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Explain how to use a horizontal number line

to order four fractions from least to greatest.

1 answer

To order four fractions from least to greatest using a horizontal number line, you can follow these steps:

  1. Understand the Fractions: Write down the four fractions you want to compare. For example, let's say they are \( \frac{1}{4} \), \( \frac{2}{3} \), \( \frac{1}{2} \), and \( \frac{3}{5} \).

  2. Find a Common Denominator (if necessary): If the fractions have different denominators, finding a common denominator can help you easily compare their values. The least common multiple (LCM) of the denominators is often the best choice. In our example, the denominators are 4, 3, and 5. The LCM of these numbers is 60.

    • Convert each fraction:
      • \( \frac{1}{4} = \frac{15}{60} \)
      • \( \frac{2}{3} = \frac{40}{60} \)
      • \( \frac{1}{2} = \frac{30}{60} \)
      • \( \frac{3}{5} = \frac{36}{60} \)

  3. Mark the Fractions on the Number Line: Draw a horizontal number line and evenly space out points to represent the fractions using a scale that includes 0 to 1 (since all fractions are between 0 and 1). You can also include some fraction equivalents, such as:

    • 0 = 0 (or \( \frac{0}{60} \))
    • \( \frac{1}{4} \) = \( \frac{15}{60} \)
    • \( \frac{1}{2} \) = \( \frac{30}{60} \)
    • \( \frac{3}{5} \) = \( \frac{36}{60} \)
    • \( \frac{2}{3} \) = \( \frac{40}{60} \)

  4. Plot Each Fraction: Place a point or marker on the number line at each calculated value:

    • Plot \( \frac{1}{4} \) at 0.25 or \( \frac{15}{60} \).
    • Plot \( \frac{1}{2} \) at 0.50 or \( \frac{30}{60} \).
    • Plot \( \frac{3}{5} \) at 0.60 or \( \frac{36}{60} \).
    • Plot \( \frac{2}{3} \) at 0.67 or \( \frac{40}{60} \).

  5. Compare the Plotted Points: Looking from left to right on the number line, identify the order of the fractions based on their positions. The point furthest to the left represents the smallest fraction, while the point furthest to the right represents the largest.

  6. Write the Fractions in Order: From the number line, you can determine the order of the fractions:

    • Least to greatest: \( \frac{1}{4} \), \( \frac{1}{2} \), \( \frac{3}{5} \), \( \frac{2}{3} \).

By visualizing the fractions on a number line, you can easily see the relative size of each and order them correctly.