Fluently Multiply and Divide Within 100
Help Questions
3rd Grade Math › Fluently Multiply and Divide Within 100
Quickly compute: $9 \times 9$.
18
72
80
81
Explanation
This question tests fluent multiplication and division within 100 (CCSS.3.OA.7), specifically computing basic facts to multiply efficiently. Fluency means calculating quickly and accurately using efficient strategies or memory. By end of Grade 3, students should know from memory all products of two one-digit numbers (0-10) and related division facts. Strategies include: (1) Using the relationship between multiplication and division (if 8×7=56, then 56÷8=7 and 56÷7=8), (2) Using properties (commutative: 7×8=8×7; distributive: 7×8=7×5+7×3=35+21=56), (3) Using known facts (know 7×7=49, so 7×8=49+7=56), (4) Direct recall from memory. In this problem, we need to compute 9×9. This is a square fact: 9×9. Choice D is correct because 9×9=81. This demonstrates fluent recall. Choice C is incorrect because this is 8×10=80, from the wrong fact family. This error occurs when students make recall errors. To build fluency with multiplication and division: Practice facts systematically (2s, 5s, 10s first, then 3s, 4s, 6s, then harder 7s, 8s, 9s). Use relationships: teach fact families so learning one fact means knowing four equations. Apply properties: if know 8×5=40, then 8×6=40+8=48 (distributive). Practice with games, flashcards, timed exercises (but low-stress). Emphasize strategies for facts not yet memorized. Connect multiplication to division constantly: every multiplication fact is also two division facts. By end of Grade 3, goal is automatic recall of all single-digit products and related divisions.
Use the relationship: if $6\times 9=54$, then $54\div 6=?$
6
8
9
48
Explanation
This question tests fluent multiplication and division within 100 (CCSS.3.OA.7), specifically using relationships between operations to divide efficiently. Fluency means calculating quickly and accurately using efficient strategies or memory. By end of Grade 3, students should know from memory all products of two one-digit numbers (0-10) and related division facts. Strategies include: (1) Using the relationship between multiplication and division (if 8×7=56, then 56÷8=7 and 56÷7=8), (2) Using properties (commutative: 7×8=8×7; distributive: 7×8=7×5+7×3=35+21=56), (3) Using known facts (know 7×7=49, so 7×8=49+7=56), (4) Direct recall from memory. In this problem, we need to use the relationship that 6×9=54 to find 54÷6. This uses the inverse relationship between multiplication and division. Choice C is correct because using the relationship: if 6×9=54, then 54÷6=9. This demonstrates understanding of operation relationships. Choice B is incorrect because this reverses the division (6÷54 instead of 54÷6). This error occurs when students make recall errors. To build fluency with multiplication and division: Practice facts systematically (2s, 5s, 10s first, then 3s, 4s, 6s, then harder 7s, 8s, 9s). Use relationships: teach fact families so learning one fact means knowing four equations. Apply properties: if know 8×5=40, then 8×6=40+8=48 (distributive). Practice with games, flashcards, timed exercises (but low-stress). Emphasize strategies for facts not yet memorized. Connect multiplication to division constantly: every multiplication fact is also two division facts. By end of Grade 3, goal is automatic recall of all single-digit products and related divisions.
