Which property is being illustrated?
(commutative, associative, distributive)
1) 3a + 2b = 2b + 3a
2) 3(a + 2) = 3a + 6
3) 3(2 + a) = 3(a +2)
4) (3⋅ 2)a = 3(2a)
THANK YOU!!
commutative: a+b = b+a or a*b = b*a
associative: (a+b)+c = a+(b+c) or (ab)c = a(bc)
distributive: a(b+c) = ab + ac
now decide
1) The property being illustrated is the commutative property because the order of the terms (3a and 2b) is being switched without affecting the overall result.
2) The property being illustrated is the distributive property because the value outside the parenthesis (3) is being distributed to the terms inside the parenthesis (a and 2).
3) The property being illustrated is also the distributive property because the value outside the parenthesis (3) is being distributed to the terms inside the parenthesis (2 and a).
4) The property being illustrated is the associative property because the grouping of terms is being changed without affecting the overall result.
1) The property being illustrated here is the commutative property. This property states that for addition or multiplication, the order of the numbers does not affect the result.
2) The property being illustrated here is the distributive property. This property states that when you multiply a number by a sum, you can distribute the multiplication to each term inside the parentheses.
3) The property being illustrated here is the commutative property. Similar to the first example, this property states that for addition, the order of the numbers does not affect the result.
4) The property being illustrated here is the associative property. This property states that when you multiply three numbers, it doesn't matter which two you multiply first.
To determine the property being illustrated in each equation, we need to understand the definitions of the commutative, associative, and distributive properties.
1) Commutative property: This property states that the order of the numbers or variables being added or multiplied does not affect the result.
2) Associative property: This property states that the grouping of numbers or variables being added or multiplied does not affect the result.
3) Distributive property: This property states that multiplying a number or variable by a sum or difference is the same as multiplying the number or variable by each term separately and then adding or subtracting the results.
Now let's analyze each equation:
1) 3a + 2b = 2b + 3a
This equation demonstrates the commutative property of addition, as it shows that when adding 3a and 2b, the result is the same regardless of the order in which they are added.
2) 3(a + 2) = 3a + 6
This equation illustrates the distributive property, as it shows that multiplying the number 3 by the sum (a + 2) is the same as multiplying 3 by each term separately and then adding the results.
3) 3(2 + a) = 3(a + 2)
This equation also demonstrates the commutative property of addition, as it shows that when adding 2 and a inside the parentheses, the order does not affect the result.
4) (3⋅2)a = 3(2a)
This equation represents the associative property of multiplication, as it shows that when multiplying 3⋅2 by a, the result is the same as multiplying 3 by 2a.
In conclusion, the properties being illustrated in each equation are:
1) Commutative property of addition.
2) Distributive property.
3) Commutative property of addition.
4) Associative property of multiplication.