1. **State the problem:** Find 3 fractions between $\frac{1}{3}$ and $\frac{1}{4}$.\n\n2. **Recall the method:** To find fractions between two fractions, we can find equivalent fractions with a common denominator and then find fractions with numerators between those of the two fractions.\n\n3. **Find a common denominator:** The denominators are 3 and 4. The least common denominator (LCD) is 12.\n\n4. **Convert the fractions:**\n$$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$$\n$$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$$\n\n5. **Find fractions between $\frac{3}{12}$ and $\frac{4}{12}$:** There are no integers between 3 and 4, so we multiply numerator and denominator by a number to get more fractions.\n\n6. **Multiply numerator and denominator by 2:**\n$$\frac{4}{12} = \frac{4 \times 2}{12 \times 2} = \frac{8}{24}$$\n$$\frac{3}{12} = \frac{3 \times 2}{12 \times 2} = \frac{6}{24}$$\n\n7. **Fractions between $\frac{6}{24}$ and $\frac{8}{24}$ are $\frac{7}{24}$. Only one fraction here. We need more, so multiply by 3:**\n$$\frac{8}{24} = \frac{8 \times 3}{24 \times 3} = \frac{24}{72}$$\n$$\frac{6}{24} = \frac{6 \times 3}{24 \times 3} = \frac{18}{72}$$\n\n8. **Fractions between $\frac{18}{72}$ and $\frac{24}{72}$ are $\frac{19}{72}$, $\frac{20}{72}$, $\frac{21}{72}$, $\frac{22}{72}$, $\frac{23}{72}$. We can pick any 3:**\n$$\frac{19}{72}, \frac{20}{72}, \frac{21}{72}$$\n\n9. **Final answer:** Three fractions between $\frac{1}{3}$ and $\frac{1}{4}$ are $\frac{19}{72}$, $\frac{20}{72}$, and $\frac{21}{72}$.