Complete: $7\times 8=56$, so $56\div 8=?$
6
7
8
48
Explanation
This question tests fluent multiplication and division within 100 (CCSS.3.OA.7), specifically using relationships between operations to divide efficiently. Fluency means calculating quickly and accurately using efficient strategies or memory. By end of Grade 3, students should know from memory all products of two one-digit numbers (0-10) and related division facts. Strategies include: (1) Using the relationship between multiplication and division (if 8×7=56, then 56÷8=7 and 56÷7=8), (2) Using properties (commutative: 7×8=8×7; distributive: 7×8=7×5+7×3=35+21=56), (3) Using known facts (know 7×7=49, so 7×8=49+7=56), (4) Direct recall from memory. In this problem, we need to use the relationship that 7×8=56 to find 56÷8. This uses the inverse relationship between multiplication and division. Choice C is correct because using the relationship: if 7×8=56, then 56÷8=7. This demonstrates understanding of operation relationships. Choice B is incorrect because this is 48÷8=6, from the wrong fact family. This error occurs when students confuse adjacent facts. To build fluency with multiplication and division: Practice facts systematically (2s, 5s, 10s first, then 3s, 4s, 6s, then harder 7s, 8s, 9s). Use relationships: teach fact families so learning one fact means knowing four equations. Apply properties: if know 8×5=40, then 8×6=40+8=48 (distributive). Practice with games, flashcards, timed exercises (but low-stress). Emphasize strategies for facts not yet memorized. Connect multiplication to division constantly: every multiplication fact is also two division facts. By end of Grade 3, goal is automatic recall of all single-digit products and related divisions.
Multiply from memory: $9 \times 7$.
16
56
63
64
Explanation
This question tests fluent multiplication and division within 100 (CCSS.3.OA.7), specifically computing basic facts to multiply efficiently. Fluency means calculating quickly and accurately using efficient strategies or memory. By end of Grade 3, students should know from memory all products of two one-digit numbers (0-10) and related division facts. Strategies include: (1) Using the relationship between multiplication and division (if 8×7=56, then 56÷8=7 and 56÷7=8), (2) Using properties (commutative: 7×8=8×7; distributive: 7×8=7×5+7×3=35+21=56), (3) Using known facts (know 7×7=49, so 7×8=49+7=56), (4) Direct recall from memory. In this problem, we need to compute 9×7. This is a multiplication fact from the 7s or 9s table. Choice A is correct because 9×7=63. This demonstrates fluent recall. Choice B is incorrect because this is 7×8=56, not 9×7=63. This error occurs when students confuse adjacent facts. To build fluency with multiplication and division: Practice facts systematically (2s, 5s, 10s first, then 3s, 4s, 6s, then harder 7s, 8s, 9s). Use relationships: teach fact families so learning one fact means knowing four equations. Apply properties: if know 8×5=40, then 8×6=40+8=48 (distributive). Practice with games, flashcards, timed exercises (but low-stress). Emphasize strategies for facts not yet memorized. Connect multiplication to division constantly: every multiplication fact is also two division facts. By end of Grade 3, goal is automatic recall of all single-digit products and related divisions.
Use commutative property: if $8\times 9=72$, what is $9\times 8$?
17
69
72
81
Explanation
This question tests fluent multiplication and division within 100 (CCSS.3.OA.7), specifically applying properties as strategies to multiply efficiently. Fluency means calculating quickly and accurately using efficient strategies or memory. By end of Grade 3, students should know from memory all products of two one-digit numbers (0-10) and related division facts. Strategies include: (1) Using the relationship between multiplication and division (if 8×7=56, then 56÷8=7 and 56÷7=8), (2) Using properties (commutative: 7×8=8×7; distributive: 7×8=7×5+7×3=35+21=56), (3) Using known facts (know 7×7=49, so 7×8=49+7=56), (4) Direct recall from memory. In this problem, we need to use the commutative property: if 8×9=72, find 9×8. This uses the commutative property. Choice C is correct because by commutative property, 9×8=8×9=72. This demonstrates efficient strategy use. Choice A is incorrect because this is 9×9=81, not 9×8=72. This error occurs when students confuse adjacent facts. To build fluency with multiplication and division: Practice facts systematically (2s, 5s, 10s first, then 3s, 4s, 6s, then harder 7s, 8s, 9s). Use relationships: teach fact families so learning one fact means knowing four equations. Apply properties: if know 8×5=40, then 8×6=40+8=48 (distributive). Practice with games, flashcards, timed exercises (but low-stress). Emphasize strategies for facts not yet memorized. Connect multiplication to division constantly: every multiplication fact is also two division facts. By end of Grade 3, goal is automatic recall of all single-digit products and related divisions.
