Common Core: 3rd Grade Math : Understanding Properties of Multiplication and the Relationship between Multiplication and Division

Study concepts, example questions & explanations for Common Core: 3rd Grade Math

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Example Questions

Example Question #11 : Understanding Properties Of Multiplication And The Relationship Between Multiplication And Division

Using the commutative property, if \displaystyle 11\times4=44 what else is known?

Possible Answers:

\displaystyle 1\times44=44

\displaystyle 4\times11=44

\displaystyle 22\times2=44

\displaystyle 44\times1=44

\displaystyle 2\times22=44

Correct answer:

\displaystyle 4\times11=44

Explanation:

The commutative property of multiplication says that we can multiply numbers in any order and our product, or answer, will be the same. 

Though all of our answer choices do equal \displaystyle 44, we started with \displaystyle 11\times4 so our answer must use those numbers, but in a different order. 

\displaystyle 11\times4=44 and \displaystyle 4\times11=44 demonstrates the commutative property of multiplication. 

Example Question #12 : Understanding Properties Of Multiplication And The Relationship Between Multiplication And Division

Using the commutative property, if \displaystyle 12\times5=60 what else is known?

 

Possible Answers:

\displaystyle 6\times10=60

\displaystyle 20\times3=60

\displaystyle 15\times4=60

\displaystyle 5\times12=60

 

\displaystyle 2\times30=60

Correct answer:

\displaystyle 5\times12=60

 

Explanation:

The commutative property of multiplication says that we can multiply numbers in any order and our product, or answer, will be the same. 

Though all of our answer choices do equal \displaystyle 60, we started with \displaystyle 12\times5 so our answer must use those numbers, but in a different order. 

\displaystyle 12\times5=60 and \displaystyle 5\times12=60 demonstrates the commutative property of multiplication. 

Example Question #13 : Understanding Properties Of Multiplication And The Relationship Between Multiplication And Division

Select the answer that demonstrates the associative property of multiplication for \displaystyle 2\times3\times4

 

 

Possible Answers:

\displaystyle 12\times2=24 and \displaystyle 2\times12=24

\displaystyle (8\times3)\times1=24 and \displaystyle 2\times(3\times4)=24

\displaystyle 8\times3=24 and \displaystyle 3\times8=24

\displaystyle (2\times3)\times4=24 and \displaystyle 2\times(3\times4)=24

\displaystyle 2\times(3\times4)=24 and \displaystyle (8\times3)\times1=24

Correct answer:

\displaystyle (2\times3)\times4=24 and \displaystyle 2\times(3\times4)=24

Explanation:

The associative property of multiplication says that we can group numbers in any order to multiply them and our product, or answer, will be the same. 

\displaystyle (2\times3)\times4=24 and \displaystyle 2\times(3\times4)=24

Example Question #11 : Understanding Properties Of Multiplication And The Relationship Between Multiplication And Division

Select the answer that demonstrates the associative property of multiplication for \displaystyle 1\times2\times3

 

Possible Answers:

\displaystyle (1\times2)\times3=12 and \displaystyle 1\times(2\times3)=12

\displaystyle 2\times3=6 and \displaystyle 3\times2=6

\displaystyle 1\times6=6 and \displaystyle 6\times6=6

\displaystyle (1\times2)\times3=6 and \displaystyle 1\times(2\times3)=6

\displaystyle 3\times2=6 and \displaystyle (1\times2)\times3=6

Correct answer:

\displaystyle (1\times2)\times3=6 and \displaystyle 1\times(2\times3)=6

Explanation:

The associative property of multiplication says that we can group numbers in any order to multiply them and our product, or answer, will be the same. 

\displaystyle (1\times2)\times3=6 and \displaystyle 1\times(2\times3)=6

Example Question #15 : Understanding Properties Of Multiplication And The Relationship Between Multiplication And Division

Select the answer that demonstrates the associative property of multiplication for \displaystyle 3\times2\times6

 

 

Possible Answers:

\displaystyle (3\times3)\times6=36 and \displaystyle 3\times(4\times6)=36

\displaystyle 4\times9=36 and \displaystyle 9\times4=36

\displaystyle (3\times3)\times6=36 and \displaystyle 3\times(2\times6)=36

\displaystyle 12\times3=36 and \displaystyle 3\times12=36

\displaystyle (3\times2)\times6=36 and \displaystyle 3\times(2\times6)=36

Correct answer:

\displaystyle (3\times2)\times6=36 and \displaystyle 3\times(2\times6)=36

Explanation:

The associative property of multiplication says that we can group numbers in any order to multiply them and our product, or answer, will be the same. 

