Apply Properties of Multiplication - 3rd Grade Math

1. What is $(2 \times 6) \times 5$ if you regroup as $2 \times (6 \times 5)$?

   $60$. Regroup: $2 \times 30 = 60$ (associative property).

2. What property of multiplication states that $a \times b = b \times a$?

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

3. Find $7 \times 6$ by using commutativity and the known fact $6 \times 7 = 42$.

   $42$. Commutative property: switching order keeps same result.

4. What is $4 \times 6$ if you know $6 \times 4 = 24$?

   $24$. Commutative property: order doesn't matter, so $4 \times 6 = 6 \times 4$.

5. What is $3 \times 5 \times 2$ if you group as $(3 \times 5) \times 2$?

   $30$. First multiply $3 \times 5 = 15$, then $15 \times 2 = 30$.

6. Find $6 \times 9$ using $6 \times (10 - 1)$.

   $54$. Calculate $6 \times 10 = 60$ minus $6 \times 1 = 6$.

7. Find $3 \times 5 \times 2$ by grouping as $3 \times (5 \times 2)$.

   $30$. First find $5 \times 2 = 10$, then $3 \times 10 = 30$.

8. What property of multiplication says $(a \times b) \times c = a \times (b \times c)$?

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

9. Identify the property used to rewrite $7 \times 9$ as $9 \times 7$.

   Commutative property of multiplication. Changing the order of factors uses the commutative property.

10. Find $9 \times 4$ using $9 \times (2 + 2)$.

    $36$. Calculate $9 \times 2 = 18$ twice, then add.

11. Rewrite $7 \times 13$ using distribution with $13 = 10 + 3$.

    $7 \times 10 + 7 \times 3$. Distributive property splits multiplication over addition.

12. Identify the property used: $8 \times (5 + 2) = (8 \times 5) + (8 \times 2)$.

    Distributive property. Multiplying a sum equals the sum of separate products.

13. What is $3 \times 5 \times 2$ if you group as $3 \times (5 \times 2)$?

    $30$. First multiply $5 \times 2 = 10$, then $3 \times 10 = 30$.

14. Find the missing number: $(6 \times \square) \times 5 = 6 \times (4 \times 5)$.

    $4$. Associative property: the missing factor must be 4.

15. Find $7 \times 8$ using $7 \times (5 + 3)$.

    $56$. Split as $7 \times 5 = 35$ plus $7 \times 3 = 21$.

16. Which expression is equivalent to $(2 \times 9) \times 5$ using the associative property?

    $2 \times (9 \times 5)$. Associative property allows regrouping the factors.

17. What is $5 \times (2 \times 7)$ if you regroup as $(5 \times 2) \times 7$?

    $70$. Regroup: $10 \times 7 = 70$ (associative property).

18. Which property justifies rewriting $6 \times 4$ as $4 \times 6$?

    Commutative property of multiplication. Order can be switched without changing the product.

19. What is $(4 \times 3) \times 2$ if you regroup as $4 \times (3 \times 2)$?

    $24$. Regroup: $4 \times 6 = 24$ (associative property).

20. What is $7 \times 8$ using $7 \times (5 + 3)$?

    $56$. $7 \times 8 = 7 \times 5 + 7 \times 3 = 35 + 21 = 56$.

21. Which property justifies changing $(3 \times 5) \times 2$ to $3 \times (5 \times 2)$?

    Associative property of multiplication. Parentheses can be moved without changing the product.

22. What is $7 \times 6$ if you know $6 \times 7 = 42$?

    $42$. Commutative property: $7 \times 6 = 6 \times 7$.

23. What property of multiplication states that $(a \times b) \times c = a \times (b \times c)$?

    Associative property of multiplication. Grouping doesn't change the product when multiplying three or more numbers.

24. Evaluate $6 \times (4 + 3)$ using the distributive property.

    $42$. Calculate $6 \times 4 = 24$ and $6 \times 3 = 18$, then add.

