Solve Multi-Step Word Problems - 4th Grade Math

1. What is $p$ if $5p = 120$?

   $p = 24$. Divide both sides by $5$: $p = 120 \div 5$.

2. What is the equation for: "After buying $3$ items at $5 each, you have $18 left from $m$ dollars."

   $m - 3 \times 5 = 18$. Start with $m$, subtract cost of 3 items.

3. What equation represents: "$24$ cookies shared equally among $6$ friends; $c$ cookies per friend"?

   $c = 24 \div 6$. Division splits total equally among groups.

4. What is the correct interpretation of a remainder when the answer must be a whole number with no leftovers (for example, full meals)?

   Round down to the number of complete groups. Partial groups can't be used in this context.

5. What is the answer to $29 \div 5$ if you need the number of buses to seat everyone (each bus seats $5$)?

   $6$ buses. $29 \div 5 = 5$ R$4$; need extra bus for remainder.

6. What is the correct order of operations for $3 + 4 \times 2$ (no parentheses)?

   Multiply first, then add. Order of operations: multiply/divide before add/subtract.

7. What is the first step to solve a multistep word problem using the four operations?

   Identify what the problem is asking you to find. Understanding the goal helps choose operations.

8. Which estimate is best for $302 \div 6$: $300 \div 6$ or $360 \div 6$?

   $300 \div 6 = 50$. $302$ is closer to $300$ than $360$.

9. What is the value of $n$ in $4n = 28$?

   $n = 7$. Divide both sides by $4$: $28 \div 4 = 7$.

10. What is the best estimate of $62 \times 19$ by rounding to the nearest ten?

    $60 \times 20 = 1200$. Round: $62 \approx 60$ and $19 \approx 20$.

11. Identify the meaning of the remainder in $29 \div 5$ if the question asks "How many groups are needed?"

    Round up to the next whole group. Need an extra group for the remainder.

12. Identify the correct interpretation of a remainder when counting full groups (for example, buses or boxes).

    Round up if any remainder means one more group is needed. Partial groups still need a full container.

13. What is the best interpretation of $45 \div 8$ when you must make identical gift bags with $8$ items each?

    You can make $5$ full bags; $5$ items remain. Quotient gives complete bags; remainder is unused.

14. What is $48 \div 6 + 5$?

    $13$. Divide first: $48 \div 6 = 8$, then $8 + 5 = 13$.

15. What does the letter represent in the equation $3n + 8 = 29$ for a word problem?

    $n$ is the unknown quantity in the situation. Letters represent unknown values we need to find.

16. What is the number of leftover pencils if $58$ pencils are packed $10$ per box?

    $8$ leftover pencils. $58 \div 10 = 5$ R$8$; remainder is leftovers.

17. What is the value of $n$ in $96 \div n = 12$?

    $n = 8$. Since $96 \div n = 12$, then $n = 96 \div 12 = 8$.

18. What is the answer to $29 \div 5$ if you need the number of leftover students after making full teams of $5$?

    $4$ students left over. $29 \div 5 = 5$ R$4$; remainder is leftover.

19. What is the best estimate of $398 + 205$ by rounding to the nearest hundred?

    $600$. Round: $398 \approx 400$ and $205 \approx 200$.

20. Identify the meaning of the remainder in $29 \div 5$ if the question asks "How many are left over?"

    The remainder is the number left over. The remainder shows what doesn't fit into equal groups.

21. What is the number of buses needed if $58$ students ride in buses of $10$ students each?

    $6$ buses. $58 \div 10 = 5$ R$8$; need $6$ for all students.

22. What does the letter $n$ represent in an equation for a word problem?

    $n$ represents the unknown quantity in the problem. Letters stand for unknown values we need to find.

23. What operation should you use for "total of equal groups," such as $6$ bags with $4$ apples each?

    Multiplication. Equal groups mean repeated addition, which is multiplication.

24. What equation represents: "$3$ packs of stickers, $12$ per pack, then give away $7$; $s$ left"?

    $s = 3 \times 12 - 7$. Total stickers minus given away equals kept.

25. What is a reasonable estimate for $198 + 403$ using rounding to the nearest hundred?

    $200 + 400 = 600$. Round each number to nearest hundred, then add.

26. What is a quick estimate for $49 \times 21$ using rounding to the nearest ten?

    $50 \times 20 = 1000$. Round both factors to nearest ten.

27. Identify the equation for: "$5$ bags with $n$ apples each, plus $7$ apples, totals $47$."

    $5n + 7 = 47$. Translates words to algebraic equation with variable.

28. Find $n$: "A total of $72$ stickers are split equally into $n$ packs of $8$." What is $n$?

    $n = 9$. $72 \div 8 = 9$ gives number of packs.

