Question

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

Answer 1

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:

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