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

Question

StartFraction 6 Over 10 EndFraction blank line StartFraction 4 Over 6 EndFraction
2 circles. One circle is divided into 10 equals parts. 6 parts are shaded. The second circle is divided into 6 equal parts. 4 parts are shaded.
is greater than
cannot be compared to
is less than
is equal to

Answer 1

To compare the two fractions \( \frac{6}{10} \) and \( \frac{4}{6} \), we can convert them to decimal form or find a common denominator.

1. Convert \( \frac{6}{10} \) to decimal: \[ \frac{6}{10} = 0.6 \]

2. Convert \( \frac{4}{6} \) to decimal: \[ \frac{4}{6} = \frac{2}{3} \approx 0.6667 \]

Now we can compare:

• \( 0.6 \) (which is \( \frac{6}{10} \))
• \( 0.6667 \) (which is \( \frac{4}{6} \))

Since \( 0.6 \) is less than \( 0.6667 \), we can conclude that:

\[ \frac{6}{10} \text{ is less than } \frac{4}{6} \]

Therefore, the correct phrase to insert is "is less than."