6th Grade Math Flashcards: Generate Equivalent Expressions

What this deck covers

This deck focuses on Generate 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: What property lets you rewrite $(ab)c$ as $a(bc)$?

Answer: Associative property of multiplication. Grouping doesn't change the product when multiplying.

Flashcard 2: What is the greatest common factor expression for $24x+18y$?

Answer: $6(4x+3y)$. Factor out GCF of 6: $6(4x) + 6(3y)$.

Flashcard 3: What property is used to rewrite $a(b+c)$ as $ab+ac$?

Answer: Distributive property. Multiplying a factor by a sum equals multiplying by each addend separately.

Flashcard 4: What is the equivalent expression when you distribute in $-4(x+3)$?

Answer: $-4x-12$. Multiply $-4$ by each term: $-4(x)+(-4)(3)$.

Flashcard 5: What is the equivalent expression when you distribute in $2(7-y)$?

Answer: $14-2y$. Multiply $2$ by each term inside: $2(7)+2(-y)$.

Flashcard 6: What is the factored form of $12a-8$ using the greatest common factor?

Answer: $4(3a-2)$. Factor out $4$: $12a÷4=3a$ and $8÷4=2$.

Flashcard 7: What is the equivalent expression for $2x+3x$ after combining like terms?

Answer: $5x$. Add coefficients of like terms: $2 + 3 = 5$.

Flashcard 8: What is the factored form of $24x+18y$ using the GCF?

Answer: $6(4x+3y)$. Factor out $6$: $24x÷6=4x$ and $18y÷6=3y$.

Flashcard 9: What is the simplified expression for $2a+5+3a-1$?

Answer: $5a+4$. Combine like terms: $2a+3a=5a$ and $5-1=4$.

Flashcard 10: What is the equivalent expression when you distribute in $3(2+x)$?

Answer: $6+3x$. Multiply $3$ by each term inside: $3(2)+3(x)$.

Flashcard 11: What is the equivalent expression for $x+x+x+x+x$ using multiplication?

Answer: $5x$. Five copies of $x$ equals $5 imes x$.

Flashcard 12: What property justifies rewriting $(a+b)+c$ as $a+(b+c)$?

Answer: Associative property of addition. Grouping doesn't matter when adding numbers.

Flashcard 13: What property lets you rewrite $a+b$ as $b+a$?

Answer: Commutative property of addition. Order doesn't matter when adding numbers.

Flashcard 14: What is the greatest common factor of $24x+18y$ as a single factor?

Answer: $6$. Both $24$ and $18$ are divisible by $6$.

Flashcard 15: What is the equivalent expression for $9+2(4-x)$ after simplifying?

Answer: $17-2x$. Distribute 2, then combine: $9 + 8 - 2x$.

Flashcard 16: What is the factored form of $15x+10$ using the greatest common factor?

Answer: $5(3x+2)$. Factor out $5$: $15x÷5=3x$ and $10÷5=2$.

Flashcard 17: What is the equivalent expression for $y+y+y$ using multiplication?

Answer: $3y$. Three copies of $y$ equals $3 imes y$.

Flashcard 18: What is the equivalent expression for $-2(3x+7)$ after distributing?

Answer: $-6x-14$. Multiply -2 by each term: $-2(3x) + -2(7)$.

Flashcard 19: What is the equivalent expression for $4x+3+2x-5$ after simplifying?

Answer: $6x-2$. Combine like terms: $(4x + 2x) + (3 - 5)$.

Flashcard 20: What is the simplified expression for $4x+3x$ by combining like terms?

Answer: $7x$. Add coefficients of like terms: $4+3=7$.

Flashcard 21: What is the equivalent expression for $5(x-4)$ after distributing?

Answer: $5x-20$. Multiply 5 by each term: $5(x) + 5(-4)$.

Flashcard 22: What is the equivalent expression when you distribute in $5(x+4)$?

Answer: $5x+20$. Multiply $5$ by each term inside: $5(x)+5(4)$.

Flashcard 23: What is the equivalent expression for rac{1}{2}(8+y) after distributing?

Answer: 4+rac{1}{2}y. Multiply rac{1}{2} by each term: rac{1}{2}(8) + rac{1}{2}(y).

Flashcard 24: What property justifies rewriting $a(b+c)$ as $ab+ac$?

Answer: Distributive property. Multiply each term inside parentheses by the outside factor.

Flashcard 25: What is the equivalent expression for $7y-2y$ after combining like terms?

Answer: $5y$. Subtract coefficients of like terms: $7 - 2 = 5$.

Flashcard 26: What is the equivalent expression for $y+y+y$ written as a product?

Answer: $3y$. Three $y$'s added equals $3$ times $y$.

Flashcard 27: What is the equivalent expression for $4(2x-5)$ after distributing?

Answer: $8x-20$. Multiply 4 by each term: $4(2x) + 4(-5)$.

Flashcard 28: What property justifies rewriting $(ab)c$ as $a(bc)$?

Answer: Associative property of multiplication. Grouping doesn't matter when multiplying numbers.

Flashcard 29: What is the factored form of $9m+6n$ using the greatest common factor?

Answer: $3(3m+2n)$. Factor out $3$: $9m÷3=3m$ and $6n÷3=2n$.

Flashcard 30: What is the equivalent expression for $3(2+x)$ after distributing?

Answer: $6+3x$. Multiply 3 by each term: $3(2) + 3(x)$.

Flashcard 31: What is the equivalent factored form of $12x+8$ using the GCF?

Answer: $4(3x+2)$. Factor out GCF of 4: $4(3x) + 4(2)$.

Flashcard 32: What is the simplified expression for $7p-2p+6-9$?

Answer: $5p-3$. Combine like terms: $7p-2p=5p$ and $6-9=-3$.

Flashcard 33: What is the equivalent factored form of $15a-20$ using the GCF?

Answer: $5(3a-4)$. Factor out GCF of 5: $5(3a) + 5(-4)$.

Flashcard 34: What property justifies rewriting $ab$ as $ba$?

Answer: Commutative property of multiplication. Order doesn't matter when multiplying numbers.

Flashcard 35: What is the equivalent expression when you distribute in $6(2x+5)$?

Answer: $12x+30$. Multiply $6$ by each term: $6(2x)+6(5)$.

Flashcard 36: What property lets you rewrite $ab$ as $ba$?

Answer: Commutative property of multiplication. Order doesn't matter when multiplying numbers.

Flashcard 37: What is the equivalent expression for $2(x+7)+3x$ after simplifying?

Answer: $5x+14$. Distribute 2, then combine: $2x + 14 + 3x$.

Flashcard 38: What property lets you rewrite $(a+b)+c$ as $a+(b+c)$?

Answer: Associative property of addition. Grouping doesn't change the sum when adding.

Flashcard 39: What property justifies rewriting $a+b$ as $b+a$?

Answer: Commutative property of addition. Order doesn't matter when adding numbers.

Flashcard 40: What is the equivalent expression for $x+x+x+x+x$ written as a product?

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