Calculate: $4 \times 7$.
21
24
27
28
Explanation
This question tests fluent multiplication and division within 100 (CCSS.3.OA.7), specifically computing basic facts to multiply efficiently. Fluency means calculating quickly and accurately using efficient strategies or memory. By end of Grade 3, students should know from memory all products of two one-digit numbers (0-10) and related division facts. Strategies include: (1) Using the relationship between multiplication and division (if 8×7=56, then 56÷8=7 and 56÷7=8), (2) Using properties (commutative: 7×8=8×7; distributive: 7×8=7×5+7×3=35+21=56), (3) Using known facts (know 7×7=49, so 7×8=49+7=56), (4) Direct recall from memory. In this problem, we need to compute 4×7. This is a multiplication fact from the 4s or 7s table. Choice C is correct because 4×7=28. This demonstrates fluent recall. Choice A is incorrect because this is 4×6=24, not 4×7=28. This error occurs when students confuse adjacent facts. To build fluency with multiplication and division: Practice facts systematically (2s, 5s, 10s first, then 3s, 4s, 6s, then harder 7s, 8s, 9s). Use relationships: teach fact families so learning one fact means knowing four equations. Apply properties: if know 8×5=40, then 8×6=40+8=48 (distributive). Practice with games, flashcards, timed exercises (but low-stress). Emphasize strategies for facts not yet memorized. Connect multiplication to division constantly: every multiplication fact is also two division facts. By end of Grade 3, goal is automatic recall of all single-digit products and related divisions.
Divide: $56 \div 7$.
7
8
9
49
Explanation
This question tests fluent multiplication and division within 100 (CCSS.3.OA.7), specifically computing basic facts to divide efficiently. Fluency means calculating quickly and accurately using efficient strategies or memory. By end of Grade 3, students should know from memory all products of two one-digit numbers (0-10) and related division facts. Strategies include: (1) Using the relationship between multiplication and division (if 8×7=56, then 56÷8=7 and 56÷7=8), (2) Using properties (commutative: 7×8=8×7; distributive: 7×8=7×5+7×3=35+21=56), (3) Using known facts (know 7×7=49, so 7×8=49+7=56), (4) Direct recall from memory. In this problem, we need to find 56÷7. This uses the inverse relationship between multiplication and division. Choice C is correct because 56÷7=8 (since 7×8=56). This demonstrates understanding of operation relationships. Choice A is incorrect because this is 49÷7=7, from the wrong fact family. This error occurs when students confuse adjacent facts. To build fluency with multiplication and division: Practice facts systematically (2s, 5s, 10s first, then 3s, 4s, 6s, then harder 7s, 8s, 9s). Use relationships: teach fact families so learning one fact means knowing four equations. Apply properties: if know 8×5=40, then 8×6=40+8=48 (distributive). Practice with games, flashcards, timed exercises (but low-stress). Emphasize strategies for facts not yet memorized. Connect multiplication to division constantly: every multiplication fact is also two division facts. By end of Grade 3, goal is automatic recall of all single-digit products and related divisions.
Find the quotient: $72 \div 8$.
