Question

Which equation can be represented using the number line?

A number line going from to 1 in increments of one-eighths. Arrows go from each mark on the line to the next up to three-fourths.
Three-fourths divided by one-eighth = 6
One-eighth divided by three-fourths = 6
6 divided by three-fourths = one-eighth
6 divided by one-eighth = three-fourths

Answer 1

To determine which equation can be represented using the number line described, we can analyze each option based on the relationship between the fractions and their division.

1. **Three-fourths divided by one-eighth = 6**:
To evaluate this, we calculate \( \frac{3/4}{1/8} \):
\[
\frac{3/4}{1/8} = \frac{3}{4} \times \frac{8}{1} = \frac{3 \times 8}{4 \times 1} = \frac{24}{4} = 6
\]
This equation is correct.

2. **One-eighth divided by three-fourths = 6**:
Calculate \( \frac{1/8}{3/4} \):
\[
\frac{1/8}{3/4} = \frac{1}{8} \times \frac{4}{3} = \frac{4}{24} = \frac{1}{6}
\]
This is incorrect.

3. **6 divided by three-fourths = one-eighth**:
Calculate \( \frac{6}{3/4} \):
\[
\frac{6}{3/4} = 6 \times \frac{4}{3} = \frac{24}{3} = 8
\]
This is incorrect.

4. **6 divided by one-eighth = three-fourths**:
Calculate \( \frac{6}{1/8} \):
\[
\frac{6}{1/8} = 6 \times 8 = 48
\]
This is also incorrect.

Out of the options presented, only the first one is valid:

**Three-fourths divided by one-eighth = 6**.

This can indeed be represented on the number line as it shows the process of dividing the fraction \( \frac{3}{4} \) by \( \frac{1}{8} \), which relates directly to the marks and increments depicted on the number line.