Question

another example!
find \\(\frac{6}{8} - \frac{4}{8}\\).
start at \\(\frac{6}{8}\\). to subtract, move \\(\frac{4}{8}\\) to the left.
the ending point is \\(\frac{2}{8}\\).
so, \\(\frac{6}{8} - \frac{4}{8} = \frac{2}{8}\\).
guided practice
do you understand?

1. in the example above, how is the denominator illustrated on the number line?

do you know how?
for 3–4, write the equation sho
each number line.
3.
start

Explanation:

Do You Understand? 1

The denominator is 8. On the number line, the interval from 0 to 1 is divided into 8 equal - length segments (or parts). This is because when dealing with fractions with a denominator of 8, like \(\frac{6}{8}\), \(\frac{4}{8}\), and \(\frac{2}{8}\), the number line is partitioned into 8 equal parts to represent these eighths. Each part of the number line corresponds to \(\frac{1}{8}\) of the whole (the interval from 0 to 1), so the denominator 8 is shown by dividing the unit (0 - 1) into 8 equal sections.

Step 1: Identify the start and end points and the movement

The start point on the number line is \(\frac{1}{5}\), and the end point is \(\frac{3}{5}\). The length of the arrow (the movement) is \(\frac{3}{5}-\frac{1}{5}\).

Step 2: Calculate the difference

We know that for fractions with the same denominator, we subtract the numerators. So \(\frac{3}{5}-\frac{1}{5}=\frac{3 - 1}{5}=\frac{2}{5}\). So the equation represented by the number line is \(\frac{1}{5}+\frac{2}{5}=\frac{3}{5}\) (since we start at \(\frac{1}{5}\) and move \(\frac{2}{5}\) to the right to reach \(\frac{3}{5}\)).

Answer:

The interval from 0 to 1 on the number line is divided into 8 equal parts, and each part represents \(\frac{1}{8}\), which illustrates the denominator 8.

Do You Know How? 3