Identify Equivalent Expressions - 6th Grade Math
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Which expression is equivalent to $ rac{3}{4}y+ rac{1}{4}y$?
Which expression is equivalent to $ rac{3}{4}y+ rac{1}{4}y$?
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$y$. Sum the fractions: $\frac{3}{4}+\frac{1}{4}=\frac{4}{4}=1$.
$y$. Sum the fractions: $\frac{3}{4}+\frac{1}{4}=\frac{4}{4}=1$.
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Find the value of $k$ so $k(x+1)$ is equivalent to $4x+4$.
Find the value of $k$ so $k(x+1)$ is equivalent to $4x+4$.
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$k=4$. Expanding gives $kx+k$; matching coefficients: $k=4$.
$k=4$. Expanding gives $kx+k$; matching coefficients: $k=4$.
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Identify whether $3x+6$ and $3(x+2)$ are equivalent.
Identify whether $3x+6$ and $3(x+2)$ are equivalent.
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Equivalent. $3(x+2)=3x+6$, which matches the first expression.
Equivalent. $3(x+2)=3x+6$, which matches the first expression.
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Which value of $x$ shows $x+5$ and $5x$ are not equivalent?
Which value of $x$ shows $x+5$ and $5x$ are not equivalent?
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$x=0$. When $x=0$: $0+5=5$ but $5(0)=0$, showing they differ.
$x=0$. When $x=0$: $0+5=5$ but $5(0)=0$, showing they differ.
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Identify the missing term so $x+\square+x$ is equivalent to $3x$.
Identify the missing term so $x+\square+x$ is equivalent to $3x$.
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$x$. Need three $x$'s total, so add one more $x$.
$x$. Need three $x$'s total, so add one more $x$.
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Identify whether $2x+3$ and $2(x+3)$ are equivalent.
Identify whether $2x+3$ and $2(x+3)$ are equivalent.
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Not equivalent. $2(x+3)=2x+6$, which differs from $2x+3$.
Not equivalent. $2(x+3)=2x+6$, which differs from $2x+3$.
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Identify the simplified expression equivalent to $7x-x$.
Identify the simplified expression equivalent to $7x-x$.
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$6x$. Subtracting one $x$ from seven $x$'s leaves six $x$'s.
$6x$. Subtracting one $x$ from seven $x$'s leaves six $x$'s.
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Which is equivalent to $2(x+y)$ using the distributive property?
Which is equivalent to $2(x+y)$ using the distributive property?
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$2x+2y$. Multiply $2$ by each term inside the parentheses.
$2x+2y$. Multiply $2$ by each term inside the parentheses.
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Identify the simplified expression equivalent to $ rac{1}{2}x+ rac{1}{2}x$.
Identify the simplified expression equivalent to $ rac{1}{2}x+ rac{1}{2}x$.
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$x$. Adding two halves gives one whole: $\frac{1}{2}+\frac{1}{2}=1$.
$x$. Adding two halves gives one whole: $\frac{1}{2}+\frac{1}{2}=1$.
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Which expression is equivalent to $2(x+5)+3(x-1)$?
Which expression is equivalent to $2(x+5)+3(x-1)$?
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$5x+7$. Expand both: $2x+10+3x-3$, then combine like terms.
$5x+7$. Expand both: $2x+10+3x-3$, then combine like terms.
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Identify the expression equivalent to $10-3(x-2)$ after simplifying.
Identify the expression equivalent to $10-3(x-2)$ after simplifying.
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$16-3x$. Distribute the $-3$: $10-3x+6=16-3x$.
$16-3x$. Distribute the $-3$: $10-3x+6=16-3x$.
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Which expression is equivalent to $5(x-4)$?
Which expression is equivalent to $5(x-4)$?
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$5x-20$. Distribute $5$ to both terms: $5 \cdot x$ and $5 \cdot (-4)$.
$5x-20$. Distribute $5$ to both terms: $5 \cdot x$ and $5 \cdot (-4)$.
