Explain or show why \(\frac12\) and \(\frac24\) are equivalent fractions.

1. The whole diagram represents 1. Shade the diagram to represent \(\frac14\).

   

2. To represent \(\frac16\) on the diagram, would you shade more or less than what you shaded for \(\frac14\)? Explain your reasoning.

1. The whole diagram represents 1. What fraction does the shaded part represent? Explain your reasoning.

   

2. Shade this diagram to represent \(\frac{2}{10}\).

   

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

1. \(\frac18\) or \(\frac{1}{10}\)
2. \(\frac{4}{10}\) or \(\frac{7}{10}\)
3. \(\frac45\) or \(\frac54\)

1. Explain or show why the point on the number line represents both \(\frac35\) and \(\frac{6}{10}\).

   

2. Explain why \(\frac{6}{10}\) and \(\frac35\) are equivalent fractions.

For each question, explain your reasoning. Use a number line if you find it helpful.

1. Is \(\frac45\) greater than or less than \(\frac12\)?

   

2. Is \(\frac45\) greater than or less than 1?

   

Fold a strip of paper to represent each fraction. How did you fold the paper to make sure the parts are the correct size for each fraction? Use the blank diagrams to show how you folded.

1. \(\frac13\)s

   

2. \(\frac15\)s

   

3. \(\frac{1}{10}\)s

   

1. Andre looks at these fraction strips and says, “Each \(\frac12\) is the same size as \(\frac13\) and another half of \(\frac13\).” Do you agree with Andre? Explain your reasoning.

   

   

2. What relationship do you see between \(\frac16\) and \(\frac14\)? Explain your reasoning.

   

   

3. Can you find a relationship between \(\frac{1}{6}\) and \(\frac{1}{8}\) using fraction strips? Explain your reasoning.