1. The problem asks to find 3 fractions between $\frac{1}{3}$ and $\frac{1}{4}$ using Method B, which involves scaling denominators and numerators. 2. First, note the fractions $\frac{1}{3} = \frac{2}{6}$ and $\frac{1}{4} = \frac{2}{8}$ as given in the method. 3. The method shows multiplying numerator and denominator by integers to generate fractions between these two. 4. For numerator 2, denominators range from 12 to 16, giving fractions: $\frac{2}{12}, \frac{2}{13}, \frac{2}{14}, \frac{2}{15}, \frac{2}{16}$. 5. For numerator 3, denominators range from 18 to 24, giving fractions: $\frac{3}{18}, \frac{3}{19}, \frac{3}{20}, \frac{3}{21}, \frac{3}{22}, \frac{3}{23}, \frac{3}{24}$. 6. Now, check which of these fractions lie strictly between $\frac{1}{4} = 0.25$ and $\frac{1}{3} \approx 0.3333$. 7. Calculate decimal values: - $\frac{2}{12} = 0.1667$ (less than 0.25, discard) - $\frac{2}{13} \approx 0.1538$ (less, discard) - $\frac{2}{14} \approx 0.1429$ (less, discard) - $\frac{2}{15} \approx 0.1333$ (less, discard) - $\frac{2}{16} = 0.125$ (less, discard) - $\frac{3}{18} = 0.1667$ (less, discard) - $\frac{3}{19} \approx 0.1579$ (less, discard) - $\frac{3}{20} = 0.15$ (less, discard) - $\frac{3}{21} \approx 0.1429$ (less, discard) - $\frac{3}{22} \approx 0.1364$ (less, discard) - $\frac{3}{23} \approx 0.1304$ (less, discard) - $\frac{3}{24} = 0.125$ (less, discard) 8. None of these fractions are between $\frac{1}{4}$ and $\frac{1}{3}$, so we need to find fractions by scaling $\frac{1}{3}$ and $\frac{1}{4}$ with a common multiplier to get fractions between them. 9. Multiply numerator and denominator of $\frac{1}{3}$ and $\frac{1}{4}$ by 4: $$\frac{1 \times 4}{3 \times 4} = \frac{4}{12}, \quad \frac{1 \times 4}{4 \times 4} = \frac{4}{16}$$ 10. Fractions between $\frac{4}{16} = 0.25$ and $\frac{4}{12} \approx 0.3333$ with denominator between 12 and 16 are: - $\frac{5}{16} = 0.3125$ - $\frac{6}{16} = 0.375$ (too big) - $\frac{5}{15} = 0.3333$ (equal to $\frac{1}{3}$) 11. Alternatively, multiply numerator and denominator by 5: $$\frac{1 \times 5}{3 \times 5} = \frac{5}{15}, \quad \frac{1 \times 5}{4 \times 5} = \frac{5}{20}$$ 12. Fractions between $\frac{5}{20} = 0.25$ and $\frac{5}{15} \approx 0.3333$ with denominators between 15 and 20: - $\frac{6}{20} = 0.3$ - $\frac{7}{20} = 0.35$ (too big) 13. So three fractions between $\frac{1}{4}$ and $\frac{1}{3}$ are: $$\frac{5}{20}, \frac{6}{20}, \frac{5}{16}$$ 14. Simplify fractions where possible: - $\frac{5}{20} = \frac{1}{4}$ (equal to lower bound, so exclude) - $\frac{6}{20} = \frac{3}{10} = 0.3$ - $\frac{5}{16} = 0.3125$ 15. Final three fractions strictly between $\frac{1}{4}$ and $\frac{1}{3}$ are: $$\frac{3}{10}, \frac{5}{16}, \frac{7}{24}$$ 16. These fractions satisfy $\frac{1}{4} < \frac{3}{10} < \frac{5}{16} < \frac{7}{24} < \frac{1}{3}$. Answer: $\boxed{\frac{3}{10}, \frac{5}{16}, \frac{7}{24}}$