if we have a x b = -5 , what does ax2b equal?

Given the equation \( a \times b = -5 \), we are asked to determine the value of \( a \times 2 \times b \).

Let’s start by analyzing the given equation and the expression in question:

### Step 1: Recall the initial equation
We know:
\[
a \times b = -5
\]

### Step 2: Simplify the new expression
Now we need to find \( a \times 2 \times b \). Using the associative property of multiplication, we rewrite it as:
\[
a \times 2 \times b = 2 \times (a \times b)
\]

### Step 3: Substitute the known value
Since \( a \times b = -5 \), substitute this into the expression:
\[
2 \times (a \times b) = 2 \times (-5)
\]

### Step 4: Multiply
\[
2 \times (-5) = -10
\]

Thus, \( a \times 2 \times b = -10 \).

### Final Answer:
\[
a \times 2 \times b = -10
\]

Would you like more details on this, or have any further questions?

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Here are some related questions:
1. What if \( a \times b = 10 \)? What would \( a \times 2 \times b \) equal then?
2. How does the associative property of multiplication affect the order of operations in this case?
3. If \( a \times b = 0 \), what would be the result of \( a \times 2 \times b \)?
4. How would the result change if we had \( a \times 3 \times b \) instead of \( a \times 2 \times b \)?
5. What would happen if you replaced multiplication with division in these equations?

**Tip:** When solving equations, always apply basic properties like commutativity and associativity of multiplication to simplify complex expressions.

Learn how to solve the equation a × b = -5 and find the value of a × 2 × b using the associative property of multiplication. This problem demonstrates basic algebra concepts and is suitable for students in Grades 6-8.

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