29. Which equation matches: "$3$ packs of pencils, $12$ pencils per pack, then give away $5$ pencils; $n$ pencils remain"?

    $n = 3 \times 12 - 5$. Total pencils minus given away equals remaining.

30. What is the best interpretation of $45 \div 8$ when $45$ people need seats in vans that hold $8$ each?

    You need $6$ vans. Round up to ensure everyone has a seat.

31. What does the letter in an equation like $3n + 5 = 20$ represent in a word problem?

    The unknown quantity in the problem. Letters stand for values we need to find.

32. What is a quick estimate for $399 \div 8$ using compatible numbers?

    $400 \div 8 = 50$. Use $400$ as it divides evenly by $8$.

33. What is the value of $n$ in $n - 19 = 35$?

    $n = 54$. Add $19$ to both sides: $35 + 19 = 54$.

34. What is a quick reasonableness check using rounding for $198 + 403$?

    $200 + 400 = 600$ (estimate). Round to nearest hundreds for quick check.

35. What is $m$ if $m = (36 \div 6) + 7$?

    $m = 13$. Parentheses first: $36 \div 6 = 6$, then $6 + 7$.

36. What is a reasonable estimate for $79 \times 6$ using rounding to the nearest ten?

    $80 \times 6 = 480$. Round 79 to 80 for easier multiplication.

37. What is $7 \times 8 - 9$?

    $47$. Multiply first: $7 \times 8 = 56$, then $56 - 9 = 47$.

38. What is the best interpretation of $45 \div 8$ when $8$ students share pencils equally and extras are allowed?

    Each gets $5$ pencils; $5$ pencils remain. $45 \div 8 = 5$ remainder $5$ for equal sharing.

39. What is the answer to $29 \div 5$ if you need the number of full teams of $5$ (no extra players allowed)?

    $5$ teams. $29 \div 5 = 5$ R$4$; only full teams count.

40. Identify the best interpretation of $31 \div 5$ when $5$ people must each get a whole number of tickets.

    Each gets $6$ tickets; $1$ ticket is unused. Remainder represents leftover tickets.

41. Identify the meaning of the remainder in $29 \div 5$ if the question asks "How many full groups?"

    Ignore the remainder; use the quotient only. Full groups means no partial groups counted.

42. What equation represents: "$5$ bags with $8$ apples each, then eat $6$ apples; $a$ apples left"?

    $a = 5 \times 8 - 6$. Total apples minus eaten equals remaining.

43. What is the number of full boxes if $58$ pencils are packed $10$ per box and only full boxes count?

    $5$ full boxes. $58 \div 10 = 5$ R$8$; only complete boxes count.

44. What equation represents: "A book has $120$ pages, read $p$ pages per day for $5$ days; $p$"?

    $5p = 120$. Pages per day times days equals total pages.

45. What operation order should you follow to evaluate $24 - 3 \times 4$?

    Multiply, then subtract: $24 - 12$. Order of operations: multiplication before subtraction.

46. Assess reasonableness: Is $48 \times 19 = 912$ reasonable using $50 \times 20$?

    Yes; $50 \times 20 = 1000$, so $912$ is reasonable. Estimate confirms answer is in correct range.

47. What is $a$ if $a = 5 \times 8 - 6$?

    $a = 34$. $5 \times 8 = 40$, then $40 - 6 = 34$.

48. What is the total cost if $4$ notebooks cost $3 each and a pen costs $2?

    $14. Calculate $4 \times 3 + 2 = 12 + 2$.

49. What operation should you use for "shared equally," such as splitting $24$ cookies among $6$ students?

    Division. Sharing equally means splitting into equal parts.

50. What is the best estimate of $815 \div 4$ using compatible numbers?

    $800 \div 4 = 200$. Use $800 \div 4$ for easier mental math.

51. What is $120 - 6 \times 15$?

    $30$. Multiply first: $6 \times 15 = 90$, then $120 - 90 = 30$.

52. What is $s$ if $s = 3 \times 12 - 7$?

    $s = 29$. $3 \times 12 = 36$, then $36 - 7 = 29$.

53. What is the best interpretation of $31 \div 5$ when packing items into boxes of $5$ and no box can be partially filled?

    You need $7$ boxes. Round up when all items must be contained.

54. What is the correct interpretation of a remainder when dividing items equally and leftovers are allowed?

    The remainder is the number of leftover items. Division shows equal shares plus extras.

55. What is $c$ if $c = 24 \div 6$?

    $c = 4$. $24$ divided by $6$ equals $4$ per person.

56. Identify the best interpretation of $31 \div 5 = 6$ remainder $1$ when sharing equally.

    Each gets $6$ and $1$ is left over. Division with remainder shows equal distribution.

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