Question

find the value of ? in each problem

1. \\(6 \times (5 \times ?) = (6 \times 5) \times 12\\)
2. \\((? \times 9) \times 3 = 16 \times (9 \times 3)\\)
3. \\((5 \times 8) \times 10 = 5 \times (? \times 10)\\)
4. \\(2 \times (? \times 6) = (2 \times 14) \times 6\\)
5. \\((? \times 6) \times 11 = 9 \times (6 \times 11)\\)
6. \\(5 \times (5 \times ?) = (5 \times 5) \times 8\\)

Explanation:

Identify the mathematical property

The problems show equations of the form \(a \times (b \times c) = (a \times b) \times c\). This is the Associative Property of Multiplication.

Apply property to Question 7

Compare both sides of \(6 \times (5 \times ?) = (6 \times 5) \times 12\).
The numbers being multiplied are \(6\), \(5\), and \(12\).
Therefore, \(? = 12\).

Apply property to Question 8

Compare both sides of \((? \times 9) \times 3 = 16 \times (9 \times 3)\).
The numbers being multiplied are \(16\), \(9\), and \(3\).
Therefore, \(? = 16\).

Apply property to Question 9

Compare both sides of \((5 \times 8) \times 10 = 5 \times (? \times 10)\).
The numbers being multiplied are \(5\), \(8\), and \(10\).
Therefore, \(? = 8\).

Apply property to Questions 10, 11, and 12

For Question 10: \(2 \times (? \times 6) = (2 \times 14) \times 6\), so \(? = 14\).
For Question 11: \((? \times 6) \times 11 = 9 \times (6 \times 11)\), so \(? = 9\).
For Question 12: \(5 \times (5 \times ?) = (5 \times 5) \times 8\), so \(? = 8\).

Answer:

No.	Problem	Answer
8	\((? \times 9) \times 3 = 16 \times (9 \times 3)\)	\(16\)
9	\((5 \times 8) \times 10 = 5 \times (? \times 10)\)	\(8\)
10	\(2 \times (? \times 6) = (2 \times 14) \times 6\)	\(14\)
11	\((? \times 6) \times 11 = 9 \times (6 \times 11)\)	\(9\)
12	\(5 \times (5 \times ?) = (5 \times 5) \times 8\)	\(8\)