Skill: Add fractions with unlike denominators

To add fractions with unlike denominators, first rewrite them with a common denominator. Then add the numerators and simplify the result.

Example:

$$\frac{2}{3}+\frac{5}{8}$$

The denominators are $3$ and $8$. Their least common multiple is $24$, so use $24$ as the common denominator.

Rewrite each fraction:

$$\frac{2}{3}=\frac{2\times 8}{3\times 8}=\frac{16}{24}$$ $$\frac{5}{8}=\frac{5\times 3}{8\times 3}=\frac{15}{24}$$

Now the fractions have the same-sized parts, so add the numerators:

$$\frac{16}{24}+\frac{15}{24}=\frac{31}{24}$$

The answer is an improper fraction. Convert it to a mixed number:

$$\frac{31}{24}=1\frac{7}{24}$$

Therefore,

$$\boxed{\frac{2}{3}+\frac{5}{8}=1\frac{7}{24}}$$

Remember: find a common denominator, make equivalent fractions, add the numerators, and simplify or convert to a mixed number if needed.