8
9
10
64
Explanation
This question tests fluent multiplication and division within 100 (CCSS.3.OA.7), specifically computing basic facts to divide efficiently. Fluency means calculating quickly and accurately using efficient strategies or memory. By end of Grade 3, students should know from memory all products of two one-digit numbers (0-10) and related division facts. Strategies include: (1) Using the relationship between multiplication and division (if 8×7=56, then 56÷8=7 and 56÷7=8), (2) Using properties (commutative: 7×8=8×7; distributive: 7×8=7×5+7×3=35+21=56), (3) Using known facts (know 7×7=49, so 7×8=49+7=56), (4) Direct recall from memory. In this problem, we need to find 72÷8. This uses the inverse relationship between multiplication and division. Choice B is correct because 72÷8=9 (since 8×9=72). This demonstrates understanding of operation relationships. Choice A is incorrect because this is 64÷8=8, from the wrong fact family. This error occurs when students confuse adjacent facts. To build fluency with multiplication and division: Practice facts systematically (2s, 5s, 10s first, then 3s, 4s, 6s, then harder 7s, 8s, 9s). Use relationships: teach fact families so learning one fact means knowing four equations. Apply properties: if know 8×5=40, then 8×6=40+8=48 (distributive). Practice with games, flashcards, timed exercises (but low-stress). Emphasize strategies for facts not yet memorized. Connect multiplication to division constantly: every multiplication fact is also two division facts. By end of Grade 3, goal is automatic recall of all single-digit products and related divisions.
Calculate quickly: $7 \times 8$.
49
54
56
57
Explanation
This question tests fluent multiplication and division within 100 (CCSS.3.OA.7), specifically computing basic facts to multiply efficiently. Fluency means calculating quickly and accurately using efficient strategies or memory. By end of Grade 3, students should know from memory all products of two one-digit numbers (0-10) and related division facts. Strategies include: (1) Using the relationship between multiplication and division (if 8×7=56, then 56÷8=7 and 56÷7=8), (2) Using properties (commutative: 7×8=8×7; distributive: 7×8=7×5+7×3=35+21=56), (3) Using known facts (know 7×7=49, so 7×8=49+7=56), (4) Direct recall from memory. In this problem, we need to compute 7×8. This is a multiplication fact from the 7s or 8s table. Choice B is correct because 7×8=56. This demonstrates fluent recall. Choice A is incorrect because this is 7×7=49, not 7×8=56. This error occurs when students confuse adjacent facts. To build fluency with multiplication and division: Practice facts systematically (2s, 5s, 10s first, then 3s, 4s, 6s, then harder 7s, 8s, 9s). Use relationships: teach fact families so learning one fact means knowing four equations. Apply properties: if know 8×5=40, then 8×6=40+8=48 (distributive). Practice with games, flashcards, timed exercises (but low-stress). Emphasize strategies for facts not yet memorized. Connect multiplication to division constantly: every multiplication fact is also two division facts. By end of Grade 3, goal is automatic recall of all single-digit products and related divisions.
Use a known fact: if $7\times 5=35$, find $7\times 6$.
35
36
41
42
Explanation
This question tests fluent multiplication and division within 100 (CCSS.3.OA.7), specifically applying properties as strategies to multiply efficiently. Fluency means calculating quickly and accurately using efficient strategies or memory. By end of Grade 3, students should know from memory all products of two one-digit numbers (0-10) and related division facts. Strategies include: (1) Using the relationship between multiplication and division (if 8×7=56, then 56÷8=7 and 56÷7=8), (2) Using properties (commutative: 7×8=8×7; distributive: 7×8=7×5+7×3=35+21=56), (3) Using known facts (know 7×7=49, so 7×8=49+7=56), (4) Direct recall from memory. In this problem, we need to use the known fact 7×5=35 to find 7×6. This uses known facts or distributive property. Choice B is correct because if 7×5=35, then 7×6=35+7=42. This demonstrates efficient strategy use. Choice D is incorrect because this is 6×6=36, from the wrong fact family. This error occurs when students confuse adjacent facts. To build fluency with multiplication and division: Practice facts systematically (2s, 5s, 10s first, then 3s, 4s, 6s, then harder 7s, 8s, 9s). Use relationships: teach fact families so learning one fact means knowing four equations. Apply properties: if know 8×5=40, then 8×6=40+8=48 (distributive). Practice with games, flashcards, timed exercises (but low-stress). Emphasize strategies for facts not yet memorized. Connect multiplication to division constantly: every multiplication fact is also two division facts. By end of Grade 3, goal is automatic recall of all single-digit products and related divisions.