Interpret the model to determine the fraction used to divide 1/3

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(1 point)
Responses

4/3
Start Fraction 4 over 3 End Fraction

1/4
Start Fraction 1 over 4 End Fraction

1/12
Start Fraction 1 over 12 End Fraction

3/4
Start Fraction 3 over 4 End Fraction

1 answer

To determine which fraction can be used to divide \( \frac{1}{3} \), we can interpret division by a fraction as multiplying by its reciprocal.

Dividing by a fraction \( x \) is equivalent to multiplying by \( \frac{1}{x} \).

For instance, if we are to divide \( \frac{1}{3} \) by \( \frac{4}{3} \), it can be expressed as:

\[ \frac{1}{3} \div \frac{4}{3} = \frac{1}{3} \times \frac{3}{4} = \frac{1 \cdot 3}{3 \cdot 4} = \frac{3}{12} = \frac{1}{4} \]

Now let's analyze the options given:

  1. \( \frac{4}{3} \): Dividing \( \frac{1}{3} \) by this gives \( \frac{1}{3} \times \frac{3}{4} = \frac{1}{4} \).
  2. \( \frac{1}{4} \): This does not represent a division by a fraction but an indication of the answer itself.
  3. \( \frac{1}{12} \): Not relevant to the fraction we are dividing by.
  4. \( \frac{3}{4} \): Dividing \( \frac{1}{3} \) by this gives \( \frac{1}{3} \div \frac{3}{4} = \frac{1}{3} \times \frac{4}{3} = \frac{4}{9} \).

The correct interpretation involves finding the reciprocal of \( \frac{1}{4} \) when dividing \( \frac{1}{3} \).

Thus, the fraction that is used to divide \( \frac{1}{3} \) and fit appropriately within context would be

\[ \frac{4}{3} \]

So the answer to the question is 4/3 (Start Fraction 4 over 3 End Fraction).