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Which property justifies rewriting $a+a+a$ as $3a$?
Which property justifies rewriting $a+a+a$ as $3a$?
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Combining like terms (repeated addition as multiplication). Adding the same term multiple times equals multiplying by the count.
Combining like terms (repeated addition as multiplication). Adding the same term multiple times equals multiplying by the count.
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Identify the expression equivalent to $6(p+1)-p$ after simplifying.
Identify the expression equivalent to $6(p+1)-p$ after simplifying.
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$5p+6$. Distribute $6$, then combine: $6p+6-p=5p+6$.
$5p+6$. Distribute $6$, then combine: $6p+6-p=5p+6$.
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Which expression is equivalent to $3(n+2)$?
Which expression is equivalent to $3(n+2)$?
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$3n+6$. Distribute $3$ to both terms inside the parentheses.
$3n+6$. Distribute $3$ to both terms inside the parentheses.
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Identify the simplified expression equivalent to $y+y+y+y$.
Identify the simplified expression equivalent to $y+y+y+y$.
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$4y$. Four $y$'s added together equals $4$ times $y$.
$4y$. Four $y$'s added together equals $4$ times $y$.
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What does it mean for two expressions to be equivalent?
What does it mean for two expressions to be equivalent?
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They have the same value for every allowed variable value. Equivalent expressions produce identical outputs for all valid inputs.
They have the same value for every allowed variable value. Equivalent expressions produce identical outputs for all valid inputs.
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Identify the expression equivalent to $(x+3)+(2x-1)$ after combining like terms.
Identify the expression equivalent to $(x+3)+(2x-1)$ after combining like terms.
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$3x+2$. Combine $x$ terms ($x+2x=3x$) and constants ($3-1=2$).
$3x+2$. Combine $x$ terms ($x+2x=3x$) and constants ($3-1=2$).
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Identify the expression equivalent to $2a+3b-a+b$ after combining like terms.
Identify the expression equivalent to $2a+3b-a+b$ after combining like terms.
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$a+4b$. Group like terms: $2a-a=a$ and $3b+b=4b$.
$a+4b$. Group like terms: $2a-a=a$ and $3b+b=4b$.
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Which expression is equivalent to $4x+9-2x$?
Which expression is equivalent to $4x+9-2x$?
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$2x+9$. Combine like terms: $4x-2x=2x$, constant stays $9$.
$2x+9$. Combine like terms: $4x-2x=2x$, constant stays $9$.
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What is the simplified form of $6(2+p)$?
What is the simplified form of $6(2+p)$?
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$12+6p$. Distribute: $6 cdot 2 + 6 cdot p = 12 + 6p$.
$12+6p$. Distribute: $6 cdot 2 + 6 cdot p = 12 + 6p$.
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What is the simplified form of $2x+3x$?
What is the simplified form of $2x+3x$?
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$5x$. Combine like terms: $(2+3)x = 5x$.
$5x$. Combine like terms: $(2+3)x = 5x$.
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What is the simplified form of $9m-m$?
What is the simplified form of $9m-m$?
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$8m$. Subtract: $9m - 1m = 8m$.
$8m$. Subtract: $9m - 1m = 8m$.
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Identify whether $x+2y$ and $2y+x$ are equivalent.
Identify whether $x+2y$ and $2y+x$ are equivalent.
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Yes, $x+2y$ is equivalent to $2y+x$. Commutative property allows reordering addition.
Yes, $x+2y$ is equivalent to $2y+x$. Commutative property allows reordering addition.
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Identify whether $x+x^2$ and $2x^2$ are equivalent.
Identify whether $x+x^2$ and $2x^2$ are equivalent.
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No, $x+x^2$ is not equivalent to $2x^2$. Can't combine unlike terms ($x$ and $x^2$).
No, $x+x^2$ is not equivalent to $2x^2$. Can't combine unlike terms ($x$ and $x^2$).
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