Questions: Draw a number line like the one shown next. Place equally spaced tick marks on your number line so that you can plot 1/3 on a tick mark without first plotting 1. Then plot 1. Explain your reasoning.

Draw a number line like the one shown next. Place equally spaced tick marks on your number line so that you can plot 1/3 on a tick mark without first plotting 1. Then plot 1. Explain your reasoning.
Transcript text: 10. Draw a number line like the one shown next. Place equally spaced tick marks on your number line so that you can plot $\frac{1}{3}$ on a tick mark without first plotting 1 . Then plot 1 . Explain your reasoning.
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Solution

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Solution Steps

Step 1: Understand the Problem

The problem requires us to draw a number line with equally spaced tick marks and plot the fraction \( \frac{1}{3} \) without first plotting 1. We also need to explain the reasoning behind the placement.

Step 2: Determine the Tick Mark Intervals

To plot \( \frac{1}{3} \) without plotting 1, we need to choose a common denominator that allows us to place \( \frac{1}{3} \) directly on a tick mark. Since \( \frac{2}{7} \) is already plotted, we need to find a common denominator for 3 and 7.

Step 3: Find a Common Denominator

The least common multiple (LCM) of 3 and 7 is 21. Therefore, we can use 21 as the common denominator for our tick marks.

Step 4: Plot the Tick Marks

We will place tick marks at intervals of \( \frac{1}{21} \). This way, we can plot \( \frac{1}{3} \) as \( \frac{7}{21} \) and \( \frac{2}{7} \) as \( \frac{6}{21} \).

Step 5: Draw the Number Line
  1. Start with 0.
  2. Place tick marks at \( \frac{1}{21}, \frac{2}{21}, \frac{3}{21}, \ldots, \frac{21}{21} \).
  3. Plot \( \frac{2}{7} \) at \( \frac{6}{21} \).
  4. Plot \( \frac{1}{3} \) at \( \frac{7}{21} \).

Final Answer

By using a common denominator of 21, we can place equally spaced tick marks at intervals of \( \frac{1}{21} \). This allows us to plot \( \frac{1}{3} \) as \( \frac{7}{21} \) without first plotting 1. The number line will have tick marks at \( \frac{1}{21}, \frac{2}{21}, \ldots, \frac{21}{21} \), with \( \frac{2}{7} \) at \( \frac{6}{21} \) and \( \frac{1}{3} \) at \( \frac{7}{21} \).

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