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QuestionIdentify the properties in these equations:
1. 9⋅(7⋅6)=(9⋅7)⋅69 \cdot(7 \cdot 6)=(9 \cdot 7) \cdot 6
2. 9⋅(7⋅6)=9⋅(6⋅79 \cdot(7 \cdot 6)=9 \cdot(6 \cdot 7
Options: A. Identity, B. Commutative, C. Distributive, D. Associative, E. Zero property.

Studdy Solution

STEP 1

Assumptions1. We have to identify the mathematical properties illustrated by the given equations. . The given properties are Identity property of multiplication, Commutative property of multiplication, Distributive property of multiplication over addition, Associative property of multiplication, and Zero multiplication property.

STEP 2

First, let's consider the equation 9⋅(7⋅6)=(9⋅7)⋅69 \cdot(7 \cdot6)=(9 \cdot7) \cdot6.
This equation shows that the grouping of numbers does not change the result of multiplication. This is the definition of the associative property of multiplication.
So, the property illustrated by 9⋅(7⋅6)=(9⋅7)⋅69 \cdot(7 \cdot6)=(9 \cdot7) \cdot6 is the associative property of multiplication.

STEP 3

Now, let's consider the equation 9⋅(7⋅6)=9⋅(6⋅7)9 \cdot(7 \cdot6)=9 \cdot(6 \cdot7).
This equation shows that the order of numbers does not change the result of multiplication. This is the definition of the commutative property of multiplication.
So, the property illustrated by 9⋅(7⋅6)=9⋅(6⋅7)9 \cdot(7 \cdot6)=9 \cdot(6 \cdot7) is the commutative property of multiplication.

STEP 4

Now, let's consider the equation 9⋅(7⋅6)=(7⋅6)⋅99 \cdot(7 \cdot6)=(7 \cdot6) \cdot9.
This equation shows that the order of numbers does not change the result of multiplication. This is the definition of the commutative property of multiplication.
So, the property illustrated by 9⋅(7⋅6)=(7⋅6)⋅99 \cdot(7 \cdot6)=(7 \cdot6) \cdot9 is the commutative property of multiplication.

STEP 5

Now, let's consider the equation 1⋅(7⋅)=7⋅1 \cdot(7 \cdot)=7 \cdot.
This equation shows that multiplying any number by1 does not change the number. This is the definition of the identity property of multiplication.
So, the property illustrated by 1⋅(7⋅)=7⋅1 \cdot(7 \cdot)=7 \cdot is the identity property of multiplication.

STEP 6

Now, let's consider the equation (3+9)⋅0=0(3+9) \cdot0=0.
This equation shows that multiplying any number by0 results in0. This is the definition of the zero multiplication property.
So, the property illustrated by (3+9)⋅0=0(3+9) \cdot0=0 is the zero multiplication property.

STEP 7

Now, let's consider the equation (9+7)(3+6)=(9+7)3+(9+7)6(9+7)(3+6)=(9+7)3+(9+7)6.
This equation shows that the product of a number and a sum is equal to the sum of the products of the number and each addend. This is the definition of the distributive property of multiplication over addition.
So, the property illustrated by (9+7)(3+6)=(9+7)3+(9+7)6(9+7)(3+6)=(9+7)3+(9+7)6 is the distributive property of multiplication over addition.

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