Divide Multi-Digit Numbers - 4th Grade Math

1. What equation shows the division relationship for quotient $q$ and remainder $r$: $d \div s = q\ \text{R}\ r$?

   $d = s\times q + r$. Dividend equals divisor times quotient plus remainder.

2. What is the quotient and remainder of $1{,}006 \div 3$?

   $335$ remainder $1$. $1006 = 3 \times 335 + 1$, leaving remainder $1$.

3. What is the quotient and remainder of $3{,}726 \div 9$?

   $414$ remainder $0$. $3726 = 9 \times 414$ with no remainder.

4. What is the quotient and remainder of $4{,}095 \div 7$?

   $585$ remainder $0$. $4095 = 7 \times 585 + 0$, divides evenly with no remainder.

5. What is the quotient and remainder of $4{,}005 \div 6$?

   $667\ \text{R}\ 3$. $6 \times 667 = 4{,}002$, and $4{,}005 - 4{,}002 = 3$.

6. What is the quotient and remainder of $802 \div 5$?

   $160\ \text{R}\ 2$. Divide: $800÷5=160$, then $2÷5$ gives remainder $2$.

7. What is the quotient and remainder of $905 \div 8$?

   $113$ remainder $1$. $905 = 8 \times 113 + 1$, so quotient is $113$ with remainder $1$.

8. What equation checks the division $983 \div 7 = 140$ remainder $3$?

   $7 \times 140 + 3 = 983$. Multiply divisor by quotient and add remainder to check division.

9. What is the quotient and remainder of $68 \div 7$?

   $9\ \text{R}\ 5$. $7 \times 9 = 63$, and $68 - 63 = 5$.

10. What is the missing remainder in $6 \times 23 + r = 140$ for $140 \div 6$?

    $r = 2$. $6 \times 23 = 138$, so $r = 140 - 138 = 2$.

11. What is the quotient and remainder of $2{,}118 \div 6$?

    $353\ \text{R}\ 0$. $6×353=2118$ exactly, no remainder.

12. Identify the missing number: $6 \times 47 + 5 = \square$.

    $287$. $6 \times 47 = 282$, then $282 + 5 = 287$.

13. What is the quotient and remainder of $2{,}345 \div 6$?

    $390\ \text{R}\ 5$. $6 \times 390 = 2{,}340$, and $2{,}345 - 2{,}340 = 5$.

14. What is the quotient and remainder of $95 \div 6$?

    $15$ remainder $5$. $95 = 6 \times 15 + 5$, so $5$ is left over after dividing.

15. What is the quotient and remainder of $1{,}248 \div 6$?

    $208$ remainder $0$. $1248 = 6 \times 208$ with no remainder.

16. What is the quotient and remainder of $458 \div 7$?

    $65$ remainder $3$. $458 = 7 \times 65 + 3$, so quotient is $65$ with remainder $3$.

17. Which is correct for $239 \div 4$: $59\ \text{R}\ 3$ or $58\ \text{R}\ 7$?

    $59\ \text{R}\ 3$. Check: $4 \times 59 + 3 = 239$ ✓, but $4 \times 58 + 7 = 239$ ✗.

18. What must be true about the remainder $r$ when dividing by a one-digit divisor $b$?

    $0 \le r < b$. Remainder must be non-negative and less than the divisor.

19. What is the quotient and remainder of $1{,}999 \div 8$?

    $249\ \text{R}\ 7$. $8×249=1992$, leaving $7$ remainder.

20. What is the quotient and remainder of $4{,}087 \div 8$?

    $510$ remainder $7$. $4087 = 8 \times 510 + 7$, leaving remainder $7$.

21. Identify the missing number: $7 \times 63 + \square = 444$.

    $3$. $444 - 441 = 3$, where $7 \times 63 = 441$.

22. What is the quotient and remainder of $73 \div 6$?

    $12$ remainder $1$. $73 = 6 \times 12 + 1$, so quotient is $12$ with remainder $1$.

23. What does the remainder mean in $47 \div 5 = 9\ \text{R}\ 2$?

    $2$ is the amount left over after making $9$ equal groups of $5$. The remainder is what's left after dividing into equal groups.

24. What is the quotient and remainder of $945 \div 7$?

    $135\ \text{R}\ 0$. Since $7×135=945$ exactly, there's no remainder.

25. What is $3{,}600 \div 9$?

    $400$. $36$ hundreds divided by $9$ equals $4$ hundreds.

26. What is the quotient and remainder of $324 \div 3$?

    $108\ \text{R}\ 0$. $324$ divides evenly by $3$ with no remainder.

27. What is the quotient and remainder of $2{,}468 \div 7$?

    $352$ remainder $4$. $2468 = 7 \times 352 + 4$, leaving remainder $4$.

28. What is the quotient and remainder of $1{,}236 \div 4$?

    $309\ \text{R}\ 0$. $1{,}236$ divides evenly by $4$ with no remainder.

29. What is the quotient and remainder of $2{,}015 \div 3$?

    $671$ remainder $2$. $2015 = 3 \times 671 + 2$, so quotient is $671$ with remainder $2$.

30. What is the quotient and remainder of $517 \div 4$?

    $129$ remainder $1$. $517 = 4 \times 129 + 1$, leaving remainder $1$.

