Use an associative property to rewrite the given algebraic expression. Once the grouping has been​ changed, simplify the resulting algebraic expression.

22​(88​x)

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Part 1

​First, rewrite the given algebraic expression using the associative property.

The algebraic expression rewritten using the associative property is

To rewrite the given algebraic expression \(22(88x)\) using the associative property, we first need to understand what the associative property of multiplication states. 

### Associative Property of Multiplication
The associative property of multiplication states that for any three numbers \(a\), \(b\), and \(c\):

\[
(a \cdot b) \cdot c = a \cdot (b \cdot c)
\]

This means that the way in which numbers are grouped in multiplication does not affect the result.

### Applying the Associative Property
Given the expression:

\[
22(88x)
\]

We can apply the associative property by regrouping the numbers. First, observe that multiplication is associative, so we can group \(22\) and \(88\) together:

\[
(22 \cdot 88) \cdot x
\]

### Simplifying the Expression
Next, let's compute the product of \(22\) and \(88\):

\[
22 \cdot 88 = 1936
\]

So, the expression simplifies to:

\[
1936x
\]

### Final Answer
The algebraic expression rewritten using the associative property is:

\[
(22 \cdot 88) \cdot x = 1936x
\]

Would you like more details on any step or have any questions?

### Follow-up Questions:
1. What is the associative property of addition, and how does it differ from multiplication?
2. How would the expression change if we used the commutative property instead of the associative property?
3. Can the associative property be used for division in the same way? Why or why not?
4. How would you apply the associative property to an expression with three different variables?
5. What are some real-world examples where the associative property of multiplication might be useful?

**Tip:** When simplifying algebraic expressions, always look for properties (like associative, commutative, and distributive) that can make calculations easier!

Learn how to rewrite and simplify the algebraic expression 22(88x) using the associative property of multiplication. Follow a step-by-step explanation to understand how grouping affects the outcome of multiplication. Suitable for students in Grades 7-9.

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