Circle the greater fraction in each pair. Explain or show your reasoning.

1. \(\frac25\) or \(\frac26\)
2. \(\frac58\) or \(\frac78\)
3. \(\frac{9}{10}\) or \(\frac{103}{100}\)

Use \(>\), \(<\), or \(=\) to make each statement true. Explain or show your reasoning.

1. \(\frac{2}{3} \> \underline{\phantom{ \hspace{0.7cm} }} \>  \frac{10}{15}\)
2. \(\frac15 \> \underline{\phantom{ \hspace{0.7cm} }} \>  \frac{22}{100}\)
3. \(\frac{10}{4} \> \underline{\phantom{ \hspace{0.7cm} }} \> \frac{45}{20}\)

A water fountain is \(\frac{7}{10}\) mile from the start of a hiking trail. A pond is \(\frac{3}{5}\) mile from the start of the trail. A hiker begins walking at the start of the trail. Which will the hiker pass first, the water fountain or the pond? Explain your reasoning.

Tyler says he grew \(\frac32\) centimeters since his height was measured 6 months ago.

Diego says, “Oh, you grew more than I did! My height went up by only \(\frac78\) inch in the past 6 months.”

Explain why Tyler did not grow more than Diego did, even though \(\frac32\) is greater than \(\frac78\).

List these fractions from least to greatest. Explain or show your reasoning.

• \(\frac13\)
• \(\frac{5}{12} \)
• \(\frac{2}{10} \)

List these fractions from least to greatest. Explain or show your reasoning.

• \(\frac{15}{8}\)
• \(\frac{215}{100}\)
• \(\frac{7}{4}\)
• \( \frac{21}{10}\)

Jada lists these fractions that are all equivalent to \(\frac12\): \(\quad \frac24, \frac{3}{6}, \frac{4}{8}, \frac{5}{10}\)

She notices that each time the numerator increases by 1, the denominator increases by 2. Will this pattern continue? Explain your reasoning.

Find a fraction that is between \(\frac25\) and \(\frac38\). Explain or show your reasoning.