Compare Expressions: Is 20x Equal to 2×10x? Step-by-Step Analysis

Expression Equivalence with Multiplication Properties

Are the expressions the same or not?

20x 20x

2×10x 2\times10x

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Step-by-step video solution

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00:00 Are the expressions equal?
00:03 Let's solve the multiplication
00:06 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Are the expressions the same or not?

20x 20x

2×10x 2\times10x

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Simplify the expression 2×10x 2 \times 10x .
  • Step 2: Compare the simplified expression with 20x 20x .

Now, let's work through each step:
Step 1: The expression 2×10x 2 \times 10x can be rewritten using associativity as 2×(10×x) 2 \times (10 \times x) .
Step 2: Apply the associative property of multiplication: (2×10)×x=20×x=20x (2 \times 10) \times x = 20 \times x = 20x .

Comparing this with the given expression, we see that both expressions are indeed the same, as they simplify to 20x 20x .

Therefore, the solution to the problem is Yes.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Associative Property: Multiplication grouping can change without affecting the result
  • Technique: Rewrite 2×10x 2 \times 10x as (2×10)×x=20x (2 \times 10) \times x = 20x
  • Check: Both expressions simplify to identical form 20x 20x

Common Mistakes

Avoid these frequent errors
  • Treating multiplication as non-associative
    Don't assume that 2×10x 2 \times 10x equals something different from 20x 20x = wrong conclusion! This ignores the fundamental property that multiplication is associative. Always remember that a×(b×c)=(a×b)×c a \times (b \times c) = (a \times b) \times c .

Practice Quiz

Test your knowledge with interactive questions

Are the expressions the same or not?

\( 3+3+3+3 \)

\( 3\times4 \)

FAQ

Everything you need to know about this question

What does it mean for expressions to be equivalent?

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Two expressions are equivalent if they have the same value for all possible values of the variable. Think of them as different ways to write the same thing!

Why can I change the grouping in multiplication?

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This is called the associative property of multiplication. It means (2×10)×x (2 \times 10) \times x gives the same result as 2×(10×x) 2 \times (10 \times x) .

How do I know which expression to simplify first?

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It doesn't matter! Pick the one that looks easier to work with. In this case, simplifying the numbers first (2×10=20 2 \times 10 = 20 ) makes it clearer.

What if the expressions looked different after simplifying?

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Then they wouldn't be equivalent! For example, 3×5x 3 \times 5x simplifies to 15x 15x , which is not the same as 20x 20x .

Can I use this method with other operations like addition?

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Yes! Addition is also associative: (2+10)+x=2+(10+x) (2 + 10) + x = 2 + (10 + x) . But be careful - subtraction and division are not associative.

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