Question

Which rational number is one tick mark to the right of Negative StartFraction 6 Over 4 EndFraction on the number line below?

A number line going from negative 2 to positive 2 in increments of 1. There are 4 equal spaces between each number.
Negative one and three-fourths
Negative 1 and one-fourth
1 and one-fourth
1 and three-fourths

Answer 1

To find out which rational number is one tick mark to the right of \(-\frac{6}{4}\), we first simplify \(-\frac{6}{4}\):

\[
-\frac{6}{4} = -\frac{3}{2} = -1.5
\]

Next, we look for one tick mark to the right of \(-\frac{3}{2}\) (or \(-1.5\)) on the number line, which increments by \(1/4\) (as there are 4 equal spaces between each whole number).

Starting from \(-1.5\), we can add \(0.25\) (which is \( \frac{1}{4} \)):

\[
-1.5 + 0.25 = -1.25
\]

The decimal \(-1.25\) can be converted back to a fraction:

\[
-1.25 = -\frac{5}{4}
\]

Now we compare \(-\frac{5}{4}\) to the given options:

- **Negative one and three-fourths**: \(-1.75 = -\frac{7}{4}\)
- **Negative 1 and one-fourth**: \(-1.25 = -\frac{5}{4}\) (Correct)
- **1 and one-fourth**: \(1.25 = \frac{5}{4}\)
- **1 and three-fourths**: \(1.75 = \frac{7}{4}\)

The rational number that is one tick mark to the right of \(-\frac{6}{4}\) is:

**Negative 1 and one-fourth**.