25. What is $7 \times 5$ if $5 \times 7 = 35$?

    $35$. Switching factors gives the same product.

26. Evaluate $(2 \times 9) \times 5$ by regrouping to make $9 \times 5$ first.

    $90$. Regroup as $2 \times (9 \times 5) = 2 \times 45 = 90$.

27. Which property justifies rewriting $(3 \times 5) \times 2$ as $3 \times (5 \times 2)$?

    Associative property of multiplication. Parentheses can be moved without changing the product.

28. Rewrite $9 \times 16$ using distribution with $16 = 20 - 4$.

    $9 \times 20 - 9 \times 4$. Distributive property splits multiplication over subtraction.

29. What is $6 \times 9$ using $6 \times (10 - 1)$?

    $54$. $6 \times 9 = 6 \times 10 - 6 \times 1 = 60 - 6 = 54$.

30. Identify the property used in $12 \times 5 = (10 \times 5) + (2 \times 5)$.

    Distributive property. Breaking 12 into $(10 + 2)$ and distributing shows distributive property.

31. What is $4 \times 13$ using $4 \times (10 + 3)$?

    $52$. $4 \times 13 = 4 \times 10 + 4 \times 3 = 40 + 12 = 52$.

32. Choose the equivalent expression for $8 \times 15$ using distribution with $15 = 10 + 5$.

    $8 \times 10 + 8 \times 5$. Distributive property breaks $15$ into $10 + 5$.

33. Find $8 \times 7$ using $8 \times (5 + 2)$.

    $56$. Split as $8 \times 5 = 40$ and $8 \times 2 = 16$, then add.

34. What is $6 \times 14$ using $6 \times (10 + 4)$?

    $84$. $6 \times 14 = 6 \times 10 + 6 \times 4 = 60 + 24 = 84$.

35. Find the missing number: $8 \times (3 + 4) = (8 \times 3) + (8 \times \square)$.

    $4$. Distributive property: $8 \times 4$ completes the equation.

36. What property of multiplication says $a \times b = b \times a$?

    Commutative property of multiplication

37. Which expression is equivalent to $5 \times (7 + 2)$ by the distributive property?

    $(5 \times 7) + (5 \times 2)$. Distributive property: multiply 5 by each addend separately.

38. What is $9 \times 3$ if $3 \times 9 = 27$?

    $27$. Commutative property: order doesn't change the product.

39. Use distribution: What is $9 \times 6$ if you rewrite as $9 \times (4 + 2)$?

    $54$. Distribute: $(9 \times 4) + (9 \times 2) = 36 + 18 = 54$.

40. Use distribution: What is $6 \times 9$ if you rewrite as $6 \times (10 - 1)$?

    $54$. Distribute: $(6 \times 10) - (6 \times 1) = 60 - 6 = 54$.

41. What property shows $a \times (b + c) = (a \times b) + (a \times c)$?

    Distributive property. Multiply each addend separately, then add the products.

42. Identify the property used to rewrite $(3 \times 5) \times 2$ as $3 \times (5 \times 2)$.

    Associative property of multiplication. Regrouping factors uses the associative property.

43. Which property justifies changing $6 \times 4$ to $4 \times 6$?

    Commutative property of multiplication. Order can be switched without changing the product.

44. What is $8 \times 7$ using $8 \times (5 + 2)$ and known facts $8 \times 5$ and $8 \times 2$?

    $56$. $8 \times 7 = 8 \times 5 + 8 \times 2 = 40 + 16 = 56$.

45. What is $4 \times 6$ if $6 \times 4 = 24$?

    $24$. Commutative property: switching order gives same product.

46. Which property justifies rewriting $8 \times 7$ as $8 \times (5 + 2)$?

    Distributive property. Breaking a factor into a sum allows separate multiplication.

47. What is $9 \times 6$ using $9 \times (5 + 1)$?

    $54$. $9 \times 6 = 9 \times 5 + 9 \times 1 = 45 + 9 = 54$.

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