Question

write an equivalent expression.
3.8 + (8x + 0.4)

choose the correct answer below.
a. (3 + 8) + 8x
b. 3.8 + (8 + 0.4)
c. (3.8 + 0.4) + 8
d. (3.8 + 0.4) + 8x

Explanation:

Step1: Recall the associative property of addition

The associative property of addition states that for any numbers \(a\), \(b\), and \(c\), \(a+(b + c)=(a + b)+c\). Also, we can rearrange the terms when adding (commutative property), but here we mainly use associative to group like terms (constants together). The original expression is \(3.8+(8x + 0.4)\). We can group \(3.8\) and \(0.4\) first because they are both constants, and then add \(8x\) later.

Step2: Apply the associative property

Using the associative property, we can rewrite \(3.8+(8x + 0.4)\) as \((3.8 + 0.4)+8x\). Let's check the options:

• Option A: \((3 + 8)+8x\) is incorrect because \(3.8\) is not \(3\) and \(8x\) term is misgrouped.
• Option B: \(3.8+(8 + 0.4)\) is incorrect because we should group the constants \(3.8\) and \(0.4\), not \(8\) and \(0.4\) ( \(8\) is the coefficient of \(x\), not a constant to be added with \(0.4\) in that way).
• Option C: \((3.8 + 0.4)+8\) is incorrect because the \(8x\) term is changed to \(8\), which is wrong.
• Option D: \((3.8 + 0.4)+8x\) matches our rewritten expression.

Answer:

D. \((3.8 + 0.4)+8x\)