Compare Fractions With Unlike Parts - 4th Grade Math

1. What is the goal of creating a common numerator when comparing fractions?

   Rewrite both fractions with the same numerator to compare denominators. With equal numerators, smaller denominator means larger fraction.

2. What symbol makes the statement true: $\frac{3}{7}$ __ $\frac{4}{9}$?

   $\frac{3}{7} < \frac{4}{9}$. Convert to 63rds: $\frac{27}{63} < \frac{28}{63}$.

3. Which fraction is greater: $\frac{3}{8}$ or $\frac{2}{5}$?

   $\frac{3}{8} < \frac{2}{5}$. Common denominator: $\frac{15}{40} < \frac{16}{40}$.

4. What symbol makes the statement true: $\frac{2}{7}$ __ $\frac{3}{10}$?

   $\frac{2}{7} < \frac{3}{10}$. Convert to 70ths: $\frac{20}{70} < \frac{21}{70}$.

5. Which comparison is correct: $\frac{4}{9} \square \frac{1}{2}$? Use $>$, $<$, or $=$.

   $\frac{4}{9} < \frac{1}{2}$. $\frac{4}{9} = \frac{8}{18}$ and $\frac{1}{2} = \frac{9}{18}$, so $\frac{4}{9} < \frac{1}{2}$.

6. What benchmark fraction is commonly used to compare fractions in Grade $4$?

   $\frac{1}{2}$. Half is a useful reference point for comparing other fractions.

7. What symbol makes this true: $\frac{5}{6}\ \square\ \frac{7}{8}$?

   $\frac{5}{6} < \frac{7}{8}$. Convert to twenty-fourths: $\frac{5}{6} = \frac{20}{24}$ and $\frac{7}{8} = \frac{21}{24}$.

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

   $\frac{4}{7} < \frac{3}{5}$. Common denominator: $\frac{20}{35} < \frac{21}{35}$.

9. What must be true about the whole when comparing $\frac{1}{3}$ of one pizza and $\frac{1}{2}$ of another pizza?

   The fractions must refer to the same-sized whole. Comparisons are only valid when fractions refer to the same whole.

10. What symbol makes the statement true: $\frac{11}{12}$ __ $\frac{7}{8}$?

    $\frac{11}{12} > \frac{7}{8}$. Convert to 24ths: $\frac{22}{24} > \frac{21}{24}$.

11. What symbol makes this true: $\frac{1}{4}\ \square\ \frac{3}{10}$?

    $\frac{1}{4} < \frac{3}{10}$. Convert to twentieths: $\frac{1}{4} = \frac{5}{20}$ and $\frac{3}{10} = \frac{6}{20}$.

12. Which comparison is correct: $\frac{3}{5} \square \frac{1}{2}$? Use $>$, $<$, or $=$.

    $\frac{3}{5} > \frac{1}{2}$. $\frac{3}{5} = \frac{6}{10}$ and $\frac{1}{2} = \frac{5}{10}$, so $\frac{3}{5} > \frac{1}{2}$.

13. Which fraction is greater: $\frac{2}{3}$ or $\frac{3}{5}$?

    $\frac{2}{3} > \frac{3}{5}$. Common denominator: $\frac{10}{15} > \frac{9}{15}$.

14. What symbol makes this true: $\frac{7}{12}\ \square\ \frac{5}{8}$?

    $\frac{7}{12} < \frac{5}{8}$. Convert to twenty-fourths: $\frac{7}{12} = \frac{14}{24}$ and $\frac{5}{8} = \frac{15}{24}$.

15. What must be true about the whole for a fraction comparison to be valid?

    The fractions must refer to the same whole (same-size unit). Can't compare $\frac{1}{2}$ of a pizza to $\frac{1}{2}$ of a cookie.

16. What symbol makes the statement true: $\frac{5}{12}$ __ $\frac{3}{8}$?

    $\frac{5}{12} > \frac{3}{8}$. Convert to 24ths: $\frac{10}{24} > \frac{9}{24}$.

