6th Grade Math Flashcards: Identify Equivalent Expressions

What this deck covers

This deck focuses on Identify Equivalent Expressions, giving you a quick way to review the definitions, rules, and examples that matter most for 6th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Identify whether $5(x-4)$ and $5x-4$ are equivalent.

Answer: No, $5(x-4)$ is equivalent to $5x-20$, not $5x-4$. Distribute: $5(x-4) = 5x - 20$.

Flashcard 2: Which expression is equivalent to rac{3}{4}y+rac{1}{4}y?

Answer: $y$. Sum the fractions: $\frac{3}{4}+\frac{1}{4}=\frac{4}{4}=1$.

Flashcard 3: What is the simplified form of $x+x+x+x+x$?

Answer: $5x$. Five $x$'s added together equals $5x$.

Flashcard 4: Identify whether $x+x^2$ and $2x^2$ are equivalent.

Answer: No, $x+x^2$ is not equivalent to $2x^2$. Can't combine unlike terms ($x$ and $x^2$).

Flashcard 5: Which expression is equivalent to $2a+3b+a-2b$?

Answer: $3a+b$. Group like terms: $(2a + a) + (3b - 2b) = 3a + b$.

Flashcard 6: Identify whether $y+y+y$ and $3y$ are equivalent.

Answer: Yes, $y+y+y$ is equivalent to $3y$. Three $y$'s added together equals $3$ times $y$.

Flashcard 7: Which expression is equivalent to $8-2(3x-1)$?

Answer: $10-6x$. Distribute $-2$: $8 - 6x + 2 = 10 - 6x$.

Flashcard 8: Identify whether rac{x}{3}+rac{x}{3}+rac{x}{3} and $x$ are equivalent.

Answer: Yes, rac{x}{3}+rac{x}{3}+rac{x}{3} is equivalent to $x$. Three thirds make a whole: rac{3}{3}x = x.

Flashcard 9: Which property justifies rewriting $a+a+a$ as $3a$?

Answer: Combining like terms (repeated addition as multiplication). Adding the same term multiple times equals multiplying by the count.

Flashcard 10: Which expression is equivalent to $6(2x+1)$?

Answer: $12x+6$. Distribute $6$ to both terms: $6 \cdot 2x + 6 \cdot 1$.

Flashcard 11: Identify the expression equivalent to $6(p+1)-p$ after simplifying.

Answer: $5p+6$. Distribute $6$, then combine: $6p+6-p=5p+6$.

Flashcard 12: Which expression is equivalent to $7y+0$?

Answer: $7y$. Adding zero doesn't change the value.

Flashcard 13: Which expression is equivalent to $9-3x+2x$?

Answer: $9-x$. Combine like terms: $-3x + 2x = -x$, so $9 - x$.

Flashcard 14: Which expression is equivalent to rac{3}{4}y+rac{1}{4}y?

Answer: $y$. Add fractions: $\frac{3}{4} + \frac{1}{4} = 1$, so $1y = y$.

Flashcard 15: Identify the expression equivalent to $(x+3)+(2x-1)$ after combining like terms.

Answer: $3x+2$. Combine $x$ terms ($x+2x=3x$) and constants ($3-1=2$).

Flashcard 16: Which expression is equivalent to $7a-a$?

Answer: $6a$. Subtracting $a$ from $7a$ leaves $6a$.

Flashcard 17: Which value of $x$ shows $x+5$ and $5x$ are not equivalent?

Answer: $x=0$. When $x=0$: $0+5=5$ but $5(0)=0$, showing they differ.

Flashcard 18: Which expression is equivalent to $5(x-4)$?

Answer: $5x-20$. Distribute $5$ to both terms: $5 \cdot x$ and $5 \cdot (-4)$.

Flashcard 19: Which expression is equivalent to $2(x-5)$?

Answer: $2x-10$. Distribute $2$ to both terms: $2 \cdot x - 2 \cdot 5$.

Flashcard 20: Find the value of $k$ so $k(x+1)$ is equivalent to $4x+4$.

Answer: $k=4$. Expanding gives $kx+k$; matching coefficients: $k=4$.

Flashcard 21: What is the simplified form of $6(2+p)$?

Answer: $12+6p$. Distribute: $6 cdot 2 + 6 cdot p = 12 + 6p$.

Flashcard 22: Which expression is equivalent to $y+y+y$?

Answer: $3y$. Adding $y$ three times equals $3$ times $y$.

Flashcard 23: Which expression is equivalent to $x+x+x+x+x$?

Answer: $5x$. Adding $x$ five times equals $5$ times $x$.

Flashcard 24: Which expression is equivalent to $4x+2x$?

Answer: $6x$. Combine like terms: $4x + 2x = (4+2)x = 6x$.

Flashcard 25: Which expression is equivalent to $10-(x+2)$?

Answer: $8-x$. Distribute the negative: $10 - x - 2 = 8 - x$.

Flashcard 26: Which expression is equivalent to $12m+4-3m$?

Answer: $9m+4$. Combine like terms: $12m - 3m = 9m$.

Flashcard 27: Identify the expression equivalent to $10-3(x-2)$ after simplifying.

