Variables and Algebraic Expressions: Simplifying expressions

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

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

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

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

Therefore, the solution to the problem is Yes.

To solve this problem, we'll analyze the expressions $3+3+3+3$ and $3 \times 4$ to determine if they are equivalent.

First, evaluate the expression $3+3+3+3$:

• Add the numbers: $3 + 3 = 6$
• Add again: $6 + 3 = 9$
• Add the last $3$: $9 + 3 = 12$

The result of $3+3+3+3$ is $12$.

Next, evaluate the expression $3 \times 4$:

• Perform the multiplication: $3 \times 4 = 12$

The result of $3 \times 4$ is also $12$.

Since both expressions result in the same number, we conclude that

The expressions are the same.

Therefore, the correct answer is Yes.

To determine if the expressions $0.5x \times 1$ and $0.5x + 0$ are the same, we will simplify each using the basic properties of arithmetic:

• Step 1: Simplifying $0.5x \times 1$
  By using the multiplicative identity, we know that multiplying any number by 1 does not change its value. Thus:
  $0.5x \times 1 = 0.5x$
• Step 2: Simplifying $0.5x + 0$
  By using the additive identity, we know that adding zero to any number does not change its value. Thus:
  $0.5x + 0 = 0.5x$
• Step 3: Comparing the simplified expressions
  From the above steps, we have:
  $0.5x \times 1 = 0.5x$ and
  $0.5x + 0 = 0.5x$

Since both expressions simplify to $0.5x$, we can conclude that the expressions are indeed the same.

Therefore, the solution to the problem is Yes.