Compare Products to Factor Sizes - 5th Grade Math

1. State the rule for how $a \times 0$ compares to $a$ when $a>0$.

   $a \times 0=0$, so it is less than $a$. Any number times zero equals zero.

2. Which is larger without multiplying: $\frac{3}{5}\times \frac{9}{10}$ or $\frac{3}{5}$?

   $\frac{3}{5}$. Since $\frac{9}{10}<1$, the product is less than $\frac{3}{5}$.

3. Which comparison is correct: $6\times \frac{13}{12}$ compared to $6$?

   $6\times \frac{13}{12}>6$. Since $\frac{13}{12}>1$, the product is greater than 6.

4. Identify whether $\frac{7}{9}\times 20$ is greater than, less than, or equal to $20$.

   Less than $20$. Since $\frac{7}{9} < 1$, the product is less than 20.

5. Choose the correct comparison: $\frac{8}{3}\times \frac{3}{8}$ __ $\frac{8}{3}$.

   $\frac{8}{3}\times \frac{3}{8} < \frac{8}{3}$. $\frac{3}{8} < 1$ makes the product smaller than $\frac{8}{3}$.

6. Find and correct the statement: For $a>0$, if $0<b<1$, then $a\times b>a$.

   Correct: if $0<b<1$, then $a\times b<a$. The original statement incorrectly uses $>$ instead of $<$.

7. Which is larger: $12$ or $12\times 1$?

   They are equal. Multiplying by 1 doesn't change the value.

8. Which comparison is correct: $14\times \frac{3}{2}$ compared to $14$?

   $14\times \frac{3}{2}>14$. Since $\frac{3}{2}>1$, the product is greater than 14.

9. What is the rule for $a\times b$ compared to $a$ when $b>1$, without multiplying?

   $a\times b$ is greater than $a$. Multiplying by a number greater than 1 increases the value.

10. Which comparison is correct: $\frac{5}{3}\times 12$ compared to $12$?

    $\frac{5}{3}\times 12>12$. Since $\frac{5}{3}>1$, the product is greater than 12.

11. What is the rule for $a\times b$ compared to $a$ when $0<b<1$, without multiplying?

    $a\times b$ is less than $a$. Multiplying by a fraction less than 1 decreases the value.

12. Which comparison is correct: $0\times \frac{9}{10}$ compared to $\frac{9}{10}$?

    $0\times \frac{9}{10}=0$. Zero times any number equals zero.

13. Which is larger without multiplying: $\frac{2}{3}\times \frac{3}{2}$ or $\frac{2}{3}$?

    $\frac{2}{3}\times \frac{3}{2}$. Since $\frac{3}{2}>1$, the product exceeds $\frac{2}{3}$.

14. Which is larger without multiplying: $\frac{7}{8}\times 9$ or $9$?

    $9$. Since $\frac{7}{8}<1$, the product is less than $9$.

15. What is true about $a\times b$ compared to $a$ when $b=1$ and $a>0$?

    $a\times b=a$. Multiplying by 1 leaves the value unchanged.

16. Identify whether $\frac{11}{10}\times 20$ is greater than, less than, or equal to $20$.

    Greater than $20$. Since $\frac{11}{10} > 1$, the product is greater than 20.

17. Identify whether $\frac{4}{9}\times 15$ is greater than, less than, or equal to $15$.

    Less than $15$. Since $\frac{4}{9}<1$, multiplying decreases $15$.

18. State the rule for how $a \times b$ compares to $a$ when $0<b<1$.

    $a \times b$ is less than $a$ (for $a>0$). Multiplying by a fraction less than 1 decreases the value.

19. Which is larger: $\frac{4}{9}$ or $\frac{4}{9}\times 0$?

    $\frac{4}{9}$ is larger. Any fraction times zero equals zero.

20. Which comparison is correct: $14\times \frac{1}{2}$ compared to $14$?

    $14\times \frac{1}{2}<14$. Since $\frac{1}{2}<1$, the product is less than 14.

