Which statement uses the distributive law?
$\begin{array}{l}
9 \times(5+3)=9 \times(3+5) \\
9 \times(5+3)=9 \times 5+9 \times 3 \\
9 \times(5+3)=(9 \times 5)+3 \\
9 \times(5+3)=9 \times 8
\end{array}$
Answer (1)
The distributive law states that a × ( b + c ) = a × b + a × c .
Statement 1 demonstrates the commutative property, not the distributive law.
Statement 2 correctly applies the distributive law: 9 × ( 5 + 3 ) = 9 × 5 + 9 × 3 .
Therefore, the statement that uses the distributive law is 9 × ( 5 + 3 ) = 9 × 5 + 9 × 3 .
Explanation
Understanding the Distributive Law The question asks us to identify which of the given statements correctly applies the distributive law. The distributive law states that for any numbers a, b, and c, a × ( b + c ) = a × b + a × c . We need to check each statement to see if it follows this rule.
Checking Each Statement Let's examine each statement:
9 × ( 5 + 3 ) = 9 × ( 3 + 5 ) : This statement shows the commutative property of addition within the parentheses (5+3 = 3+5), but it doesn't demonstrate the distributive law.
9 × ( 5 + 3 ) = 9 × 5 + 9 × 3 : This statement correctly applies the distributive law. It shows that multiplying 9 by the sum of 5 and 3 is the same as multiplying 9 by 5 and 9 by 3, and then adding the results.
9 × ( 5 + 3 ) = ( 9 × 5 ) + 3 : This statement is incorrect. It only multiplies 9 by 5 and then adds 3, which is not the distributive law.
9 × ( 5 + 3 ) = 9 × 8 : This statement simply calculates the sum inside the parentheses first and then multiplies, which is a correct arithmetic operation but not an application of the distributive law.
Identifying the Correct Statement Based on the above analysis, the statement that correctly uses the distributive law is: 9 × ( 5 + 3 ) = 9 × 5 + 9 × 3 .
Examples
The distributive law is useful in everyday situations. For example, suppose you want to buy 7 bags of apples and oranges, each bag containing 3 apples and 5 oranges. Using the distributive law, you can calculate the total number of apples and oranges as 7 × ( 3 + 5 ) = 7 × 3 + 7 × 5 = 21 + 35 = 56 . So, you have a total of 56 fruits.
