Generate Equivalent Expressions - 6th Grade Math

1. What property lets you rewrite $(ab)c$ as $a(bc)$?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    $5x$. Five copies of $x$ equals $5 \times x$.

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

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

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

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

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

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

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

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

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

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

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

    $3y$. Three copies of $y$ equals $3 \times y$.

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

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

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

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

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

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

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

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

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

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

23. What is the equivalent expression for $\frac{1}{2}(8+y)$ after distributing?

    $4+\frac{1}{2}y$. Multiply $\frac{1}{2}$ by each term: $\frac{1}{2}(8) + \frac{1}{2}(y)$.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

34. What property justifies rewriting $ab$ as $ba$?

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

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

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

36. What property lets you rewrite $ab$ as $ba$?

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

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

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

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

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

39. What property justifies rewriting $a+b$ as $b+a$?

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

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

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

Study these flashcards