Divide Whole Numbers by Unit Fractions - 5th Grade Math

1. What is $1 \div \frac{1}{b}$ for a whole number $b$?

   $b$. One whole contains $b$ pieces of size $\frac{1}{b}$.

2. Identify the missing number: $\square \div \frac{1}{6} = 42$.

   $7$. Since $7 \times 6 = 42$, so $7 \div \frac{1}{6} = 42$.

3. What is $15 \div \frac{1}{10}$?

   $150$. Since $15 \div \frac{1}{10} = 15 \times 10 = 150$.

4. What is $5 \div \frac{1}{8}$?

   $40$. Apply the rule: $5 \div \frac{1}{8} = 5 \times 8$.

5. What is $6 \div \frac{1}{2}$?

   $12$. Since $6 \div \frac{1}{2} = 6 \times 2$.

6. What is $10 \div \frac{1}{10}$?

   $100$. Since $10 \div \frac{1}{10} = 10 \times 10$.

7. What is $5 \div \frac{1}{5}$?

   $25$. Since $5 \div \frac{1}{5} = 5 \times 5 = 25$.

8. What is $0 \div \frac{1}{7}$?

   $0$. Zero divided by any non-zero number equals zero.

9. What is $11 \div \frac{1}{11}$?

   $121$. Since $11 \div \frac{1}{11} = 11 \times 11 = 121$.

10. Identify the missing number: $9 \div \frac{1}{\square} = 72$.

    $8$. Since $9 \times 8 = 72$, so $9 \div \frac{1}{8} = 72$.

11. What is the rule for dividing a whole number $n$ by a unit fraction $\frac{1}{b}$?

    $n \div \frac{1}{b} = n \times b$. Dividing by a unit fraction equals multiplying by its denominator.

12. What is $2 \div \frac{1}{12}$?

    $24$. Since $2 \div \frac{1}{12} = 2 \times 12$.

13. What does $n \div \frac{1}{b}$ represent in words?

    How many $/b$ units are in $n$. Counts how many pieces of size $\frac{1}{b}$ fit into $n$ whole units.

14. What is $4 \div \frac{1}{8}$?

    $32$. Since $4 \div \frac{1}{8} = 4 \times 8 = 32$.

15. What is $7 \div \frac{1}{3}$?

    $21$. Apply the rule: $7 \div \frac{1}{3} = 7 \times 3$.

16. What is $3 \div \frac{1}{9}$?

    $27$. Since $3 \div \frac{1}{9} = 3 \times 9$.

17. What is $12 \div \frac{1}{6}$?

    $72$. Apply the rule: $12 \div \frac{1}{6} = 12 \times 6$.

18. Which expression is equivalent to $6 \div \frac{1}{4}$: $6 \times 4$ or $6 \times \frac{1}{4}$?

    $6 \times 4$. Dividing by $\frac{1}{4}$ means multiplying by 4.

19. What is $4 \div \frac{1}{7}$?

    $28$. Since $4 \div \frac{1}{7} = 4 \times 7$.

20. What is the unit fraction divisor in $5 \div \frac{1}{b} = 35$?

    $\frac{1}{7}$. Since $5 \times 7 = 35$, the divisor is $\frac{1}{7}$.

21. What is $11 \div \frac{1}{2}$?

    $22$. Since $11 \div \frac{1}{2} = 11 \times 2$.

22. What is $6 \div \frac{1}{2}$?

    $12$. Since $6 \div \frac{1}{2} = 6 \times 2 = 12$.

23. What is $8 \div \frac{1}{4}$?

    $32$. Since $8 \div \frac{1}{4} = 8 \times 4$.

24. What is $15 \div \frac{1}{3}$?

    $45$. Since $15 \div \frac{1}{3} = 15 \times 3$.

25. What is $1 \div \frac{1}{8}$?

    $8$. Since $1 \div \frac{1}{8} = 1 \times 8$.

26. Find $n$ if $n \div \frac{1}{4} = 28$.

    $7$. Since $n \times 4 = 28$, divide both sides by 4.

27. What is $9 \div \frac{1}{6}$?

    $54$. Since $9 \div \frac{1}{6} = 9 \times 6$.

28. Identify the equivalent multiplication for $n \div \frac{1}{b}$.

    $n \times b$. Dividing by $\frac{1}{b}$ is the same as multiplying by $b$.

29. What is $12 \div \frac{1}{8}$?

    $96$. Since $12 \div \frac{1}{8} = 12 \times 8$.

30. What does $n \div \frac{1}{b}$ represent in words when $n$ is a whole number?

    How many $\frac{1}{b}$-size parts are in $n$ wholes. Counts how many pieces of size $\frac{1}{b}$ fit into $n$ wholes.

31. What is $7 \div \frac{1}{5}$?

    $35$. Since $7 \div \frac{1}{5} = 7 \times 5$.

32. Find $n$ if $n \div \frac{1}{6} = 54$.

    $9$. Since $n \times 6 = 54$, divide both sides by 6.

33. What is $0 \div \frac{1}{b}$ for any whole number $b$?

    $0$. Zero divided by any fraction equals zero.

34. What is $5 \div \frac{1}{3}$?

    $15$. Since $5 \div \frac{1}{3} = 5 \times 3$.

35. What does $n \div \frac{1}{b}$ equal for whole numbers $n$ and $b$?

    $n \times b$. Dividing by a unit fraction is the same as multiplying by its denominator.

36. Identify the missing number: $x = 10 \div \frac{1}{4}$. What is $x$?

    $40$. Since $10 \div \frac{1}{4} = 10 \times 4 = 40$.

37. What is $14 \div \frac{1}{4}$?

    $56$. Since $14 \div \frac{1}{4} = 14 \times 4$.

38. What is $14 \div \frac{1}{7}$?

    $98$. Since $14 \div \frac{1}{7} = 14 \times 7 = 98$.

39. What is $9 \div \frac{1}{5}$?

    $45$. Apply the rule: $9 \div \frac{1}{5} = 9 \times 5$.

40. What is $2 \div \frac{1}{3}$?

    $6$. Since $2 \div \frac{1}{3} = 2 \times 3 = 6$.

41. What is $3 \div \frac{1}{12}$?

    $36$. Since $3 \div \frac{1}{12} = 3 \times 12 = 36$.

42. What is $0 \div \frac{1}{5}$?

    $0$. Zero divided by any non-zero number equals zero.

43. What is the value of $1 \div \frac{1}{b}$ for whole number $b$?

    $b$. One whole contains $b$ parts of size $\frac{1}{b}$.

44. What is $7 \div \frac{1}{2}$?

    $14$. Since $7 \div \frac{1}{2} = 7 \times 2 = 14$.

45. What is $18 \div \frac{1}{9}$?

    $162$. Since $18 \div \frac{1}{9} = 18 \times 9 = 162$.

46. What is $9 \div \frac{1}{3}$?

    $27$. Since $9 \div \frac{1}{3} = 9 \times 3 = 27$.

47. What is $13 \div \frac{1}{2}$?

    $26$. Since $13 \div \frac{1}{2} = 13 \times 2 = 26$.

48. What is $8 \div \frac{1}{4}$?

    $32$. Since $8 \div \frac{1}{4} = 8 \times 4 = 32$.

49. What is $20 \div \frac{1}{5}$?

    $100$. Since $20 \div \frac{1}{5} = 20 \times 5 = 100$.

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