- A farmer has chickens and cows on his farm. He has 60 chickens, which is 5 times as many as the number of cows. Each cow produces 3 gallons of milk per day. If the farmer sells milk for $2 per gallon, how much money does he make from milk in one day?
Answer: $72 from milk daily
Number of cows: 60 ÷ 5 = 12 cows. Total milk: 12 × 3 = 36 gallons per day. Money earned: 36 × $2 = $72 per day. Choice A stops at the gallons amount. Choice C uses 60 × 2 incorrectly. Choice D uses 60 × 3 × 2 incorrectly.
- Ms. Wong's class has collected 3 cans so far and needs 15 cans total for their art project. How many more cans do they need to collect?
Answer: 12 more cans needed
12 more cans is correct because 15−3=12. 3 more cans is incorrect because it mistakenly subtracts in the wrong direction. 9 more cans is incorrect because it does not match either number in the problem. 15 more cans is incorrect because it ignores the 3 cans already collected. - Yuki has 6 comic books. Carlos has 8 times as many comic books as Yuki. How many comic books does Carlos have?
Answer: 48 comic books
Carlos has 48 comic books because 8 times as many means multiplying 6 by 8, which is 48. Choice A adds 6 and 8 instead of multiplying. Choice B repeats the multiplier instead of the total. Choice C uses 7 instead of 8 as the multiplier.
- Sofia has 8 stickers. Jamal has 5 times as many stickers as Sofia. How many stickers does Jamal have?
Answer: 40 stickers
Jamal has 40 stickers because "times as many" means multiplying: 8 × 5 = 40. Choice B adds 8 + 5 instead, treating "times as many" like "more than." Choice A adds 5 extra onto the correct product. Choice D repeats Sofia's total instead of finding Jamal's.
- A bakery sold 144 muffins on Saturday. They sold 6 times as many muffins as cookies on Saturday. On Sunday, they sold 4 times as many cookies as they sold on Saturday. How many cookies did they sell on Sunday?
Answer: 96 cookies on Sunday
Saturday's cookie total equals 144 muffins divided by 6, which is 24 cookies. Sunday's cookies are 4 times that amount: 4 x 24 = 96. Choice A (24) stops after finding Saturday's total and forgets to multiply by 4. Choice D (576) multiplies the muffin count instead of the cookie count. Choice B (36) doesn't match either step of the correct calculation.
- Jamal has 42 baseball cards. Sofia has 6 baseball cards. How many times as many baseball cards does Jamal have as Sofia?
Answer: 7
The correct answer is C, 7, because 42 divided by 6 equals 7. Choice A, 48, comes from adding 42 and 6 instead of dividing. Choice B, 36, comes from subtracting 6 from 42 instead of dividing. Choice D, 6, simply restates Sofia's number of cards instead of comparing the two amounts.
- A movie theater has 3 screens. Screen 1 has 120 seats. Screen 2 has 4 times as many seats as Screen 3. Screen 1 has 2 times as many seats as Screen 3. If all screens are completely full for a show, how many people are watching movies total?
Answer: 420 people watching movies
Since Screen 1 has 2 times as many seats as Screen 3, Screen 3 has 120 / 2 = 60 seats. Screen 2 has 4 times as many seats as Screen 3, or 4 x 60 = 240 seats. Adding all three screens gives 120 + 60 + 240 = 420 people. Choices A, B, and C come from mixing up which screen the multipliers apply to.
- A toy store has red, blue, and green bouncy balls. There are 48 red balls, which is 6 times as many as blue balls. The green balls number 3 times as many as blue balls. What is the total number of bouncy balls in the store?
Answer: 80 total bouncy balls
Blue balls: 48 ÷ 6 = 8 blue balls. Green balls: 8 × 3 = 24 green balls. Total: 48 + 8 + 24 = 80 balls. Choice A adds 48 + 8 only. Choice B adds 48 + 24 only. Choice D incorrectly calculates green balls as 48 + 8 = 56, then adds all incorrectly.
- Sofia has 36 stickers. Jamal has 9 stickers. Sofia has how many times as many stickers as Jamal?