31. What is $6{,}000 \div 6$?

    $1{,}000$. $6$ thousands divided by $6$ equals $1$ thousand.

32. What is the quotient and remainder of $1{,}444 \div 8$?

    $180$ remainder $4$. $1444 = 8 \times 180 + 4$, so quotient is $180$ with remainder $4$.

33. What is the missing remainder $r$ in $256 = 9 \times 28 + r$?

    $4$. $9 \times 28 = 252$, so $r = 256 - 252 = 4$.

34. What is the quotient and remainder of $2{,}304 \div 6$?

    $384$ remainder $0$. $2304 = 6 \times 384 + 0$, divides evenly with no remainder.

35. What is the quotient and remainder of $84 \div 7$?

    $12$ remainder $0$. $84 = 7 \times 12$ with no remainder since $84$ is divisible by $7$.

36. What is the missing dividend: $\square \div 9 = 72\ \text{R}\ 4$?

    $652$. Dividend = $9 \times 72 + 4 = 648 + 4 = 652$.

37. What is the quotient and remainder of $1{,}004 \div 9$?

    $111\ \text{R}\ 5$. $9×111=999$, so $1004-999=5$ remainder.

38. What is the quotient and remainder of $1{,}248 \div 4$?

    $312\ \text{R}\ 0$. $4×312=1248$ exactly, so remainder is $0$.

39. What is the quotient and remainder of $3{,}482 \div 9$?

    $386\ \text{R}\ 8$. $9 \times 386 = 3{,}474$, and $3{,}482 - 3{,}474 = 8$.

40. What is the quotient and remainder of $1{,}365 \div 7$?

    $195$ remainder $0$. $1365 = 7 \times 195$ exactly.

41. What is the quotient and remainder of $457 \div 8$?

    $57\ \text{R}\ 1$. $8 \times 57 = 456$, and $457 - 456 = 1$.

42. What is the quotient and remainder of $2{,}304 \div 9$?

    $256$ remainder $0$. $2304 = 9 \times 256$ exactly, no remainder.

43. What is the value of $r$ if $6{,}172 \div 7 = 881\ \text{R}\ r$?

    $5$. $7 \times 881 = 6{,}167$, so $r = 6{,}172 - 6{,}167 = 5$.

44. Which option is a valid remainder when dividing by $7$: $0$, $7$, or $9$?

    $0$. Only $0$ is valid; remainders must be less than divisor $7$.

45. What equation checks that quotient $q$ and remainder $r$ are correct for $a \div b$?

    $a = bq + r$, with $0 \le r < b$. Division algorithm: dividend equals divisor times quotient plus remainder.

46. What is the quotient and remainder of $2{,}052 \div 6$?

    $342$ remainder $0$. $2052 = 6 \times 342$ with no remainder.

47. Which option is a correct check for $728 \div 9 = 80$ remainder $8$?

    $9 \times 80 + 8 = 728$. Verifies by multiplying divisor times quotient plus remainder.

48. What is the missing quotient $q$ in $1{,}152 = 8q + 0$?

    $144$. $q = 1152 \div 8 = 144$ since remainder is $0$.

49. What is the quotient of $3{,}600 \div 8$ using place value?

    $450$. $3{,}600 \div 8 = 450$ with no remainder.

50. What is the quotient and remainder of $3{,}505 \div 6$?

    $584$ remainder $1$. $3505 = 6 \times 584 + 1$, leaving remainder $1$.

51. What is the quotient and remainder of $1{,}007 \div 5$?

    $201$ remainder $2$. $1007 = 5 \times 201 + 2$, so quotient is $201$ with remainder $2$.

52. What is $6 \times 300 + 6 \times 40 + 6 \times 2$ equal to (as in an area model)?

    $2{,}052$. Distributive property: $6(300 + 40 + 2) = 6 \times 342$.

53. What must be true about the remainder $r$ in $d = s\times q + r$ when dividing by $s$?

    $0 \le r < s$. Remainder must be non-negative and less than divisor.

54. What is the quotient and remainder of $2{,}019 \div 5$?

    $403$ remainder $4$. $2019 = 5 \times 403 + 4$, leaving remainder $4$.

55. What is the quotient and remainder of $1{,}000 \div 7$?

    $142\ \text{R}\ 6$. $7 \times 142 = 994$, and $1{,}000 - 994 = 6$.

56. What is the quotient and remainder of $432 \div 8$?

    $54$ remainder $0$. $432 = 8 \times 54$ exactly, so no remainder.

57. What is the quotient and remainder of $999 \div 4$?

    $249$ remainder $3$. $999 = 4 \times 249 + 3$, so quotient is $249$ with remainder $3$.

58. What must be true about the remainder $r$ in $n \div d = q$ remainder $r$?

    $0 \le r < d$. The remainder must be non-negative and less than the divisor.

59. Identify the missing quotient: $8 \times \square + 6 = 310$.

    $38$. $(310 - 6) \div 8 = 304 \div 8 = 38$.

60. What is the quotient and remainder of $3{,}999 \div 8$?

    $499$ remainder $7$. $3999 = 8 \times 499 + 7$, leaving remainder $7$.

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