## Introductory Algebra for College Students (7th Edition)

$$-\frac{13}{40}$$
To subtract fractions, we need to make sure the denominators are the same. If the denominators are not the same, then we need to find equivalent fractions with the same denominators. To find an equation fraction, we first find the least common denominator of the fractions. For fractions that have denominators of $5$ and $8$, the least common denominator would be $40$ because both $5$ and $8$ can go into $40$ evenly. For $\frac{4}{5}$, we see how many times the denominator $5$ goes into $40$ and multiply it by the numerator, $4$. So we have: $$\frac{4}{5} = \frac{32}{40}$$ We do the same thing for $\frac{9}{8}$. We see how many times the denominator $8$ goes into $40$ and multiply that number by the numerator, $9$, to get: $$\frac{9}{8} = \frac{45}{40}$$ Now that we have equivalent fractions with the same denominator, we can subtract them: $$\frac{32}{40} - \frac{45}{40}$$ We subtract the numerators and keep the denominator: $$\frac{-13}{40}$$ The fraction can no longer be simplified.