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On the number line, is Desmond correct? Explain why or why not.

Mathematics

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Step-by-step solution

4 steps
  1. Determine the value represented by the dot on the number line.

    The number line between 0 and 1 is divided into 6 equal segments. The dot is located on the 4th mark from 0.
    Therefore, the dot represents the fraction 46\frac{4}{6}.

  2. Evaluate Desmond's first claim

    212\frac{2}{12} represents the dot.
    To compare 212\frac{2}{12} with 46\frac{4}{6}, we can simplify 212\frac{2}{12}:

    212=2÷212÷2=16\frac{2}{12} = \frac{2 \div 2}{12 \div 2} = \frac{1}{6}

    Since 16≠46\frac{1}{6} \neq \frac{4}{6}, 212\frac{2}{12} does not represent the dot.

  3. Evaluate Desmond's second claim

    36\frac{3}{6} represents the dot.
    Comparing 36\frac{3}{6} with 46\frac{4}{6}, we see that they are not equal.
    Since 36≠46\frac{3}{6} \neq \frac{4}{6}, 36\frac{3}{6} does not represent the dot.

  4. Conclude whether Desmond is correct.

    Desmond is incorrect. The dot on the number line represents 46\frac{4}{6}. Neither 212\frac{2}{12} (which simplifies to 16\frac{1}{6}) nor 36\frac{3}{6} is equivalent to 46\frac{4}{6}.

    Desmond is incorrect.

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