Operations and Algebraic Thinking: Solving Two-Step Word Problems with the Four Operations (CCSS.3.OA.7)
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3rd Grade Math › Operations and Algebraic Thinking: Solving Two-Step Word Problems with the Four Operations (CCSS.3.OA.7)
Which equation shows the same value as $4 \times 9$?
$4 + 9$
$(4 \times 10) - 4$
$(4 + 9) \times 2$
$4 \times (9 + 4)$
Explanation
Using the distributive property over subtraction: $4 \times 9 = 4 \times (10 - 1) = (4 \times 10) - (4 \times 1) = 40 - 4 = 36$. The others do not equal 36.
How can the distributive property help solve $6 \times 8$?
$6 \times 8 = (6 \times 4) + (6 \times 4)$
$6 \times 8 = (6 + 8) + (6 + 8)$
$6 \times 8 = (8 \times 3) + 2$
$6 \times 8 = (6 \times 10) + (6 \times 2)$
Explanation
Break 8 into $4 + 4$: $6 \times 8 = 6 \times (4 + 4) = (6 \times 4) + (6 \times 4) = 24 + 24 = 48$. The other options are not correct uses of the distributive property or do not equal 48.
Which expression is equal to $7 \times 6$?
$6 \times 8$
$(7 \times 6) + 7$
$6 \times (7 + 1)$
$(7 \times 3) + (7 \times 3)$
Explanation
Use the distributive property with $6 = 3 + 3$: $7 \times 6 = 7 \times (3 + 3) = (7 \times 3) + (7 \times 3) = 21 + 21 = 42$.
Are these expressions equal: $(2 \times 5) \times 3$ and $2 \times (5 \times 3)$?
No, changing parentheses changes the value.
Yes, they are equal by the commutative property.
Yes, they are equal by the associative property of multiplication.
No, because multiplication must be done left to right.
Explanation
Associative property: grouping does not change the product. $(2 \times 5) \times 3 = 10 \times 3 = 30$ and $2 \times (5 \times 3) = 2 \times 15 = 30$.