1. Shade the first diagram to represent \(5 \times 0.07\).
2. What is the value of \(5 \times 0.07\)? Explain or show your reasoning.
3. What is the value of \(5 \times 0.2\)? Use the second diagram if it is helpful.

1. Mai says that \(7 \times 0.4\) and \(7 \times 0.04\) have the same value of 28. Do you agree? Explain or show your reasoning.
2. Explain why \(8 \times 0.03 = (8 \times 3) \times 0.01\).

1. Explain why each expression has the same value as \(9 \times 0.45\).

   \((9 \times 0.4) + (9 \times 0.05)\)

   \((9 \times 45) \div 100\)

   \((10 \times 0.45) - (1 \times 0.45)\)

2. Find the value of \(9 \times 0.45\) using one of the expressions or your own strategy.

1. Explain or show why \(5.6 \times 3.4 = (56 \times 34) \times 0.01\).

2. Use this strategy to calculate \(5.6 \times 3.4\).

Diego finds the value of \(17.5 \times 3.3\). He says, "I know \(\frac{175}{10} \times \frac{33}{10} = \frac{175~ \times ~33}{100}\), so I just find \(175 \times 33\) and then divide by 100."

1. Explain or show why Diego's method works.

2. Use his method to find the value of \(17.5 \times 3.3\).

1. Han says the diagram shows \(4 \times 0.5 = 2\). Label the diagram to show Han's reasoning.

   

2. Mai says it shows \(10 \times 0.2 = 2\). Label the diagram to show Mai's reasoning.

   

3. What other products can the diagram represent? Explain or show your reasoning.