Comparing Fractions - SSAT Middle Level Quantitative

1. Which is greater: $ \frac{7}{10}$ or $ \frac{3}{4}$?

   $\frac{3}{4}$. Because $7 \times 4 = 28 < 3 \times 10 = 30$.

2. Which is greater: $ \frac{7}{12}$ or $ \frac{5}{9}$?

   $\frac{7}{12}$. Because $7 \times 9 = 63 > 5 \times 12 = 60$.

3. Which is greater: $ \frac{9}{25}$ or $ \frac{2}{5}$?

   $\frac{2}{5}$. Because $9 \times 5 = 45 < 2 \times 25 = 50$.

4. Which is greater: $ \frac{10}{21}$ or $ \frac{3}{7}$?

   $\frac{10}{21}$. Because $10 \times 7 = 70 > 3 \times 21 = 63$.

5. Which is greater: $ \frac{12}{17}$ or $ \frac{5}{8}$?

   $\frac{12}{17}$. Because $12 \times 8 = 96 > 5 \times 17 = 85$.

6. Which is greater: $ \frac{1}{2}$ or $ \frac{3}{7}$?

   $\frac{1}{2}$. Because $1 \times 7 = 7 > 3 \times 2 = 6$.

7. Which is greater: $ \frac{7}{8}$ or $ \frac{11}{12}$?

   $\frac{11}{12}$. Because $7 \times 12 = 84 < 11 \times 8 = 88$.

8. Which is greater: $ \frac{3}{10}$ or $ \frac{7}{25}$?

   $\frac{3}{10}$. Because $3 \times 25 = 75 > 7 \times 10 = 70$.

9. What method compares $ \frac{a}{b}$ and $ \frac{c}{d}$ by checking whether $ad$ is greater than $bc$?

   Cross-multiplication: compare $ad$ and $bc$. This method determines if $\frac{a}{b} > \frac{c}{d}$ by checking if $ad > bc$ when denominators are positive.

10. Which is greater: $ \frac{3}{7}$ or $ \frac{4}{9}$?

    $\frac{4}{9}$. Because $3 \times 9 = 27 < 4 \times 7 = 28$.

11. Which is greater: $ \frac{5}{12}$ or $ \frac{2}{5}$?

    $\frac{5}{12}$. Because $5 \times 5 = 25 > 2 \times 12 = 24$.

12. Which is greater: $ \frac{4}{11}$ or $ \frac{3}{8}$?

    $\frac{3}{8}$. Because $4 \times 8 = 32 < 3 \times 11 = 33$.

13. Which is greater: $ \frac{13}{20}$ or $ \frac{2}{3}$?

    $\frac{2}{3}$. Because $13 \times 3 = 39 < 2 \times 20 = 40$.

14. Which is greater: $ \frac{8}{9}$ or $ \frac{9}{10}$?

    $\frac{9}{10}$. Because $8 \times 10 = 80 < 9 \times 9 = 81$.

15. Which is greater: $ \frac{6}{13}$ or $ \frac{7}{15}$?

    $\frac{7}{15}$. Because $6 \times 15 = 90 < 7 \times 13 = 91$.

16. Which is greater: $ \frac{4}{9}$ or $ \frac{5}{12}$?

    $\frac{4}{9}$. Because $4 \times 12 = 48 > 5 \times 9 = 45$.

17. Which is greater: $ \frac{9}{14}$ or $ \frac{2}{3}$?

    $\frac{2}{3}$. Because $9 \times 3 = 27 < 2 \times 14 = 28$.

18. What must be true about $b$ and $d$ before using cross-multiplication on $ \frac{a}{b}$ and $ \frac{c}{d}$?

    $b>0$ and $d>0$ (positive denominators). Positive denominators ensure the inequality direction remains the same after cross-multiplying.

19. Which is greater: $ \frac{5}{7}$ or $ \frac{3}{4}$?

    $\frac{3}{4}$. Because $5 \times 4 = 20 < 3 \times 7 = 21$.

20. Which is greater: $ \frac{5}{6}$ or $ \frac{7}{9}$?

    $\frac{5}{6}$. Because $5 \times 9 = 45 > 7 \times 6 = 42$.

21. Which is greater: $ \frac{11}{15}$ or $ \frac{3}{5}$?

    $\frac{11}{15}$. Because $11 \times 5 = 55 > 3 \times 15 = 45$.

22. Which is greater: $ \frac{2}{9}$ or $ \frac{1}{4}$?

    $\frac{1}{4}$. Because $2 \times 4 = 8 < 1 \times 9 = 9$.

23. Which is greater: $ \frac{14}{15}$ or $ \frac{9}{10}$?

    $\frac{14}{15}$. Because $14 \times 10 = 140 > 9 \times 15 = 135$.

24. Which is greater: $ \frac{9}{16}$ or $ \frac{5}{8}$?

    $\frac{5}{8}$. Because $9 \times 8 = 72 < 5 \times 16 = 80$.

25. Which is greater: $ \frac{6}{17}$ or $ \frac{7}{19}$?

    $\frac{7}{19}$. Because $6 \times 19 = 114 < 7 \times 17 = 119$.

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