7\right)-5\left(2a+9\right)}{50}$$

Do the multiplications in 2\left(5a-7\right)-5\left(2a+9\right).

$$\frac{10a-14-10a-45}{50}$$

Combine like terms in 10a-14-10a-45.

$$\frac{-59}{50}$$

Fraction \frac{-59}{50} can be rewritten as -\frac{59}{50} by extracting the negative sign.

$$-\frac{59}{50}$$

Factor

$$-\frac{59}{50} = -1\frac{9}{50} = -1.18$$

Solution Steps

Factor out \frac{1}{50}.

$$\frac{2\left(5a-7\right)-5\left(2a+9\right)}{50}$$

Simplify.

$$-\frac{59}{50}$$