For each of the following, identify the whole-number property being illustrated.
(a) 2(3 + 4) = 2(4 + 3)
(b) 5 + 7 = 7 + 5
(c) 1 • 14 = 14 = 14 • 1
(d) 5(9 + 3) = 5 • 9 + 5 • 3
(e) 2 + (3 + 2) = (2 + 3) + 2
(f) 5(3 • 4) = (5 • 3)4
are e, and f associative, and a distributive?
Your Solution
To identify the whole-number property being illustrated for each of the given equations, we need to understand the definitions of the properties involved.
(a) The equation 2(3 + 4) = 2(4 + 3) illustrates the commutative property of addition. This property states that changing the order of the addends does not change the sum.
(b) The equation 5 + 7 = 7 + 5 illustrates the commutative property of addition.
(c) The equation 1 • 14 = 14 = 14 • 1 illustrates the multiplicative identity property. This property states that any number multiplied by 1 is equal to the original number.
(d) The equation 5(9 + 3) = 5 • 9 + 5 • 3 illustrates the distributive property of multiplication over addition. This property states that when multiplying a number by the sum of two other numbers, you can distribute the multiplication to each addend separately and then add the results.
(e) The equation 2 + (3 + 2) = (2 + 3) + 2 illustrates the associative property of addition. This property states that changing the grouping of the addends does not change the sum.
(f) The equation 5(3 • 4) = (5 • 3)4 illustrates the associative property of multiplication.
To summarize:
(a) Commutative property of addition.
(b) Commutative property of addition.
(c) Multiplicative identity property.
(d) Distributive property of multiplication over addition.
(e) Associative property of addition.
(f) Associative property of multiplication.
Additionally, based on the given equations, we can determine that the equations (e) and (f) illustrate the associative property, and equation (d) illustrates the distributive property.
I hope this helps!