Question

plot the fractions on the number line. drag each marker to the correct place on the line. ask your learning coach to help you.

Explanation:

Step1: Simplify each fraction

• For $\frac{2}{8}$, simplify by dividing numerator and denominator by 2: $\frac{2\div2}{8\div2}=\frac{1}{4}$
• For $\frac{2}{4}$, simplify by dividing numerator and denominator by 2: $\frac{2\div2}{4\div2}=\frac{1}{2}$
• $\frac{5}{5} = 1$ (since any non - zero number divided by itself is 1)
• $\frac{2}{1}=2$ (any number divided by 1 is the number itself)

Step2: Analyze the number line

The number line is from 0 to 2. Let's assume the number of intervals between 0 and 1 (and between 1 and 2) is the same. Let's count the number of small ticks between 0 and 1. From 0 to 1, if we look at the position of 1 (where $\frac{5}{5}$ is placed), we can see that the distance from 0 to 1 is divided into, let's say, 8 small intervals (we can check with the fraction $\frac{2}{8}$ which is $\frac{1}{4}$, but maybe a better way is to see the position of each fraction:

• $\frac{2}{8}=\frac{1}{4}$: On a number line from 0 to 1, if we divide 0 - 1 into 4 equal parts, $\frac{1}{4}$ is at the first mark after 0 (if we divide 0 - 1 into 4 parts: 0, $\frac{1}{4}$, $\frac{2}{4}$, $\frac{3}{4}$, 1)
• $\frac{2}{4}=\frac{1}{2}$: This is at the mid - point of 0 and 1, so it's at the 4th tick (if 0 - 1 is divided into 8 ticks, $\frac{1}{2}$ is at the 4th tick: 0, $\frac{1}{8}$, $\frac{2}{8}$, $\frac{3}{8}$, $\frac{4}{8}=\frac{1}{2}$, $\frac{5}{8}$, $\frac{6}{8}$, $\frac{7}{8}$, 1)
• $\frac{5}{5} = 1$: This is at the position labeled 1 on the number line.
• $\frac{2}{1}=2$: This is at the position labeled 2 on the number line.

Step3: Place the markers

• $\frac{2}{8}$: Should be placed at the position corresponding to $\frac{1}{4}$ on the number line (close to 0, 2 ticks from 0 if we consider 8 - tick division of 0 - 1)
• $\frac{2}{4}$: Should be placed at the mid - point of 0 and 1 (4 ticks from 0 in 8 - tick division)
• $\frac{5}{5}$: Is already placed at 1 (correct, since $\frac{5}{5}=1$)
• $\frac{2}{1}$: Is already placed at 2 (correct, since $\frac{2}{1}=2$)

Answer:

To plot the fractions:

• $\frac{2}{8}$: Place it at the position $\frac{1}{4}$ on the number line (close to 0, 2 small intervals from 0 if 0 - 1 is divided into 8 intervals).
• $\frac{2}{4}$: Place it at the mid - point of 0 and 1 (4 small intervals from 0 if 0 - 1 is divided into 8 intervals).
• $\frac{5}{5}$ is correctly placed at 1.
• $\frac{2}{1}$ is correctly placed at 2.