17. What symbol makes this true: $\frac{2}{3}\ \square\ \frac{3}{5}$?

    $\frac{2}{3} > \frac{3}{5}$. Convert to fifteenths: $\frac{2}{3} = \frac{10}{15}$ and $\frac{3}{5} = \frac{9}{15}$.

18. What symbol makes the statement true: $\frac{7}{10}$ __ $\frac{3}{4}$?

    $\frac{7}{10} < \frac{3}{4}$. Convert to 20ths: $\frac{14}{20} < \frac{15}{20}$.

19. Which symbol means "greater than" when comparing fractions?

    $>$. The open side points to the larger fraction.

20. What symbol makes this true: $\frac{4}{9}\ \square\ \frac{1}{2}$?

    $\frac{4}{9} < \frac{1}{2}$. Compare to $\frac{1}{2}$: $\frac{4}{9}$ is less than half since $4 < 4.5$.

21. What benchmark fraction is often used to compare fractions quickly in Grade 4?

    The benchmark fraction $\frac{1}{2}$. Easy to see if fractions are more or less than half.

22. Which comparison is correct: $\frac{5}{10} \square \frac{1}{2}$? Use $>, <$, or $=$.

    $\frac{5}{10} = \frac{1}{2}$. $\frac{5}{10}$ simplifies to $\frac{1}{2}$, so they're equal.

23. What symbol makes the statement true: $\frac{6}{11}$ __ $\frac{5}{9}$?

    $\frac{6}{11} < \frac{5}{9}$. Convert to 99ths: $\frac{54}{99} < \frac{55}{99}$.

24. What is the first step to compare $\frac{a}{b}$ and $\frac{c}{d}$ using common denominators?

    Rewrite both with denominator $bd$ (or an LCM). Finding a common denominator allows direct comparison of numerators.

25. What symbol makes this true: $\frac{6}{8} \square \frac{3}{4}$?

    $\frac{6}{8} = \frac{3}{4}$. Both simplify to $\frac{3}{4}$ when reduced.

26. What symbol makes the statement true: $\frac{4}{9}$ __ $\frac{1}{2}$?

    $\frac{4}{9} < \frac{1}{2}$. $\frac{4}{9} = \frac{8}{18}$ and $\frac{1}{2} = \frac{9}{18}$, so $\frac{4}{9} < \frac{1}{2}$.

27. Which comparison is valid: compare $\frac{1}{2}$ of a small pizza to $\frac{1}{3}$ of a large pizza, yes or no?

    No, because the wholes are different sizes. Different-sized wholes make the comparison invalid.

28. What symbol should you use if two fractions represent the same amount of the same whole?

    Use the symbol $=$. Equal fractions represent the same portion of the whole.

29. What symbol makes this true: $\frac{9}{11} \square \frac{5}{6}$?

    $\frac{9}{11} < \frac{5}{6}$. Convert to sixty-sixths: $\frac{9}{11} = \frac{54}{66}$ and $\frac{5}{6} = \frac{55}{66}$.

30. What symbol makes this true: $\frac{5}{12} \square \frac{1}{2}$?

    $\frac{5}{12} < \frac{1}{2}$. Compare numerators to half the denominator: $5 < 6$, so less than $\frac{1}{2}$.

31. What symbol makes the statement true: $\frac{9}{16}$ __ $\frac{5}{8}$?

    $\frac{9}{16} < \frac{5}{8}$. Convert to 16ths: $\frac{9}{16} < \frac{10}{16}$.

32. Which fraction is greater: $\frac{9}{10}$ or $\frac{5}{6}$?

    $\frac{9}{10} > \frac{5}{6}$. Common denominator: $\frac{27}{30} > \frac{25}{30}$.

33. What must be true about the whole for a fraction comparison using $>$, $<$, or $=$ to be valid?

    Both fractions must refer to the same whole. Can't compare $\frac{1}{2}$ of a pizza to $\frac{1}{3}$ of a cookie fairly.

34. What is the comparison method called when you rewrite fractions with the same numerator?

    Common numerators. Fractions are rewritten with the same top number to compare denominators.

35. What symbol makes this true: $\frac{3}{4} \square \frac{5}{8}$?

    $\frac{3}{4} > \frac{5}{8}$. Convert to eighths: $\frac{3}{4} = \frac{6}{8}$, and $\frac{6}{8} > \frac{5}{8}$.

