Question

1. draw a number line to show \\(\frac{1}{4}\\) and \\(\frac{2}{8}\\) are equivalent.

Explanation:

Step1: Understand the fractions

We have two fractions, $\frac{1}{4}$ and $\frac{2}{8}$. First, simplify $\frac{2}{8}$ by dividing numerator and denominator by 2: $\frac{2\div2}{8\div2}=\frac{1}{4}$. So they are equivalent.

Step2: Draw the number line

1. Draw a horizontal line. Mark 0 on the left and 1 on the right (since we're dealing with fractions between 0 and 1, but these fractions are $\frac{1}{4}$ which is 0.25).
2. Divide the segment from 0 to 1 into 4 equal parts (for $\frac{1}{4}$). The first mark after 0 is $\frac{1}{4}$.
3. Alternatively, divide the segment from 0 to 1 into 8 equal parts (for $\frac{2}{8}$). The second mark after 0 (since $\frac{2}{8}$ means 2 out of 8 parts) is at $\frac{2}{8}$, which is the same position as $\frac{1}{4}$ on the 4 - part division.

Answer:

To show $\frac{1}{4}$ and $\frac{2}{8}$ are equivalent on a number line:

1. Draw a number line from 0 to 1.
2. Divide the interval [0,1] into 4 equal sub - intervals. The point at $\frac{1}{4}$ (1st sub - interval mark) represents $\frac{1}{4}$.
3. Divide the interval [0,1] into 8 equal sub - intervals. The point at $\frac{2}{8}$ (2nd sub - interval mark) will coincide with the $\frac{1}{4}$ mark from the 4 - part division, showing they are equivalent. (Visually, the number line can be represented as: 0 ---- $\frac{1}{4}$ ($\frac{2}{8}$) ---- $\frac{2}{4}$ ---- $\frac{3}{4}$ ---- 1 when divided into 4 parts, or 0 -- $\frac{1}{8}$ -- $\frac{2}{8}$ ($\frac{1}{4}$) -- $\frac{3}{8}$ -- $\frac{4}{8}$ -- $\frac{5}{8}$ -- $\frac{6}{8}$ -- $\frac{7}{8}$ -- 1 when divided into 8 parts, and the $\frac{1}{4}$ and $\frac{2}{8}$ marks are at the same location.)