Question

Which phrase should be inserted on the line to correctly compare the two fractions? Use the models to help.


StartFraction 7 Over 8 EndFraction blank line StartFraction 2 Over 4 EndFraction

StartFraction 7 Over 8 EndFraction

StartFraction 2 Over 4 EndFraction
A circle divided into 8 equal parts. 7 parts are shaded. A circle divided into 4 equal parts. 2 parts are shaded.

is greater than
cannot be compared to
is less than
is equal to

Answer 1

To compare the fractions \( \frac{7}{8} \) and \( \frac{2}{4} \), we can first simplify \( \frac{2}{4} \).

\( \frac{2}{4} \) simplifies to \( \frac{1}{2} \).

Now, comparing \( \frac{7}{8} \) and \( \frac{1}{2} \):

To compare the two fractions directly, we can convert \( \frac{1}{2} \) to have a common denominator with \( \frac{7}{8} \).

The common denominator of \( \frac{7}{8} \) and \( \frac{1}{2} \) is 8.

Converting \( \frac{1}{2} \):

\[
\frac{1}{2} = \frac{4}{8}
\]

Now we can compare \( \frac{7}{8} \) with \( \frac{4}{8} \):

\[
\frac{7}{8} > \frac{4}{8}
\]

Thus, the correct comparison is:

\( \frac{7}{8} \) is greater than \( \frac{2}{4} \).

So the phrase you should insert is **"is greater than."**