Solve Multiplicative Comparison Word Problems
Help Questions
4th Grade Math › Solve Multiplicative Comparison Word Problems
Sofia has 36 stickers. Jamal has 9 stickers. Sofia has how many times as many stickers as Jamal? Write an equation with $?$ and solve.
4 times as many
3 times as many
27 times as many
45 times as many
Explanation
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 Sofia has 36 stickers and Jamal has 9 stickers, asking how many times as many stickers Sofia has as Jamal, identifying 36 as the product, 9 as the reference quantity, and asking for the multiplier, with the equation 36 = ? × 9 requiring division to solve. Choice B is correct because dividing product by reference: 36 ÷ 9 = 4 times as many, which demonstrates understanding of multiplicative comparison and choosing the correct operation. Choice A represents subtracting instead of dividing (36 - 9 = 27), which happens when students confuse multiplicative with additive comparison or think of 'difference' instead of 'times.' 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.
Emma ran 27 laps, which is 3 times as many laps as Marcus ran. Write an equation with ? for the unknown and solve. How many laps did Marcus run?
24 laps
3 laps
9 laps
81 laps
Explanation
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 ran 27 laps which is 3 times as many as Marcus, identifying 27 as the product, 3 as the multiplier, and asking for the reference quantity (Marcus's laps); the equation is 27 = 3 × ?, requiring division to solve. Choice A is correct because dividing product by multiplier: 27 ÷ 3 = 9 laps, demonstrating understanding of multiplicative comparison and choosing the correct operation. Choice B represents using multiplication instead of division (27 × 3 = 81), which happens when students choose the wrong inverse operation or confuse finding the reference with finding the product. 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.
Sofia has 24 pencils. Jamal has 6 times as many pencils as Sofia. This is “times as many,” not “more than.” How many pencils does Jamal have?
18 pencils
144 pencils
30 pencils
6 pencils
Explanation
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 Sofia has 24 pencils and Jamal has 6 times as many as Sofia, identifying 24 as the reference quantity, 6 as the multiplier, and asking for the product (Jamal's pencils), requiring multiplication to solve. Choice B is correct because multiplying reference × multiplier: 24 × 6 = 144 pencils, which demonstrates understanding of multiplicative comparison and choosing the correct operation. Choice A represents adding instead of multiplying (24 + 6 = 30), which happens when students don't understand 'times as many' means multiply and confuse it with 'more than.' 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.
Chen saved $45, which is 5 times as much as Amir saved. Write an equation with a symbol for the unknown: $45 = 5 \times a$. How much money did Amir save?
$9
$40
$50
$225
Explanation
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 $A = n \times B$, 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 $45 which is 5 times as much as Amir saved, identifying $45 as the product, 5 as the multiplier, and asking for the reference quantity (Amir's savings), with the equation $45 = 5 \times a$ requiring division to solve. Choice A is correct because dividing product by multiplier: $45 \div 5 = 9$, which demonstrates understanding of multiplicative comparison and choosing the correct operation. Choice D represents multiplying instead of dividing ($45 \times 5 = 225$), which happens when students choose the wrong inverse operation or confuse when to multiply versus divide. 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: $ \text{Product} = \text{Multiplier} \times \text{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' = $5 \times 7 = 35$, 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.
Emma ran 27 laps. Marcus ran 9 laps. Emma ran how many times as many laps as Marcus? Write an equation using $?$ and solve.
2
3
18
36
Explanation
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 ran 27 laps and Marcus ran 9 laps, asking how many times as many laps Emma ran as Marcus, identifying 27 as the product, 9 as the reference quantity, and asking for the multiplier, with the equation 27 = ? × 9 requiring division to solve. Choice B is correct because dividing the product by the reference, 27 ÷ 9 = 3, gives the multiplier (3 times as many), demonstrating understanding of multiplicative comparison and choosing the correct operation. Choice A represents subtracting instead of dividing (27 - 9 = 18), which happens when students confuse multiplicative with additive comparison or use subtraction thinking of '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 reference if multiplier unknown; practice with bar models and language distinction to avoid confusing 'times as many' with 'more than.'
Keisha has 45 shells. This is 5 times as many shells as Maya has. Write an equation with $?$ for the unknown and solve. How many shells does Maya have?
5 shells
40 shells
9 shells
50 shells
Explanation
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 Keisha has 45 shells, which is 5 times as many as Maya has, identifying 45 as the product, 5 as the multiplier, and asking for the reference quantity (Maya's shells), with the equation 45 = 5 × ? requiring division to solve. Choice A is correct because dividing the product by the multiplier, 45 ÷ 5 = 9, gives the reference quantity, demonstrating understanding of multiplicative comparison and choosing the correct operation. Choice B represents multiplying instead of dividing (45 × something or miscalculation to 40), which happens when students choose the wrong operation or confuse when to multiply versus divide. 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.'
Keisha read 54 pages, which is 6 times as many pages as Maya read. How many pages did Maya read? Write an equation using $?$ for the unknown.
6 pages
9 pages
48 pages
60 pages
Explanation
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 Keisha read 54 pages which is 6 times as many as Maya read, identifying 54 as the product, 6 as the multiplier, and asking for the reference quantity (Maya's pages), with the equation 54 = 6 × ? requiring division to solve. Choice A is correct because dividing product by multiplier: 54 ÷ 6 = 9 pages, which demonstrates understanding of multiplicative comparison and choosing the correct operation. Choice B represents multiplying instead of dividing (54 × something, but perhaps 54 - 6 = 48), which happens when students choose the wrong inverse operation 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.
Sofia read 32 pages, which is 4 times as many pages as Jamal read. Write an equation with ? for the unknown and solve. How many pages did Jamal read?
28 pages
8 pages
4 pages
128 pages
Explanation
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 Sofia read 32 pages which is 4 times as many as Jamal, identifying 32 as the product, 4 as the multiplier, and asking for the reference quantity (Jamal's pages); the equation is 32 = 4 × ?, requiring division to solve. Choice B is correct because dividing product by multiplier: 32 ÷ 4 = 8 pages, demonstrating understanding of multiplicative comparison and choosing the correct operation. Choice C represents using multiplication instead of division (32 × 4 = 128), which happens when students choose the wrong inverse operation or confuse finding the reference with finding the product. 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.
Chen saved $48, which is 6 times as much as Amir saved. This is a multiplicative comparison, not “more than.” Write an equation with a symbol for the unknown and solve. How much did Amir save?
$8
$42
$54
$288
Explanation
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.'
Sofia has 8 stickers. Jamal has 5 times as many stickers as Sofia. How many stickers does Jamal have? (This is “times as many,” not “more than.”)
13 stickers
45 stickers
8 stickers
40 stickers
Explanation
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 $A = n \times B$, 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 Sofia has 8 stickers and Jamal has 5 times as many as Sofia, identifying 8 as the reference quantity, 5 as the multiplier, and asking for the product (Jamal's stickers), with the equation $? = 5 \times 8$ requiring multiplication to solve. Choice B is correct because multiplying the reference by the multiplier, $8 \times 5 = 40$, gives the product, demonstrating understanding of multiplicative comparison and choosing the correct operation. Choice A represents using addition instead of multiplication (8 + 5 = 13), which happens when students don't understand 'times as many' means multiply or confuse with additive comparison. 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 $ \text{Product} = \text{Multiplier} \times \text{Reference} $, multiplying if product unknown; practice with bar models and language distinction to avoid confusing 'times as many' with 'more than.'