Question

A number line going from negative 1 to 0. There are 5 equal spaces between the numbers. The line contains negative 1, A, B, C, D, 0.
Which point on the number line represents −4
5
?

A
B
C
D

Answer 1

To determine which point on the number line represents \(-\frac{4}{5}\), let's first clarify the setup of your number line.

You indicated the number line goes from \(-1\) to \(0\) with 5 equal spaces in between. This implies:

1. The starting point is \(-1\).
2. The ending point is \(0\).
3. There are 5 intervals between these points which means you will have 6 total points: \(-1\), \(A\), \(B\), \(C\), \(D\), and \(0\).

To find the value of each point, we can divide the interval between \(-1\) and \(0\) into 5 equal parts. The distance between \(-1\) and \(0\) is:

\[
0 - (-1) = 1
\]

Dividing this distance by 5 gives:

\[
\frac{1}{5} = 0.2
\]

Now we can find the values of \(A\), \(B\), \(C\), and \(D\):

- \(A = -1 + \frac{1}{5} = -1 + 0.2 = -0.8\)
- \(B = -1 + 2 \cdot \frac{1}{5} = -1 + 0.4 = -0.6\)
- \(C = -1 + 3 \cdot \frac{1}{5} = -1 + 0.6 = -0.4\)
- \(D = -1 + 4 \cdot \frac{1}{5} = -1 + 0.8 = -0.2\)

Now we have:

- \(A = -0.8\)
- \(B = -0.6\)
- \(C = -0.4\)
- \(D = -0.2\)

Next, we can find \(-\frac{4}{5}\):

\[
-\frac{4}{5} = -0.8
\]

From our calculations, we see that \(A\) represents \(-0.8\) which is equal to \(-\frac{4}{5}\).

Therefore, the point on the number line that represents \(-\frac{4}{5}\) is:

**A**.