Interpret Fraction Multiplication Products - 5th Grade Math

1. What is the value of $\frac{3}{4}\times 20$ using $3\times 20\div 4$?

   $15$. Calculate: $3 \times 20 = 60$, then $60 \div 4 = 15$.

2. What is $\frac{6}{8}\times 16$ using "take $6$ of the $8$ equal parts"?

   $12$. $16 \div 8 = 2$ per part, so $6$ parts = $12$.

3. What is $\frac{7}{10}\times 50$ interpreted as $7$ parts of $50$ split into $10$ equal parts?

   $35$. Each part is $\frac{50}{10}=5$, so $7$ parts equals $7\times 5=35$.

4. What does $\frac{a}{b}\times q$ represent using "$\frac{1}{b}$ of $q$"?

   $a\times\left(\frac{1}{b}\times q\right)$. First find $\frac{1}{b}$ of $q$, then multiply by $a$.

5. Which expression matches "$a$ parts of $q$ after splitting $q$ into $b$ equal parts"?

   $\frac{a}{b}\times q$. This notation means multiply $\frac{a}{b}$ by $q$.

6. What is $\frac{5}{6} \times 24$ by first finding $\frac{24}{6}$?

   $20$. Each part is $\frac{24}{6}=4$, so $5$ parts equals $5\times 4=20$.

7. What is $\frac{4}{7}\times 21$ interpreted as $4$ parts of $21$ split into $7$ equal parts?

   $12$. Each part is $\frac{21}{7}=3$, so $4$ parts equals $4\times 3=12$.

8. What is $\frac{3}{5}\times 20$ by partitioning $20$ into $5$ equal parts?

   $12$. $20 \div 5 = 4$ per part, so $3$ parts = $12$.

9. What does $\frac{1}{b}\times q$ represent using equal parts of $q$?

   One of $b$ equal parts of $q$. Taking one part when $q$ is divided into $b$ equal pieces.

10. What is $\frac{3}{8}\times 24$ using "$24$ split into $8$ equal parts, take $3$"?

    $9$. $24 \div 8 = 3$ per part, so $3$ parts = $9$.

11. What is the missing denominator $b$ if $ $ $\frac{3}{b}\times 24=18$?

    $4$. Since $\frac{3}{b} \times 24 = 18$, we need $72 \div b = 18$, so $b = 4$.

12. What is $\frac{9}{4}\times 8$ using $9\times 8\div 4$?

    $18$. Following the sequence: $9\times 8=72$, then $72\div 4=18$.

13. What is $\frac{2}{3} \times 18$ using the operations $2 \times 18 \div 3$?

    $12$. Following the sequence: $2 \times 18=36$, then $36 \div 3=12$.

14. What is one part when $q$ is partitioned into $b$ equal parts?

    $\frac{q}{b}$. Dividing $q$ by $b$ gives the size of each equal part.

15. Identify the correct interpretation: $ $ $\frac{3}{8}\times q$ is $3$ parts after splitting $q$ into how many equal parts?

    $8$ equal parts. The denominator tells us how many equal parts to create.

16. What is $\frac{1}{3}\times 27$ interpreted as one of $3$ equal parts?

    $9$. $27 \div 3 = 9$, which is one equal part.

17. What is $\frac{3}{10}\times 70$ by first finding $\frac{1}{10}$ of $70$?

    $21$. $\frac{1}{10}$ of $70$ is $7$, so $3$ parts = $21$.

18. What is $\frac{3}{4}\times 16$ using $3\times 16\div 4$?

    $12$. Following the sequence: $3\times 16=48$, then $48\div 4=12$.

19. What is the value of $a$ if $\frac{a}{6}\times 24=20$?

    $5$. Since $\frac{a}{6}\times 24=20$, we get $4a=20$, so $a=5$.

20. What does $ $ $\frac{a}{b}\times q$ mean when $q$ is split into $b$ equal parts?

    $a$ parts of $q$ after partitioning $q$ into $b$ equal parts. The fraction tells us how many parts to take after dividing $q$ into $b$ equal pieces.

