Solve Multiplicative Comparison Word Problems - 4th Grade Math

1. What is $x$ if "A tree is $6$ times as tall as a $5$ ft bush" and $x$ is the tree height?

   $x = 30$. Tree is $6 \times 5 = 30$ ft tall.

2. Choose the correct equation: "Mia has $18$ pencils. She has $3$ times as many as Leo."

   $18 = 3\ell$. Mia's 18 pencils equals 3 times Leo's amount ($\ell$).

3. What is the unknown in $n = 6 \times 9$ if the word problem asks for the larger amount?

   $n$. $n$ represents the product, which is the larger amount.

4. Identify the equation for: "Lee has $3$ times as many marbles as Sam." Use $S$ and $L$.

   $L = 3S$. Lee's marbles equal 3 times Sam's marbles.

5. Find $x$: "Mia has $28$ stickers, which is $4$ times as many as Noah."

   $x = 7$. Divide: $28 \div 4 = 7$ stickers for Noah.

6. Identify the equation for: "Sam has $3$ times as many marbles as Lee." Use $S$ and $L$.

   $S = 3L$. Sam's marbles equal 3 times Lee's marbles.

7. Find the larger amount: Ben has $7$ marbles. Ava has $4$ times as many as Ben.

   $28$. Multiply: $7 \times 4 = 28$ marbles.

8. Find $x$: "A movie is $2$ times as long as $45$ minutes" where $x$ is the movie length in minutes.

   $x = 90$. Movie is $2 \times 45 = 90$ minutes long.

9. What equation matches: "Liam has $4$ times as many stickers as Mia" (Mia = $m$, Liam = $l$)?

   $l = 4m$. Liam has $4$ times Mia's amount, so multiply $m$ by $4$.

10. Find and correct the equation error: "$A$ is $3$ times as many as $B$," written as $A=B+3$.

    Correct equation: $A = 3B$. "Times as many" requires multiplication, not addition.

11. Find $x$: "$63$ is $7$ times as many as $x$."

    $x = 9$. Divide: $63 \div 7 = 9$.

12. What does the phrase "$3$ times as many" mean in a multiplicative comparison?

    The larger amount equals $3 \times$ the smaller amount. In multiplicative comparison, one quantity is a multiple of another.

13. What is $x$ if "A jar holds $5$ times as many marbles as $9$ marbles" and $x$ is the jar amount?

    $x = 45$. Jar holds $5 \times 9 = 45$ marbles.

14. What is $x$ if "Sam has $3$ times as many coins as $8$ coins" and $x$ is Sam's coins?

    $x = 24$. Sam has $3 \times 8 = 24$ coins.

15. Which comparison is additive: "$12$ fewer than" or "$3$ times as many"?

    "$12$ fewer than" is additive. 'Fewer than' indicates subtraction, which is additive comparison.

16. What equation matches: "Sara has $4$ times as many stickers as Tom," if Tom has $t$ stickers?

    $s = 4t$. Sara's amount equals 4 times Tom's amount.

17. What is $x$ if "A cat weighs $24$ lb, which is $3$ times as much as a kitten" and $x$ is the kitten's weight?

    $x = 8$. Kitten weighs $24 \div 3 = 8$ lb.

18. What is the unknown in $x = 5 \times 7$?

    $x$. The variable before the equals sign is the unknown.

19. Find $x$: "A ribbon is $4$ times as long as a $6$ cm ribbon."

    $x = 24$. Multiply: $4 \times 6 = 24$ cm.

20. What does the phrase "$5$ fewer than" mean: additive or multiplicative comparison?

    Additive comparison. "Fewer than" indicates subtraction, not multiplication.

21. Identify the unknown: "$P$ is $7$ times $Q$." Which is larger, $P$ or $Q$ (assume $Q>0$)?

    $P$ is larger. When multiplying by a factor greater than 1, the result is larger.

22. Find and correct the equation for "$18$ is $3$ times as many as $x$": Is it $18 = 3 + x$ or $18 = 3x$?

    Correct: $18 = 3x$. Multiplicative comparison uses multiplication, not addition.

23. What does the phrase "$a$ times as much as $b$" mean in an equation?

    $a \times b$. "Times as much" means multiply the quantities together.

24. Identify whether this is additive or multiplicative: "Jin has $6$ more books than Kai."

    Additive comparison. "More" indicates addition, not multiplication.

25. Which comparison is multiplicative: "$12$ more than $3$" or "$12$ times as many as $3$"?

    "$12$ times as many as $3$". "Times as many" uses multiplication; "more than" uses addition.

26. Identify whether this is additive or multiplicative: "Jin has $6$ times as many books as Kai."

    Multiplicative comparison. "Times as many" indicates multiplication.

