To determine which fraction, when reduced, is equal to the fraction represented by the model (where four out of five parts of the rectangle are shaded), we first express the shaded area as a fraction:
\[ \text{Fraction shaded} = \frac{\text{Shaded parts}}{\text{Total parts}} = \frac{4}{5} \]
Next, we will check each of the given fractions to see if it reduces to \(\frac{4}{5}\).
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For \(\frac{20}{30}\):
- The greatest common divisor (GCD) of 20 and 30 is 10.
- Reducing: \(\frac{20 \div 10}{30 \div 10} = \frac{2}{3}\), which is not \(\frac{4}{5}\).
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For \(\frac{12}{16}\):
- The GCD of 12 and 16 is 4.
- Reducing: \(\frac{12 \div 4}{16 \div 4} = \frac{3}{4}\), which is not \(\frac{4}{5}\).
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For \(\frac{28}{35}\):
- The GCD of 28 and 35 is 7.
- Reducing: \(\frac{28 \div 7}{35 \div 7} = \frac{4}{5}\), which matches \(\frac{4}{5}\).
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For \(\frac{12}{14}\):
- The GCD of 12 and 14 is 2.
- Reducing: \(\frac{12 \div 2}{14 \div 2} = \frac{6}{7}\), which is not \(\frac{4}{5}\).
The only fraction that reduces to \(\frac{4}{5}\) is:
\(\frac{28}{35}\)
So the correct response is:
2835 \(\frac{28}{35}\)