Question

graph \\(\frac{6}{8}\\) and \\(\frac{5}{8}\\) on the number line.

compare \\(\frac{6}{8}\\) and \\(\frac{5}{8}\\).

\\(\frac{6}{8} < \frac{5}{8}\\)

\\(\frac{6}{8} > \frac{5}{8}\\)

Explanation:

🆕 New Concept Discovered: Graphing and Comparing Fractions on a Number Line
Visualizing parts of a whole on a line

Step 1: Understand the number line intervals

The number line starts at \(0\) and ends at \(1\).

Let's count the total number of equal parts (intervals) between \(0\) and \(1\):
There are \(8\) equal spaces. This means each tick mark represents an eighth:

$$ \frac{1}{8}, \frac{2}{8}, \frac{3}{8}, \frac{4}{8}, \frac{5}{8}, \frac{6}{8}, \frac{7}{8}, \frac{8}{8} \text{ (which is } 1\text{)} $$

Step 2: Graph the fractions

To place the fractions on the number line, we count the tick marks starting from \(0\):

• To graph \(\frac{5}{8}\), count \(5\) tick marks to the right of \(0\). Place a point there.
• To graph \(\frac{6}{8}\), count \(6\) tick marks to the right of \(0\). Place a point there.

Step 3: Compare the fractions

On a number line, numbers further to the right are larger.

Since \(\frac{6}{8}\) is to the right of \(\frac{5}{8}\), it is the larger fraction:

$$ \frac{6}{8} > \frac{5}{8} $$

Answer:

• Graphing on the number line:
• Place a point on the 5th tick mark to the right of \(0\) for \(\frac{5}{8}\).
• Place a point on the 6th tick mark to the right of \(0\) for \(\frac{6}{8}\).

• Comparison:

Select the option:

$$ \frac{6}{8} > \frac{5}{8} $$