Answer: $16-3x$. Distribute the $-3$: $10-3x+6=16-3x$.

Flashcard 28: What is the simplified form of $3(4-t)$?

Answer: $12-3t$. Distribute: $3 cdot 4 - 3 cdot t = 12 - 3t$.

Flashcard 29: What does it mean for two expressions to be equivalent?

Answer: They have the same value for every allowed variable value. Equivalent expressions produce identical outputs for all valid inputs.

Flashcard 30: Identify whether $x+5+x$ and $2x+5$ are equivalent.

Answer: Equivalent. Rearranging gives $x + x + 5 = 2x + 5$.

Flashcard 31: Which expression is equivalent to $4x+9-2x$?

Answer: $2x+9$. Combine like terms: $4x-2x=2x$, constant stays $9$.

Flashcard 32: Which expression is equivalent to $2(x+5)+3(x-1)$?

Answer: $5x+7$. Expand both: $2x+10+3x-3$, then combine like terms.

Flashcard 33: Find and correct the error: $4(x+1)=4x+1$.

Answer: Correct: $4(x+1)=4x+4$. Must distribute $4$ to both terms inside parentheses.

Flashcard 34: Identify the simplified expression equivalent to $7x-x$.

Answer: $6x$. Subtracting one $x$ from seven $x$'s leaves six $x$'s.

Flashcard 35: Which is equivalent to $2(x+y)$ using the distributive property?

Answer: $2x+2y$. Multiply $2$ by each term inside the parentheses.

Flashcard 36: Identify whether $2x+3$ and $2(x+3)$ are equivalent.

Answer: Not equivalent. $2(x+3)=2x+6$, which differs from $2x+3$.

Flashcard 37: Identify whether $3x+6$ and $3(x+2)$ are equivalent.

Answer: Equivalent. $3(x+2)=3x+6$, which matches the first expression.

Flashcard 38: Which expression is equivalent to rac{1}{2}x+rac{1}{2}x?

Answer: $x$. Add fractions: rac{1}{2} + rac{1}{2} = 1, so $1x = x$.

Flashcard 39: What is the simplified form of $2x+3x$?

Answer: $5x$. Combine like terms: $(2+3)x = 5x$.

Flashcard 40: Identify the missing term so $x+\square+x$ is equivalent to $3x$.

Answer: $x$. Need three $x$'s total, so add one more $x$.

Flashcard 41: Which expression is equivalent to $3(n+2)$?

Answer: $3n+6$. Distribute $3$ to both terms inside the parentheses.

Flashcard 42: Identify whether $2(x+5)+3x$ and $5x+10$ are equivalent.

Answer: Yes, $2(x+5)+3x$ simplifies to $5x+10$. Distribute first: $2x+10+3x = 5x+10$.

Flashcard 43: Which expression is equivalent to $5(x+1)+2x$?

Answer: $7x+5$. Distribute $5$, then combine like terms: $5x + 5 + 2x = 7x + 5$.

Flashcard 44: Identify whether $3(x+2)$ and $3x+6$ are equivalent.

Answer: Yes, $3(x+2)$ is equivalent to $3x+6$. Distribute: $3(x+2) = 3x + 6$.

Flashcard 45: Which expression is equivalent to $2(x+4)+3(x+4)$?

Answer: $5(x+4)$. Factor out $(x+4)$: $(2+3)(x+4) = 5(x+4)$.

Flashcard 46: Identify whether $3(x-4)$ and $3x-12$ are equivalent.

Answer: Equivalent. Distributing $3$ gives $3x - 12$, matching the second expression.

Flashcard 47: Identify whether $2(x+3)$ and $2x+3$ are equivalent.

Answer: No, $2(x+3)$ is equivalent to $2x+6$, not $2x+3$. Distribute: $2(x+3) = 2 cdot x + 2 cdot 3 = 2x+6$.

Flashcard 48: What is the simplified form of $4a-2a$?

Answer: $2a$. Combine like terms: $4a-2a = (4-2)a = 2a$.

Flashcard 49: What is the simplified form of $9m-m$?

Answer: $8m$. Subtract: $9m - 1m = 8m$.

Flashcard 50: Identify whether $x+2y$ and $2y+x$ are equivalent.

Answer: Yes, $x+2y$ is equivalent to $2y+x$. Commutative property allows reordering addition.

Flashcard 51: Identify the simplified expression equivalent to $y+y+y+y$.

Answer: $4y$. Four $y$'s added together equals $4$ times $y$.

Flashcard 52: Which expression is equivalent to $1 ext{ }x$?

Answer: $x$. Multiplying by $1$ doesn't change the value.

Flashcard 53: Identify the expression equivalent to $2a+3b-a+b$ after combining like terms.

Answer: $a+4b$. Group like terms: $2a-a=a$ and $3b+b=4b$.

Flashcard 54: Which expression is equivalent to $3(b+2)$?

Answer: $3b+6$. Distribute $3$ to both terms: $3 \cdot b + 3 \cdot 2$.

Flashcard 55: Identify the simplified expression equivalent to rac{1}{2}x+rac{1}{2}x.

Answer: $x$. Adding two halves gives one whole: $\frac{1}{2}+\frac{1}{2}=1$.