Divide Multi-Digit Numbers - 6th Grade Math

1. What is $6{,}529 \div 4$ written as a quotient with remainder?

   $1{,}632\,R^1$. $4$ goes into $65$ sixteen times with $1$ left, into $12$ three times, into $9$ twice.

2. What is $672\div 8$ using the standard algorithm?

   $84$. $8$ goes into $67$ eight times, then into $52$ six times, and into $48$ six times.

3. What is $4{,}095 \div 5$ using the standard algorithm?

   $819$. $5$ goes into $40$ eight times, into $9$ once, into $45$ nine times.

4. Identify the missing quotient digit: In $672 \div 8$, after $67 \div 8 = 8$, what is the next quotient digit?

   $4$. After $8 \times 8 = 64$, subtract to get $3$, bring down $2$ to get $32 \div 8 = 4$.

5. What is $735 \div 7$ using the standard algorithm?

   $105$. $7$ goes into $73$ ten times, into $35$ five times.

6. What is the quotient of $14{,}352 \div 9$ using the standard algorithm?

   $1{,}594\frac{2}{3}$. The remainder $6$ as a fraction over divisor $9$ gives $\frac{6}{9}=\frac{2}{3}$.

7. What is the quotient of $72{,}000 \div 9$ using the standard algorithm?

   $8{,}000$. Since $72000=72×1000$ and $72÷9=8$, the result is $8×1000=8000$.

8. Find the error: A student wrote $438 \div 3 = 14\,R18$. What is the correct result?

   $146$. Remainder $18 > 3$ (divisor), so continue dividing: $438 \div 3 = 146$.

9. What is $6{,}048 \div 12$ using the standard algorithm?

   $504$. $12$ goes into $60$ five times, into $4$ zero times, into $48$ four times.

10. What is $936\div 9$ using the standard algorithm?

    $104$. $9$ goes into $93$ ten times, then into $36$ four times exactly.

11. What check confirms a division answer is correct for $a\div b=q$ with remainder $r$?

    $a=bq+r$ with $0\le r<b$. This equation verifies division: dividend equals divisor times quotient plus remainder.

12. What is the quotient of $9{,}600 \div 12$ using the standard algorithm?

    $800$. Divide: $96÷12=8$, bring down zeros to get $800$.

13. What is the quotient and remainder of $14{,}352 \div 9$ using the standard algorithm?

    $1{,}594\ \text{R}\ 6$. Standard division gives quotient $1594$ with remainder $6$.

14. What is the quotient of $5,544 \div 12$ using the standard algorithm?

    $462$. Divide $5544$ by $12$: $55÷12=4$ R7, $74÷12=6$ R2, $24÷12=2$.

15. What is the quotient and remainder of $9{,}999 \div 8$ using the standard algorithm?

    $1{,}249\ \text{R}\ 7$. Divide $9999$ by $8$: quotient is $1249$ with remainder $7$.

16. What is the quotient of $1{,}365 \div 7$ using the standard algorithm?

    $195$. Divide step by step: $13÷7=1$ R6, $66÷7=9$ R3, $35÷7=5$.

17. What is $5607\div 3$ using the standard algorithm?

    $1869$. $3$ divides evenly: $5607 = 3 \times 1869$.

18. What is $5040\div 7$ using the standard algorithm?

    $720$. $7$ divides evenly: $5040 = 7 \times 720$.

19. What is the quotient of $1{,}248 \div 6$ using the standard algorithm?

    $208$. Work left to right: $12÷6=2$, $4÷6=0$ R4, $48÷6=8$.

20. What is the first step in the standard algorithm for $847 \div 6$?

    Divide the leftmost digits: $8 \div 6$. Start with the leftmost digit(s) that form a number $\geq$ divisor.

21. What is $2184\div 12$ using the standard algorithm?

    $182$. $12$ goes into $21$ once, into $98$ eight times, and into $24$ twice.

22. What is the quotient of $945 \div 5$ using the standard algorithm?

    $189$. Divide systematically: $9÷5=1$ R4, $44÷5=8$ R4, $45÷5=9$.

23. What is $8{,}017 \div 6$ written as a quotient with remainder?

    $1{,}336\,R^1$. $6$ goes into $80$ thirteen times with $2$ left, into $21$ three times, into $37$ six times.

24. What is $3{,}500 \div 40$ using the standard algorithm?

    $87\,R20$. $40$ goes into $350$ eight times with $30$ left, into $300$ seven times.

25. What is $5{,}832 \div 9$ using the standard algorithm?

    $648$. $9$ goes into $58$ six times, into $43$ four times, into $72$ eight times.

26. What is $9{,}072 \div 7$ using the standard algorithm?

    $1{,}296$. $7$ goes into $90$ twelve times, into $67$ nine times, into $42$ six times.