21. Which is larger: $15$ or $15\times 0$?

    $15$ is larger. Zero times any number equals zero.

22. Which comparison is correct: $\frac{2}{5}\times \frac{3}{4}$ compared to $\frac{2}{5}$?

    $\frac{2}{5}\times \frac{3}{4}<\frac{2}{5}$. Since $\frac{3}{4}<1$, the product is less than $\frac{2}{5}$.

23. Which is larger: $\frac{3}{5}$ or $\frac{3}{5}\times \frac{9}{10}$?

    $\frac{3}{5}$ is larger. Multiplying by $\frac{9}{10} < 1$ gives a smaller result.

24. Which is larger without multiplying: $14\times 1$ or $14$?

    They are equal. Multiplying by $1$ leaves the value unchanged.

25. What is true about $a\times b$ compared to $a$ when $0<b<1$ and $a>0$?

    $a\times b<a$. Multiplying by a fraction less than 1 decreases the value.

26. What is the rule for $a\times b$ compared to $a$ when $b=1$, without multiplying?

    $a\times b$ equals $a$. Multiplying by 1 leaves the value unchanged.

27. Identify the correct sign: \left(\frac{9}{10}\right)\times 30\; _ \;30

    $<$. Since $\frac{9}{10}<1$, the product is less than 30.

28. Choose the correct comparison: $9\times \frac{2}{3}$ __ $9$.

    $9\times \frac{2}{3} < 9$. $\frac{2}{3} < 1$ makes the product smaller.

29. Which statement is true for $a>0$ if $a\times b<a$?

    $0<b<1$. The product is less than $a$ when the other factor is between 0 and 1.

30. Which is larger without multiplying: $\frac{5}{4}\times 12$ or $12$?

    $\frac{5}{4}\times 12$. Since $\frac{5}{4}>1$, the product is greater than $12$.

31. Which comparison is correct: $\frac{8}{9}\times 0$ compared to $\frac{8}{9}$?

    $\frac{8}{9}\times 0=0$. Zero times any number equals zero.

32. What is true about $a\times b$ compared to $a$ when $b=0$ and $a>0$?

    $a\times b=0$. Any number multiplied by 0 equals 0.

33. Which is larger: $8$ or $8\times \frac{5}{4}$?

    $8\times \frac{5}{4}$ is larger. Since $\frac{5}{4} > 1$, multiplying increases the value.

34. Identify whether $6\times \frac{1}{6}$ is greater than, less than, or equal to $6$.

    Less than $6$. $\frac{1}{6} < 1$, so the product is less than 6.

35. Which statement is always true for $a>0$ and $b>0$: $a\times b>a$ or $a\times b<a$ when $0<b<1$?

    $a\times b<a$. When $0<b<1$, multiplying decreases the value of $a$.

36. Identify whether $1\times \frac{13}{7}$ is greater than, less than, or equal to $\frac{13}{7}$.

    Equal to $\frac{13}{7}$. Multiplying by $1$ doesn't change the value.

37. Which comparison is correct: $\frac{3}{4}\times 9$ compared to $9$?

    $\frac{3}{4}\times 9<9$. Since $\frac{3}{4}<1$, the product is less than 9.

38. State the rule for how $a \times b$ compares to $a$ when $b=1$.

    $a \times 1=a$. Multiplying by 1 leaves any number unchanged.

39. Choose the correct comparison: $\frac{5}{6}\times 1$ __ $\frac{5}{6}$.

    $\frac{5}{6}\times 1 = \frac{5}{6}$. Multiplying by 1 keeps the value the same.

40. Which comparison is correct: $6\times \frac{11}{12}$ compared to $6$?

    $6\times \frac{11}{12}<6$. Since $\frac{11}{12}<1$, the product is less than 6.

