Question

Perform the indicated operation. Write all results in lowest terms. $$-\frac{2}{5}+\frac{9}{10}$$

Short answer

Answer: $\frac{1}{2}$

Step-by-step solution

Find the least common denominator (LCD)

To add these fractions, we need to find the least common denominator. In this case, the LCD for both fractions is the smallest multiple of both denominators (5 and 10), which is 10.

Rewrite the fractions with the LCD as the new denominator

Now that we have the LCD, we can rewrite each fraction with the new denominator: $$-\frac{2}{5} \cdot \frac{2}{2} = -\frac{4}{10}$$ $$\frac{9}{10}$$

Perform the addition

With both fractions having the same denominator, we can now add them together. When adding fractions, we add the numerators and keep the denominators the same: $$-\frac{4}{10} + \frac{9}{10} = \frac{9-4}{10} = \frac{5}{10}$$

Simplify the result

Now, we need to make sure that our result is in its lowest terms. To do this, find the greatest common divisor (GCD) of the numerator and the denominator, and then divide both by the GCD. The GCD of 5 and 10 is 5: $$\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}$$ The final answer is: $$\frac{1}{2}$$