Answer: 4 times as many
4 times as many is correct because 36÷9=4. 45 times as many is incorrect because it results from adding instead of dividing. 3 times as many is incorrect because it does not match the actual quotient. 27 times as many is incorrect because it results from subtracting instead of dividing (36−9=27). - At a carnival, the Ferris wheel has 36 seats. This is 9 times as many seats as the bumper car ride. The roller coaster has 5 times as many seats as the bumper cars, but 12 of its seats are broken. How many working seats does the roller coaster have?
Answer: 8 working roller coaster seats
The bumper cars have 36÷9=4 seats. The roller coaster has 5×4=20 seats, but 12 are broken, leaving 20−12=8 working seats. Choice B does not match any correct intermediate step. Choice C gives the roller coaster's total seats before subtracting the broken ones. Choice D uses an incorrect number of bumper car seats. - Maya has 8 trading cards. Keisha has 4 times as many trading cards as Maya. How many trading cards does Keisha have?
Answer: 32 trading cards
32 trading cards is correct because 4×8=32. 4 trading cards is incorrect because it uses only one of the two given numbers. 12 trading cards is incorrect because it results from adding instead of multiplying (8+4=12). 40 trading cards is incorrect because it results from multiplying by 5 instead of 4. - Emma has 7 marbles. Marcus has 49 marbles. Marcus has how many times as many marbles as Emma? Use the equation 49=?×7.
Answer: 7 times as many
This question tests 4th grade ability to multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison (CCSS.4.OA.2). Multiplicative comparison uses 'times as many/much' language—'A is n times as many as B' means A = n × B, where A is the larger quantity (product), n is the multiplier (how many times), and B is the reference quantity (what's being multiplied). This is different from additive comparison ('A is n more than B' means A = B + n). To solve multiplicative comparisons: if finding the larger quantity (product), multiply; if finding how many times (multiplier) or the reference quantity, divide. This problem states Emma has 7 marbles and Marcus has 49 marbles, asking how many times as many Marcus has as Emma, identifying 49 as the product, 7 as the reference quantity, and asking for the multiplier, with the equation 49 = ? × 7 requiring division to solve. Choice B is correct because dividing product by reference: 49 ÷ 7 = 7 times as many, which demonstrates understanding of multiplicative comparison and choosing the correct operation. Choice A represents multiplying instead of dividing (7 × 6 = 42, perhaps miscounting), which happens when students divide in the wrong direction or confuse operations. To help students: Distinguish multiplicative from additive comparison. MULTIPLICATIVE: 'times as many/much' → multiply or divide. ADDITIVE: 'more than, less than' → add or subtract. For multiplicative problems, identify three parts: (1) Reference quantity (being compared to), (2) Multiplier (how many times), (3) Product (result). Then: Product = Multiplier × Reference. If product unknown → multiply. If multiplier unknown → divide product by reference. If reference unknown → divide product by multiplier. Use bar models: draw small bar for reference, large bar for product (n times as long), label multiplier. Compare: '5 times as many as 7' = 5 × 7 = 35, but '5 more than 7' = 7 + 5 = 12 (very different!). Practice distinguishing language. Watch for: confusing 'times as many' with 'more than,' using addition when should multiply, dividing wrong direction, and not identifying which quantity is unknown.
- Maria has 24 stickers. She has 3 times as many stickers as Tom. Tom has twice as many stickers as Lisa. How many stickers does Lisa have?
Answer: 4 stickers
First, find how many stickers Tom has: Since Maria has 3 times as many as Tom, and Maria has 24, then 24 ÷ 3 = 8 stickers for Tom. Next, find Lisa's stickers: Since Tom has twice as many as Lisa, and Tom has 8, then 8 ÷ 2 = 4 stickers for Lisa. Choice B incorrectly stops at Tom's amount. Choice C uses additive thinking (24 - 12). Choice D confuses the multiplicative relationships.
- Chen saved $48, which is 6 times as much as Amir saved. How much did Amir save?