21. What is $ $ $\frac{a}{b}\times q$ when $a=b$ (for example, $\frac{5}{5}\times q$)?

    $q$. When numerator equals denominator, the fraction equals $1$, so $1 \times q = q$.

22. What is $\frac{4}{7}\times 21$ by first finding $\frac{1}{7}$ of $21$?

    $12$. $\frac{1}{7}$ of $21$ is $3$, so $4$ parts = $12$.

23. What is $a$ parts when $q$ is partitioned into $b$ equal parts?

    $a\times\frac{q}{b}$. Take $a$ copies of each part, which has size $\frac{q}{b}$.

24. What is the value of $q$ if $\frac{2}{5}\times q=8$?

    $20$. Since $\frac{2}{5}\times q=8$, we solve: $q=8\div\frac{2}{5}=8\times\frac{5}{2}=20$.

25. What is the value of $q$ if $\frac{3}{4}\times q=15$?

    $20$. Since $\frac{3}{4}\times q=15$, we solve: $q=15\div\frac{3}{4}=15\times\frac{4}{3}=20$.

26. What is $\frac{a}{b}\times q$ written as a single fraction with numerator $a\times q$?

    $\frac{a\times q}{b}$. Multiplying by $\frac{a}{b}$ is the same as $\frac{a\times q}{b}$.

27. What is $\frac{2}{5}\times 15$ interpreted as $2$ parts of $15\div 5$?

    $6$. $15 \div 5 = 3$ per part, so $2$ parts = $6$.

28. What is $ $ $\frac{1}{6}\times 48$ interpreted as one part when $48$ is split into $6$ equal parts?

    $8$. One part of $48$ divided into $6$ equal parts is $48 \div 6 = 8$.

29. What sequence of operations is equivalent to $\frac{a}{b}\times q$?

    $a\times q\div b$. Multiply by numerator, then divide by denominator.

30. What is the value of $ $ $\frac{2}{5}\times 30$ by partitioning $30$ into $5$ equal parts?

    $12$. Each part is $30 \div 5 = 6$, so $2$ parts equals $2 \times 6 = 12$.

31. What is $\frac{5}{2}\times 6$ interpreted as $5$ parts of $6\div 2$?

    $15$. $6 \div 2 = 3$ per part, so $5$ parts = $15$.

32. What is $\frac{1}{8}\times 32$ interpreted as $1$ part of $32$ split into $8$ equal parts?

    $4$. One part of $32$ divided into $8$ equal parts is $\frac{32}{8}=4$.

33. What is $\frac{3}{4}\times 12$ using $3\times 12\div 4$?

    $9$. $3 \times 12 = 36$, then $36 \div 4 = 9$.

34. What is $\frac{2}{3}\times 9$ using $2\times 9\div 3$?

    $6$. $2 \times 9 = 18$, then $18 \div 3 = 6$.

35. What is $\frac{9}{10} \times 40$ by taking $9$ of the $10$ equal parts of $40$?

    $36$. Each part is $40 \div 10 = 4$, so $9$ parts equals $9 \times 4 = 36$.

36. What is $\frac{5}{2} \times 6$ interpreted as $5$ parts of $6$ split into $2$ equal parts?

    $15$. Each part is $\frac{6}{2}=3$, so $5$ parts equals $5\times 3=15$.

37. What is $\frac{3}{5} \times 20$ interpreted as $3$ parts of $20$ split into $5$ equal parts?

    $12$. Each part is $\frac{20}{5}=4$, so $3$ parts equals $3\times 4=12$.

38. What is $\frac{4}{3}\times 9$ using $4\times 9\div 3$?

    $12$. $4 \times 9 = 36$, then $36 \div 3 = 12$.

39. What is $ $ $\frac{3}{10}\times 50$ by finding one-tenth first?

    $15$. One-tenth is $50 \div 10 = 5$, so $3$ tenths equals $3 \times 5 = 15$.

