Which fraction is less than the fraction represented by the model?


A circle divided into 8 equal parts. 5 parts are shaded.

Three-fourths
StartFraction 11 Over 16 EndFraction
StartFraction 13 Over 16 EndFraction
StartFraction 2 Over 4 EndFraction

1 answer

First, let's determine the fraction represented by the model. If a circle is divided into 8 equal parts and 5 parts are shaded, the fraction represented by the model is:

\[ \frac{5}{8} \]

Now, let's compare \(\frac{5}{8}\) with each of the given options.

  1. Three-fourths: \(\frac{3}{4}\) is equivalent to \(\frac{6}{8}\) when converted to have a common denominator.

    • \(\frac{3}{4} = \frac{6}{8}\) (greater than \(\frac{5}{8}\))
  2. StartFraction 11 Over 16: To compare \(\frac{11}{16}\) with \(\frac{5}{8}\), we need a common denominator. The least common multiple of 8 and 16 is 16.

    • Convert \(\frac{5}{8}\) to have a denominator of 16: \[ \frac{5}{8} = \frac{10}{16} \]
    • Since \(11 > 10\), \(\frac{11}{16}\) (greater than \(\frac{5}{8}\))
  3. StartFraction 13 Over 16: As with the previous step:

    • \(13 > 10\) means \(\frac{13}{16}\) is also greater than \(\frac{5}{8}\).
  4. StartFraction 2 Over 4: \(\frac{2}{4}\) simplifies to \(\frac{1}{2}\).

    • To compare \(\frac{1}{2}\) with \(\frac{5}{8}\): \(\frac{1}{2} = \frac{4}{8}\) (less than \(\frac{5}{8}\)).

Thus, the fraction that is less than \(\frac{5}{8}\) is:

\[ \boxed{\frac{2}{4}} \]