27. What is the factor $k$ if $L$ is $k$ times $S$, and $L=27$ and $S=9$?

    $k = 3$. Find the factor: $27 \div 9 = 3$.

28. Find Leos pencils: Mia has $18$ pencils, which is $3$ times Leos amount.

    $6$. Divide: $18 \div 3 = 6$ pencils.

29. Identify the operation: In "$6$ times as many," do you multiply or divide?

    Multiply. 'Times as many' always means multiply in word problems.

30. Which equation matches: "A number $x$ is $5$ times as many as $45$"?

    $x = 5 \times 45$. The unknown is 5 times the given value.

31. What operation finds the larger amount when you know the smaller amount and the factor?

    Multiply: $\text{larger} = \text{factor} \times \text{smaller}$. To find the larger quantity in multiplicative comparison.

32. Find $o$: "There are $18$ apples, which is $2$ times the number of oranges $o$."

    $o = 9$. Divide both sides by 2: $18 \div 2 = 9$.

33. Which equation matches "$A$ is $6$ more than $B$": $A=6B$ or $A=B+6$?

    $A = B + 6$. "More than" indicates addition, not multiplication.

34. What equation matches: "A book costs $3$ times as much as a pen" (book = $b$, pen = $p$)?

    $b = 3p$. Book costs $3$ times pen's price, so multiply $p$ by $3$.

35. What is $x$ if "A ribbon is $4$ times as long as $6$ cm" and $x$ is the ribbon length?

    $x = 24$. Ribbon is $4 \times 6 = 24$ cm long.

36. Which comparison is multiplicative: "$8$ more than" or "$8$ times as many"?

    "$8$ times as many" is multiplicative. 'Times as many' indicates multiplication, not addition.

37. Identify the operation: In "$\frac{1}{4}$ as many," do you multiply or divide?

    Multiply by $\frac{1}{4}$ (or divide by $4$). A fraction 'as many' means multiply by that fraction.

38. Which equation matches "$A$ is $6$ times as many as $B$": $A=6B$ or $A=B+6$?

    $A = 6B$. "Times as many" means multiply, not add.

39. What does the phrase "$a$ times larger than $b$" mean for CCSS.4.OA.2 problems?

    Use multiplication: $b \times a$ (not $b + a$). "Times larger" means multiply, not add, in grade 4 contexts.

40. What operation finds the smaller amount when you know the larger amount and the factor?

    Divide: $\text{smaller} = \text{larger} \div \text{factor}$. To find the smaller quantity in multiplicative comparison.

41. What does the phrase "$3$ times as many" mean in a comparison problem?

    It means multiply the smaller amount by $3$. In multiplicative comparison, 'times as many' indicates multiplication.

42. What is $x$ if "$56$ is $7$ times as many as a number $x$"?

    $x = 8$. Divide: $56 \div 7 = 8$.

43. Find $x$: "$9$ is $3$ times as many as $x$."

    $x = 3$. Divide: $9 \div 3 = 3$.

44. Identify the operation: "$24$ is $3$ times as many as $8$." What operation relates $24$ and $8$?

    Multiplication: $8 \times 3 = 24$. "3 times as many as 8" means $3 \times 8 = 24$.

45. What number is $8$ times as many as $5$?

    $40$. Multiply: $8 \times 5 = 40$.

46. Choose the correct equation: "There are $18$ apples, which is $2$ times the number of oranges $o$."

    $18 = 2o$. The number of apples equals 2 times the oranges.

47. Find $x$: "A tree is $5$ times as tall as a $3$ ft shrub."

    $x = 15$. Multiply: $5 \times 3 = 15$ ft.

48. What is $36$ divided by $4$ in a "times as many" comparison (smaller amount)?

    $9$. Divide to find the smaller amount: $36 \div 4 = 9$.

49. What does the phrase "$4$ times as many as" mean: additive or multiplicative comparison?

    Multiplicative comparison. "Times as many" indicates one quantity is a multiple of another.

50. Which equation matches: "$45$ is $5$ times as many as a number $x$"?

    $45 = 5x$. The larger amount equals 5 times the smaller amount.

51. What is $6$ times as many as $7$?

    $42$. Multiply: $6 \times 7 = 42$.

52. Find $x$: "A box holds $3$ times as many pencils as a box with $8$ pencils."

    $x = 24$. Multiply: $3 \times 8 = 24$ pencils.

53. Find $x$: "A $48$-inch rope is $6$ times as long as a shorter rope."

    $x = 8$. Divide: $48 \div 6 = 8$ inches.

54. Find $x$: "A $36$-page chapter is $3$ times as long as a shorter chapter."

    $x = 12$. Divide: $36 \div 3 = 12$ pages.

55. What is $x$ if "$63$ is $9$ times as many as $x$"?

    $x = 7$. Divide: $63 \div 9 = 7$.

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