36. What symbol makes the statement true: $\frac{8}{15}$ __ $\frac{1}{2}$?

    $\frac{8}{15} > \frac{1}{2}$. $\frac{8}{15} = \frac{16}{30}$ and $\frac{1}{2} = \frac{15}{30}$, so $\frac{8}{15} > \frac{1}{2}$.

37. Which fraction is greater: $\frac{5}{12}$ or $\frac{1}{3}$?

    $\frac{5}{12} > \frac{1}{3}$. Common denominator: $\frac{5}{12} > \frac{4}{12}$.

38. What does the symbol $>$ mean when comparing two fractions?

    $>$ means the left fraction is greater than the right fraction. It indicates the first value is larger than the second.

39. What is the goal of creating a common denominator when comparing fractions?

    Rewrite both fractions with the same denominator to compare numerators. With equal denominators, larger numerator means larger fraction.

40. What symbol makes this true: $\frac{8}{15}\ \square\ \frac{1}{2}$?

    $\frac{8}{15} > \frac{1}{2}$. Compare to $\frac{1}{2}$: $\frac{8}{15}$ is greater since $8 > 7.5$.

41. What benchmark fraction is commonly used to compare fractions quickly in Grade $4$?

    The benchmark fraction is $\frac{1}{2}$. Half is easy to visualize and compare other fractions against.

42. What symbol makes this true: $\frac{2}{7}\ \square\ \frac{1}{3}$?

    $\frac{2}{7} < \frac{1}{3}$. Convert to twenty-firsts: $\frac{2}{7} = \frac{6}{21}$ and $\frac{1}{3} = \frac{7}{21}$.

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

    $\frac{11}{12} > \frac{7}{8}$. Common denominator: $\frac{22}{24} > \frac{21}{24}$.

44. What symbol makes the statement true: $\frac{5}{8}$ __ $\frac{3}{5}$?

    $\frac{5}{8} > \frac{3}{5}$. Convert to 40ths: $\frac{25}{40} > \frac{24}{40}$.

45. What symbol makes the statement true: $\frac{5}{6}$ __ $\frac{6}{7}$?

    $\frac{5}{6} < \frac{6}{7}$. Convert to 42nds: $\frac{35}{42} < \frac{36}{42}$.

46. What does the symbol $<$ mean when comparing two fractions?

    $<$ means the left fraction is less than the right fraction. It indicates the first value is smaller than the second.

47. Which symbol means "less than" when comparing fractions?

    $<$. The pointed side points to the smaller fraction.

48. Which symbol means "equal to" when comparing fractions?

    $=$. Shows that two fractions have the same value.

49. Which fraction is greater: $\frac{3}{4}$ or $\frac{5}{8}$?

    $\frac{3}{4} > \frac{5}{8}$. Common denominator: $\frac{6}{8} > \frac{5}{8}$.

50. What is the comparison method called when you rewrite fractions with the same denominator?

    Common denominators. Fractions are rewritten with the same bottom number for easy comparison.

51. What does the symbol $=$ mean when comparing two fractions?

    $=$ means the two fractions are equal in value. It indicates both values represent the same amount.

52. Which fraction is greater: $\frac{7}{12}$ or $\frac{5}{8}$?

    $\frac{7}{12} < \frac{5}{8}$. Common denominator: $\frac{14}{24} < \frac{15}{24}$.

53. What symbol makes this true: $\frac{7}{10} \square \frac{2}{3}$?

    $\frac{7}{10} > \frac{2}{3}$. Convert to thirtieths: $\frac{7}{10} = \frac{21}{30}$ and $\frac{2}{3} = \frac{20}{30}$.

54. What symbol makes the statement true: $\frac{3}{4}$ __ $\frac{2}{3}$?

    $\frac{3}{4} > \frac{2}{3}$. Convert to common denominator: $\frac{9}{12} > \frac{8}{12}$.

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

    $\frac{5}{6} > \frac{7}{9}$. Common denominator: $\frac{15}{18} > \frac{14}{18}$.

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