Generating Equivalent Expressions Using Properties of Operations(TEKS.Math.6.7.D)
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Texas 6th Grade Math › Generating Equivalent Expressions Using Properties of Operations(TEKS.Math.6.7.D)
What is the equivalent expression for $7a + 3a$?
$21a$
$10a$
$a^{10}$
$a$
Explanation
Factor the common $a$ using the distributive property: $7a + 3a = (7+3)a = 10a$. The distributive property justifies rewriting $ab+ac$ as $(b+c)a$ (factoring), then add $7+3=10$.
Rewrite using the distributive property: $4(x + 3)$
$4x + 3$
$x + 12$
$4x + 3x$
$4x + 12$
Explanation
Distribute $4$ to each term inside the parentheses: $4(x+3) = 4\cdot x + 4\cdot 3 = 4x + 12$.
Which property justifies this step? $6 + y = y + 6$
Commutative property of addition
Associative property of addition
Identity property of addition
Distributive property
Explanation
The commutative property of addition states that changing the order of addends does not change the sum: $a+b=b+a$. Here, $6+y=y+6$.
Which property allows you to change the grouping in $(2 \cdot 5) \cdot x$ to $2 \cdot (5 \cdot x)$?
Commutative property of multiplication
Identity property of multiplication
Associative property of multiplication
Distributive property
Explanation
The associative property of multiplication states that the way factors are grouped does not change the product: $(ab)c = a(bc)$. Here, $(2\cdot 5)\cdot x = 2\cdot(5\cdot x)$.
What is the equivalent expression for $x + (-x) + 7$?
$x + 7$
$7$
$-x + 7$
$2x + 7$
Explanation
Use the additive inverse: $x + (-x) = 0$. Then use the additive identity: $0 + 7 = 7$. So $x + (-x) + 7 = 7$.