Name 3 fractions that are equivalent to \(\frac25\). Explain or show your reasoning.

Explain why the fractions \(\frac{10}{3}\) and \(\frac{40}{12}\) are equivalent.

Find 2 fractions equivalent to \(\frac{10}{6}\). Explain or show why they are equivalent to \(\frac{10}{6}\). Use the number line if you think it is helpful.

Jada says that \(\frac75\) is equivalent to \(\frac{14}{10}\) because the numerator and denominator of \(\frac{14}{10}\) are each 2 times the numerator and denominator of \(\frac75\).

1. Explain why Jada’s reasoning is correct.

2. Use Jada’s method to find another fraction equivalent to \(\frac75\).

Mai is thinking of a fraction. She gives several clues to help you guess her fraction. Try to guess Mai’s fraction after each clue.

1. My fraction is equivalent to \(\frac23\).
2. The numerator of my fraction is greater than 10.
3. A factor of my numerator is 8.
4. The numbers 8 and 5 are a factor pair of my numerator.

Think of a fraction: \(\underline{\hspace{1.5cm}}\)

Write several clues so a friend or family member can guess your fraction. Then present the clues one at a time and ask them to make a guess after each one.

1. My fraction is equivalent to \(\underline{\hspace{1.5cm}}\).

2. The numerator of my fraction is less than \(\underline{\hspace{1.5cm}}\).

3. One multiple of my numerator is \(\underline{\hspace{1.5cm}}\).

4. A factor pair of my denominator is \(\underline{\hspace{1.5cm}}\) and \(\underline{\hspace{1.5cm}}\).

1. Diego says he shaded \(\frac{10}{20}\) of the diagram. Do you agree with Diego? Explain your reasoning.

   

2. Shade \(\frac{18}{24}\) of the diagram. Explain how you know \(\frac{18}{24}\) is shaded.