Answer: $8
This question tests 4th grade ability to multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison (CCSS.4.OA.2). Multiplicative comparison uses 'times as many/much' language—'A is n times as many as B' means A = n × B, where A is the larger quantity (product), n is the multiplier (how many times), and B is the reference quantity (what's being multiplied). This is different from additive comparison ('A is n more than B' means A = B + n). To solve multiplicative comparisons: if finding the larger quantity (product), multiply; if finding how many times (multiplier) or the reference quantity, divide. This problem states Chen saved $48, which is 6 times as much as Amir saved, identifying $48 as the product, 6 as the multiplier, and asking for the reference quantity (Amir's savings), with the equation 48 = 6 × ? requiring division to solve. Choice A is correct because dividing the product by the multiplier, 48 ÷ 6 = 8, gives the reference quantity, demonstrating understanding of multiplicative comparison and choosing the correct operation. Choice C represents subtracting instead of dividing (48 - 6 = 42), which happens when students confuse the operations or misinterpret 'times as much' as an additive difference. To help students: Distinguish multiplicative from additive comparison—MULTIPLICATIVE: 'times as many/much' → multiply or divide; ADDITIVE: 'more than, less than' → add or subtract. For multiplicative problems, identify three parts: (1) Reference quantity, (2) Multiplier, (3) Product, then use Product = Multiplier × Reference, dividing product by multiplier if reference unknown; practice with bar models and language distinction to avoid confusing 'times as many' with 'more than.'
- Marcus ran 28 laps, which is 7 times as many laps as Emma ran. How many laps did Emma run?
Answer: 4 laps
Since Marcus ran 7 times as many laps as Emma, dividing his total by 7 gives Emma's laps: 28 / 7 = 4. Choice C (7 laps) mistakes the multiplier itself for the answer. Choices B (21) and D (35) come from subtracting or adding instead of dividing.
- Carlos has 12 toy cars. Yuki has 3 times as many toy cars as Carlos. How many toy cars does Yuki have?
Answer: 36 toy cars
Choice D is correct because Yuki has 3 times as many toy cars as Carlos, and 3 times 12 is 36. Choice A is incorrect because 9 is less than Carlos's own total, which does not match 3 times as many. Choice B is incorrect because it does not result from multiplying 12 by 3. Choice C is incorrect because it simply repeats Carlos's total instead of tripling it.
- Keisha has 45 shells. This is 5 times as many shells as Maya has. How many shells does Maya have?
Answer: 9 shells
9 shells is correct because 45÷5=9. 50 shells is incorrect because it results from adding instead of dividing. 5 shells is incorrect because it matches the multiplier itself rather than the answer. 40 shells is incorrect because it results from subtracting instead of dividing. - Jake collected 56 baseball cards last month. This month he collected 7 times as many cards as his friend Sam collected this month. If Jake collected the same number this month as last month, how many cards did Sam collect this month?
Answer: 8 baseball cards this month
Jake collected 56 cards this month too, and that equals 7 times what Sam collected. Dividing 56 by 7 gives 8 cards for Sam. Choice C (49) subtracts 7 from 56 instead of dividing. Choice D (63) adds 7 to 56 instead of dividing. Choice A (7) mistakes the multiplier itself for the answer.
- Carlos has 10 toy cars. Yuki has 3 times as many toy cars as Carlos. How many toy cars does Yuki have?
Answer: 30 toy cars
30 toy cars is correct because 3×10=30. 13 toy cars is incorrect because it results from adding instead of multiplying. 7 toy cars is incorrect because it results from subtracting instead of multiplying. 3 toy cars is incorrect because it matches the multiplier itself rather than the answer. - Emma ran 27 laps, which is 3 times as many laps as Marcus ran. How many laps did Marcus run?
Answer: 9 laps
The correct answer is A, 9 laps. Since Emma's 27 laps are 3 times as many as Marcus ran, dividing gives 27 divided by 3 equals 9. Choice B, 3 laps, comes from dividing by 9 instead of 3. Choice C, 81 laps, comes from multiplying 27 by 3 instead of dividing. Choice D, 24 laps, comes from subtracting 3 from 27 instead of dividing.
