A rectangle is divided into five equal parts by vertical lines. Four of the five parts are shaded.

Which fraction, when reduced, is equal to the fraction represented by the given model?

(1 point)
Responses

2030
Start Fraction 20 over 30 End Fraction

1216
Start Fraction 12 over 16 End Fraction

2835
Start Fraction 28 over 35 End Fraction

1214
Start Fraction 12 over 14 End Fraction

1 answer

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 \(\frac{4}{5}\).

  1. 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 \(\frac{4}{5}\).
  2. 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 \(\frac{4}{5}\).
  3. 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 \(\frac{4}{5}\).
  4. 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 \(\frac{28}{35}\)