40. What is the missing value $q$ if $ $ $\frac{3}{5}\times q=12$?

    $20$. If three-fifths of $q$ is $12$, then $q = 12 \div 3 \times 5 = 20$.

41. What is $\frac{4}{7} \times 21$ using $4 \times 21 \div 7$?

    $12$. Calculate: $4 \times 21 = 84$, then $84 \div 7 = 12$.

42. What is $ $ $\frac{7}{9}\times 27$ using partitioning into $9$ equal parts?

    $21$. Each part is $27 \div 9 = 3$, so $7$ parts equals $7 \times 3 = 21$.

43. What is $\frac{0}{b} \times q$ for any nonzero $b$?

    $0$. Zero parts of any quantity always equals zero.

44. What is $\frac{7}{10}\times 50$ interpreted as $7$ parts of $50\div 10$?

    $35$. $50 \div 10 = 5$ per part, so $7$ parts = $35$.

45. What is the missing numerator $a$ if $ $ $\frac{a}{6}\times 30=20$?

    $4$. Since $\frac{a}{6} \times 30 = 20$, we need $a \times 5 = 20$, so $a = 4$.

46. What is $ $ $\frac{2}{3}\times 18$ interpreted as $2$ parts when $18$ is split into $3$ equal parts?

    $12$. Each part is $18 \div 3 = 6$, so $2$ parts equals $2 \times 6 = 12$.

47. What is $\frac{9}{4}\times 8$ using $9\times 8\div 4$?

    $18$. $9 \times 8 = 72$, then $72 \div 4 = 18$.

48. What sequence of operations is equivalent to $ $ $\frac{a}{b}\times q$?

    $a\times q\div b$. Multiply by the numerator first, then divide by the denominator.

49. What is $ $ $\frac{5}{8}\times 32$ using the idea of $5$ parts out of $8$ equal parts?

    $20$. Each part is $32 \div 8 = 4$, so $5$ parts equals $5 \times 4 = 20$.

50. What is $\frac{3}{5} \times 25$ using $3 \times 25 \div 5$?

    $15$. Calculate: $3 \times 25 = 75$, then $75 \div 5 = 15$.

51. What is $\frac{6}{5}\times 25$ using the sequence $6\times 25\div 5$?

    $30$. Following the sequence: $6\times 25=150$, then $150\div 5=30$.

52. Identify the missing step: $\frac{a}{b}\times q=\frac{a\times q}{\square}$; what is $\square$?

    $b$. Denominator stays the same when converting to division.

53. What sequence of operations is equivalent to $\frac{a}{b} \times q$?

    $a \times q \div b$. Multiply first, then divide - equivalent to multiplying by the fraction.

54. Identify the missing value: $\frac{a}{b}\times q=a\times\frac{q}{\square}$.

    $b$. The denominator $b$ becomes the divisor in the equivalent expression.

55. What does $\frac{a}{b}\times q$ mean in words using "partition $q$ into $b$ equal parts"?

    $a$ parts when $q$ is partitioned into $b$ equal parts. The fraction tells us how many parts to take after dividing $q$.

56. What is the missing value $q$ if $ $ $\frac{1}{4}\times q=6$?

    $24$. If one-fourth of $q$ is $6$, then $q = 6 \times 4 = 24$.

57. What is $\frac{4}{9} \times 27$ by first finding one part $\frac{27}{9}$?

    $12$. Each part is $\frac{27}{9}=3$, so $4$ parts equals $4\times 3=12$.

58. What is $\frac{5}{6}\times 18$ using $5\times 18\div 6$?

    $15$. $5 \times 18 = 90$, then $90 \div 6 = 15$.

59. What does $\frac{a}{b} \times q$ mean using equal parts of $q$?

    $a$ parts of $q$ when $q$ is split into $b$ equal parts. The fraction tells us how many parts to take after dividing $q$ into $b$ equal pieces.

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