The associative law of multiplication states that the way in which numbers are grouped in a multiplication operation does not change the product. In other words, for any numbers \( a \), \( b \), and \( c \),
\[ (a \cdot b) \cdot c = a \cdot (b \cdot c) \]
Let's evaluate each of the given statements to see which one uses the associative law of multiplication:
1. \( (5 \cdot 6) \cdot 2 = 2 \cdot (5 \cdot 6) \)
This statement does not use the associative law. It is rearranging the terms on opposite sides of the equality, which is more akin to the commutative property.
2. \( (5 \cdot 6) \cdot 2 = 5 \cdot (12 \cdot 1) \)
This statement does not use the associative law. It changes the multiplication factors on one side of the equation.
3. \( (5 \cdot 6) \cdot 2 = 2 \cdot (15 \cdot 2) \)
This statement does not use the associative law. It changes the numbers on both sides of the equation arbitrarily.
4. \( (5 \cdot 6) \cdot 2 = 5 \cdot (6 \cdot 2) \)
This is the correct statement that uses the associative law of multiplication:
\[ (a \cdot b) \cdot c = a \cdot (b \cdot c) \]
Here, \( a = 5 \), \( b = 6 \), and \( c = 2 \).
Therefore, the statement that uses the associative law of multiplication is:
\[ (5 \cdot 6) \cdot 2 = 5 \cdot (6 \cdot 2) \]
Which of the following statements uses the associative law of multiplication?
(5*6) * 2 = 2 * (5*6)
(5*6)*2=5*(12*1)
(5*6)*2=2*(15*2)
(5*6)*2=5*(6*2)
1 answer