Question

an expression is shown.

$-0.4 \cdot -2$

which number line represents the expression?

a.

<number line with tick marks at -3.2, -2.4, -1.6, -0.8, 0, 0.8, 1.6, 2.4, 3.2; a pink curved arrow from 0 to 0.8>

b.

<number line with tick marks at -3.2, -2.4, -1.6, -0.8, 0, 0.8, 1.6, 2.4, 3.2; a pink curved arrow from -0.8 to 0>

c.

<number line with tick marks at -3.2, -2.4, -1.6, -0.8, 0, 0.8, 1.6, 2.4, 3.2; a pink curved arrow from -1.6 to -0.8>

d.

<number line with tick marks at -3.2, -2.4, -1.6, -0.8, 0, 0.8, 1.6, 2.4, 3.2; a pink curved arrow from 0 to 0.8>

Explanation:

Step1: Calculate the expression

First, we calculate the value of the expression \(-0.4 \cdot -2\). When multiplying two negative numbers, the result is positive. So, \(-0.4 \times -2 = 0.8\).

Step2: Analyze the number line movements

The expression \(-0.4 \cdot -2\) can be thought of as starting from 0, and since we have a multiplication of two negative numbers (which is equivalent to a positive scaling), we are looking for a number line that represents a movement or a point at \(0.8\) (since the result is \(0.8\)). Let's check the options:

• Option A: The pink curve is around 0 to 0.8? Wait, no, the number line has markings. Wait, actually, when we calculate \(-0.4 \times -2 = 0.8\), so we need a number line that shows the result at \(0.8\). Let's re - evaluate:
• The operation \(-0.4\times -2\) is a multiplication. The result is \(0.8\). So we need a number line where the relevant part (the pink curve or the point) is at \(0.8\).
• Option D: The pink curve is between 0 and \(0.8\) (or at \(0.8\) direction). Wait, let's recast:
• The product \(-0.4\times -2 = 0.8\). So we need a number line that represents the result \(0.8\). Let's check the options:
• Option A: The pink curve is near 0 to 0.8? No, looking at the number lines:
• Option D: The pink curve is from 0 towards \(0.8\) (since the result is \(0.8\)). Wait, let's re - check the calculation: \(-0.4\times -2 = 0.8\). So the number line that represents this should have the relevant marking (the pink curve) indicating a positive value (since the product is positive) and at \(0.8\). So the correct number line is D. Wait, let's confirm:
• The expression is \(-0.4\times -2\). The result is \(0.8\). So we need a number line where the pink curve (representing the operation) ends at or near \(0.8\). Option D has the pink curve between 0 and \(0.8\) (or moving towards \(0.8\)), which matches the result of \(0.8\).

Answer:

D