27. What is the quotient of $84{,}600 \div 30$ using the standard algorithm?

    $2{,}820$. Divide $84600$ by $30$: same as $8460÷3=2820$.

28. What does the digit written above the dividend represent in long division?

    A digit of the quotient. Each digit shows how many times the divisor fits into that portion.

29. What is $7{,}410 \div 6$ using the standard algorithm?

    $1{,}235$. $6$ goes into $74$ twelve times, into $21$ three times, into $30$ five times.

30. What is the check method for division using multiplication and subtraction?

    Check: $(\text{divisor}\times\text{quotient})+\text{remainder}=\text{dividend}$. Multiply quotient by divisor, add remainder to verify.

31. What is the quotient of $8{,}736 \div 16$ using the standard algorithm?

    $546$. Divide $8736$ by $16$: $87÷16=5$ R7, $73÷16=4$ R9, $96÷16=6$.

32. What is $1{,}248 \div 6$ using the standard algorithm?

    $208$. $6$ goes into $12$ twice, into $4$ zero times, into $48$ eight times.

33. What is $9{,}600 \div 15$ using the standard algorithm?

    $640$. $15$ goes into $96$ six times, into $60$ four times, into $0$ zero times.

34. What is the quotient of $864 \div 3$ using the standard algorithm?

    $288$. Divide each digit from left to right: $8÷3=2$, $6÷3=2$, $4÷3=1$ with remainder.

35. What is the rule for the remainder when dividing whole numbers?

    Remainder $<$ divisor. The remainder must always be less than what you're dividing by.

36. What is the quotient of $4{,}095 \div 9$ using the standard algorithm?

    $455$. Work through each digit: $40÷9=4$ R4, $49÷9=5$ R4, $45÷9=5$.

37. What is the quotient of $6{,}615 \div 15$ using the standard algorithm?

    $441$. Divide $6615$ by $15$: $66÷15=4$ R6, $61÷15=4$ R1, $15÷15=1$.

38. What is $7392\div 6$ using the standard algorithm?

    $1232$. $6$ divides evenly: $7392 = 6 \times 1232$.

39. What is the quotient of $7{,}488 \div 24$ using the standard algorithm?

    $312$. Divide $7488$ by $24$: $74÷24=3$ R2, $28÷24=1$ R4, $48÷24=2$.

40. What is the quotient of $2{,}304 \div 8$ using the standard algorithm?

    $288$. Each place divides evenly: $23÷8=2$ R7, $70÷8=8$ R6, $64÷8=8$.

41. What is the quotient of $9{,}801 \div 3$ using the standard algorithm?

    $3{,}267$. Divide each digit by $3$: $9÷3=3$, $8÷3=2$ R2, $20÷3=6$ R2, $21÷3=7$.

42. What is $9999\div 9$ using the standard algorithm?

    $1111$. Each digit is $9$, and $9 div 9 = 1$ for each place value.

43. What is $96 \div 3$ using the standard algorithm?

    $32$. $9 \div 3 = 3$, $6 \div 3 = 2$, so $96 \div 3 = 32$.

44. What is the quotient of $3{,}276 \div 4$ using the standard algorithm?

    $819$. Divide step by step: $32÷4=8$, $7÷4=1$ R3, $36÷4=9$.

45. What is $2{,}304 \div 8$ using the standard algorithm?

    $288$. $8$ goes into $23$ twice, into $70$ eight times, into $64$ eight times.

46. What is $1008\div 6$ using the standard algorithm?

    $168$. $6$ divides evenly: $1008 = 6 \times 168$.

47. What is $1440\div 12$ using the standard algorithm?

    $120$. $12$ goes into $14$ once, into $24$ twice, and into $0$ zero times.

48. What is the quotient and remainder of $8{,}019 \div 11$ using the standard algorithm?

    $729\ \text{R}\ 0$. Since $729×11=8019$ exactly, the remainder is $0$.

49. What is the meaning of the remainder in $53 \div 5 = 10\,R^3$?

    The leftover amount: $3$ not evenly divisible by $5$. The remainder is what's left after dividing evenly.

50. What is the quotient and remainder of $3{,}457 \div 6$ using the standard algorithm?

    $576\ \text{R}\ 1$. Divide $3457$ by $6$ to get quotient $576$ with remainder $1$.

51. What is the quotient of $5{,}040 \div 8$ using the standard algorithm?

    $630$. Work through: $50÷8=6$ R2, $24÷8=3$, $40÷8=5$ with no remainder.

52. What is the quotient of $12{,}096 \div 7$ using the standard algorithm?

    $1{,}728$. Divide $12096$ by $7$: work through to get $1728$ with no remainder.

53. What is the quotient of $975 \div 5$ using the standard algorithm?

    $195$. Divide systematically: $9÷5=1$ R4, bring down 7 to get $47÷5=9$ R2, then $25÷5=5$.

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