\displaystyle (3\times2)\times6=36 and \displaystyle 3\times(2\times6)=36

Example Question #562 : Operations & Algebraic Thinking

Select the answer that demonstrates the associative property of multiplication for \displaystyle 4\times2\times5

 

 

Possible Answers:

\displaystyle (4\times6)\times5=40 and \displaystyle 4\times(2\times5)=40

\displaystyle (4\times3)\times5=40 and \displaystyle 4\times(3\times5)=40

\displaystyle (4\times6)\times5=40 and \displaystyle 4\times(7\times5)=40

\displaystyle (4\times2)\times5=40 and \displaystyle 4\times(2\times5)=40

\displaystyle 5\times8=40 and \displaystyle 8\times5=40

Correct answer:

\displaystyle (4\times2)\times5=40 and \displaystyle 4\times(2\times5)=40

Explanation:

The associative property of multiplication says that we can group numbers in any order to multiply them and our product, or answer, will be the same. 

\displaystyle (4\times2)\times5=40 and \displaystyle 4\times(2\times5)=40

Example Question #563 : Operations & Algebraic Thinking

Select the answer that demonstrates the associative property of multiplication for \displaystyle 5\times2\times3

 

Possible Answers:

\displaystyle (5\times4)\times3=30 and \displaystyle 5\times(2\times3)=30

\displaystyle (5\times4)\times3=30 and \displaystyle 5\times(4\times3)=30

\displaystyle 5\times6=30 or \displaystyle 6\times5=30

\displaystyle (5\times2)\times3=30 and \displaystyle 5\times(2\times3)=30

\displaystyle (5\times2)\times3=30 and \displaystyle 5\times(1\times3)=30

Correct answer:

\displaystyle (5\times2)\times3=30 and \displaystyle 5\times(2\times3)=30

Explanation:

The associative property of multiplication says that we can group numbers in any order to multiply them and our product, or answer, will be the same. 

\displaystyle (5\times2)\times3=30 and \displaystyle 5\times(2\times3)=30

Example Question #14 : Understanding Properties Of Multiplication And The Relationship Between Multiplication And Division

Select the answer that demonstrates the associative property of multiplication for \displaystyle 6\times1\times3

 

 

Possible Answers:

\displaystyle (6\times1)\times3=18 and \displaystyle 6\times(1\times3)=18

\displaystyle (6\times4)\times3=18 and \displaystyle 6\times(4\times3)=18

\displaystyle (6\times2)\times3=18 and \displaystyle 6\times(1\times3)=18

\displaystyle 2\times9=18 and \displaystyle 9\times2=18

\displaystyle (6\times1)\times3=18 and \displaystyle 6\times(3\times3)=18

Correct answer:

\displaystyle (6\times1)\times3=18 and \displaystyle 6\times(1\times3)=18

Explanation:

The associative property of multiplication says that we can group numbers in any order to multiply them and our product, or answer, will be the same. 

\displaystyle (6\times1)\times3=18 and \displaystyle 6\times(1\times3)=18

Example Question #391 : How To Multiply

Select the answer that demonstrates the associative property of multiplication for \displaystyle 7\times3\times2

 

Possible Answers:

\displaystyle (7\times2)\times2=42 and \displaystyle 7\times(3\times2)=21

\displaystyle (7\times3)\times2=42 and \displaystyle 7\times(3\times2)=21

\displaystyle (7\times3)\times2=42 and \displaystyle 7\times(4\times2)=21

\displaystyle 21\times2=42 and \displaystyle 2\times21=42

\displaystyle (7\times5)\times2=42 and \displaystyle 7\times(5\times2)=21

Correct answer:

\displaystyle (7\times3)\times2=42 and \displaystyle 7\times(3\times2)=21

Explanation:

The associative property of multiplication says that we can group numbers in any order to multiply them and our product, or answer, will be the same. 

\displaystyle (7\times3)\times2=42 and \displaystyle 7\times(3\times2)=21

Example Question #19 : Understanding Properties Of Multiplication And The Relationship Between Multiplication And Division

Select the answer that demonstrates the associative property of multiplication for \displaystyle 8\times1\times2

Possible Answers:

\displaystyle (8\times1)\times2=16 and \displaystyle 8\times(1\times2)=16

\displaystyle (8\times2)\times2=16 and \displaystyle 8\times(1\times2)=16

\displaystyle (8\times2)\times2=16 and \displaystyle 8\times(2\times2)=16

\displaystyle (8\times1)\times2=16 and \displaystyle 8\times(3\times2)=16

\displaystyle 4\times4=16 and \displaystyle 8\times2=16

Correct answer:

\displaystyle (8\times1)\times2=16 and \displaystyle 8\times(1\times2)=16

Explanation:

The associative property of multiplication says that we can group numbers in any order to multiply them and our product, or answer, will be the same. 

\displaystyle (8\times1)\times2=16 and \displaystyle 8\times(1\times2)=16

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