Expressions and Equations: Generating Equivalent Expressions with Properties of Operations (CCSS.6.EE.3)
Common Core 6th Grade Math · Learn by Concept
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Common Core 6th Grade Math › Expressions and Equations: Generating Equivalent Expressions with Properties of Operations (CCSS.6.EE.3)
Which expression is equivalent to $3(x+4)$?
$3x+12$
$x+12$
$3x+4$
$7x+12$
Explanation
Distribute $3$ to both terms: $3\cdot x+3\cdot 4=3x+12$. The other choices forget to distribute to one term or combine unlike terms.
Which expression is equivalent to $24x+18y$?
$6x(4+3y)$
$12(2x+3y)$
$6(4x+3y)$
$6(4x+18y)$
Explanation
Factor out the GCF $6$: $24x+18y=6(4x)+6(3y)=6(4x+3y)$. The other choices either factor incorrectly or change the values.
Which expression is equivalent to $2x+5x+3$?
$7x+8$
$7x+3$
$7+3x$
$7x+3x$
Explanation
Combine like terms: $2x+5x=7x$, and the constant $+3$ stays the same, giving $7x+3$. The other choices combine unlike terms or add the constant incorrectly.
A rectangle has length $x+4$ and width $3$. Which expression is equivalent to its area?
$x(3+4)$
$3x+4$
$x+7$
$3x+12$
Explanation
Area is $(x+4)\cdot 3=3(x+4)=3x+12$. The other choices either fail to distribute or combine unlike terms.
Which expression is equivalent to $3(x + 4)$?
$3x + 4$
$3x + 12$
$7x + 12$
$12x + 3$
Explanation
Distribute 3 to both terms: $3 \cdot x = 3x$ and $3 \cdot 4 = 12$, so $3(x+4) = 3x + 12$.
Which expression is equivalent to $2x + 5x + 3$?
$7x + 8$
$7 + 3x$
$10x + 3$
$7x + 3$
Explanation
Combine like terms: $2x + 5x = 7x$. The constant $3$ stays the same, so the result is $7x + 3$.
Which expression is equivalent to $24x + 18y$?
$6(4x + 3y)$
$6(24x + 18y)$
$12(2x + 3y)$
$6(4x + 3)$
Explanation
Factor the greatest common factor 6: $24x \div 6 = 4x$ and $18y \div 6 = 3y$, so $24x + 18y = 6(4x + 3y)$.
Which expression is equivalent to $5(2y - 3)$?
$10y + 15$
$5y - 3$
$10y - 15$
$7y - 3$
Explanation
Distribute 5 to both terms: $5 \cdot 2y = 10y$ and $5 \cdot (-3) = -15$, so $5(2y - 3) = 10y - 15$.
Which expression is equivalent to $3(x + 4)$?
$3x + 12$
$3x + 4$
$x + 12$
$7x$
Explanation
Distribute $3$ to both terms: $3 \cdot x + 3 \cdot 4 = 3x + 12$. Choices B and C forget to distribute to one term; D incorrectly combines unlike terms.
Which expression is equivalent to $2x + 5x$?
$10x$
$7x$
$7$
$7x^2$
Explanation
Combine like terms: $2x + 5x = (2 + 5)x = 7x$. Choice A multiplies coefficients, C drops the variable, and D changes the power.