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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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All Common Core: 3rd Grade Math Resources

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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 $11\times4=44$ $\displaystyle 11\times4=44$ what else is known?

Possible Answers:

$1\times44=44$ $\displaystyle 1\times44=44$

$4\times11=44$ $\displaystyle 4\times11=44$

$22\times2=44$ $\displaystyle 22\times2=44$

$44\times1=44$ $\displaystyle 44\times1=44$

$2\times22=44$ $\displaystyle 2\times22=44$

Correct answer:

$4\times11=44$ $\displaystyle 4\times11=44$

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 $11\times4$ $\displaystyle 11\times4$ so our answer must use those numbers, but in a different order.

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

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

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

Possible Answers:

$6\times10=60$ $\displaystyle 6\times10=60$

$20\times3=60$ $\displaystyle 20\times3=60$

$15\times4=60$ $\displaystyle 15\times4=60$

$5\times12=60$ $\displaystyle 5\times12=60$

$2\times30=60$ $\displaystyle 2\times30=60$

Correct answer:

$5\times12=60$ $\displaystyle 5\times12=60$

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 $12\times5$ $\displaystyle 12\times5$ so our answer must use those numbers, but in a different order.

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

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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 $2\times3\times4$ $\displaystyle 2\times3\times4$

Possible Answers:

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

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

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

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

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

Correct answer:

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

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.

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

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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 $1\times2\times3$ $\displaystyle 1\times2\times3$

Possible Answers:

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

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

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

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

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

Correct answer:

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

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.

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

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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 $3\times2\times6$ $\displaystyle 3\times2\times6$

Possible Answers:

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

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

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

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

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

Correct answer:

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

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.

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

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Example Question #16 : Understanding Properties Of Multiplication And The Relationship Between Multiplication And Division

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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.

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

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Example Question #17 : Understanding Properties Of Multiplication And The Relationship Between Multiplication And Division

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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.

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

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Example Question #18 : Understanding Properties Of Multiplication And The Relationship Between Multiplication And Division

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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.

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

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Example Question #391 : How To Multiply

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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.

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

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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 $8\times1\times2$ $\displaystyle 8\times1\times2$

Possible Answers:

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

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

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

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

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

Correct answer:

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

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.

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

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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

All Common Core: 3rd Grade Math Resources

Example Questions

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

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

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

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

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

Example Question #16 : Understanding Properties Of Multiplication And The Relationship Between Multiplication And Division

Example Question #17 : Understanding Properties Of Multiplication And The Relationship Between Multiplication And Division

Example Question #18 : Understanding Properties Of Multiplication And The Relationship Between Multiplication And Division

Example Question #391 : How To Multiply

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

All Common Core: 3rd Grade Math Resources

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