On Monday, Leo memorizes $\frac{3}{5}$ of his trumpet solo. On Tuesday, he memorizes $\frac{1}{3}$ more. What fraction of his solo does he have left to memorize?

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1/15? And is so, why? – Paul Anthony Sep 25 '12 at 23:10
If you get an answer that satisfies you, it's good manners to click on the check mark to the left of the answer. "Accepting" an answer in this way gives reputation points to the answerer and may increase the chances that someone will be more inclined to answer yor subsequent questions. – Rick Decker Sep 30 '12 at 18:46

To be able to compare fractions, it is helpful to find a common denominator. The denominators are $3$ and $5$, so $3 \cdot 5 = 15$ is a good choice for a common denominator.
If we want to rewrite $\frac{3}{5}$ with a denominator of $15$, we should multiply the top and bottom by $3$. Doing so shows us that $\frac{3}{5}$ is the same as $\frac{9}{15}$.
Similarly, we can turn $\frac{1}{3}$ into $\frac{5}{15}$ (multiply the top and bottom by $5$ this time).
Now the problem can be read differently. Imagine his trumpet solo is broken into $15$ parts. He memorized $9$ parts on the first day and $5$ parts on the second day. This means he has memorized $14$ of the $15$ total parts, and so has $1$ part out of $15$ (or $\frac{1}{15}$) remaining to learn.