41. Which comparison is correct: $\frac{8}{9}\times 1$ compared to $\frac{8}{9}$?

    $\frac{8}{9}\times 1=\frac{8}{9}$. Multiplying by 1 gives the same value.

42. Choose the correct comparison: $9\times \frac{4}{3}$ __ $9$.

    $9\times \frac{4}{3} > 9$. $\frac{4}{3} > 1$ makes the product larger.

43. What is true about $a\times b$ compared to $a$ when $b>1$ and $a>0$?

    $a\times b>a$. Multiplying by a number greater than 1 increases the value.

44. Identify whether $\frac{2}{7}\times \frac{7}{2}$ is greater than, less than, or equal to $\frac{2}{7}$.

    Greater than $\frac{2}{7}$. $\frac{7}{2} > 1$, so the product exceeds $\frac{2}{7}$.

45. State the rule for how $a \times b$ compares to $a$ when $b > 1$.

    $a \times b$ is greater than $a$ (for $a>0$). When multiplying by a number greater than 1, the product increases.

46. Choose the correct comparison: $\frac{3}{2}\times 8$ is $<$, $>$, or $=$ $8$.

    $>$. Since $\frac{3}{2}>1$, the product is greater than $8$.

47. Which statement is always true for $a>0$ and $b>0$: $a\times b>a$ or $a\times b<a$ when $b>1$?

    $a\times b>a$. When $b>1$, multiplying increases the value of $a$.

48. Identify the correct sign: $\left(\frac{11}{10}\right)\times 30\;\_\;30$

    $>$. Since $\frac{11}{10}>1$, the product is greater than 30.

49. Identify whether $6\times \frac{6}{1}$ is greater than, less than, or equal to $6$.

    Greater than $6$. $\frac{6}{1} = 6 > 1$, so the product is greater than 6.

50. Which comparison is correct: $\frac{2}{5}\times \frac{7}{4}$ compared to $\frac{2}{5}$?

    $\frac{2}{5}\times \frac{7}{4}>\frac{2}{5}$. Since $\frac{7}{4}>1$, the product is greater than $\frac{2}{5}$.

51. Which is larger: $\frac{3}{5}$ or $\frac{3}{5}\times \frac{9}{8}$?

    $\frac{3}{5}\times \frac{9}{8}$ is larger. Multiplying by $\frac{9}{8} > 1$ gives a larger result.

52. Which is larger: $8$ or $8\times \frac{3}{4}$?

    $8$ is larger. Since $\frac{3}{4} < 1$, multiplying decreases the value.

53. Identify whether $\frac{9}{8}\times 20$ is greater than, less than, or equal to $20$.

    Greater than $20$. Since $\frac{9}{8}>1$, multiplying increases $20$.

54. Which comparison is correct: $1\times \frac{7}{8}$ compared to $\frac{7}{8}$?

    $1\times \frac{7}{8}=\frac{7}{8}$. Multiplying by 1 gives the same value.

55. Choose the correct comparison: $9\times \frac{1}{5}$ is $<$, $>$, or $=$ $9$.

    $<$. Since $\frac{1}{5}<1$, the product is less than $9$.

56. Which is larger without multiplying: $\frac{7}{6}\times \frac{5}{6}$ or $\frac{5}{6}$?

    $\frac{7}{6}\times \frac{5}{6}$. Since $\frac{7}{6}>1$, the product is greater than $\frac{5}{6}$.

57. Which is larger without multiplying: $18\times \frac{2}{3}$ or $18$?

    $18$. Since $\frac{2}{3}<1$, the product is less than $18$.

58. Which is larger without multiplying: $6\times \frac{11}{10}$ or $6$?

    $6\times \frac{11}{10}$. Since $\frac{11}{10}>1$, the product is greater than $6$.

59. Which statement is true for $a>0$ if $a\times b>a$?

    $b>1$. The product exceeds $a$ when the other factor is greater than 1.

Study these flashcards