• 0.7 (or equivalent). Sample reasoning: 
  • $700 \div 100$ is 7, so $70 \div 100$ is one tenth of 7, which is 0.7.
  • $70 \div 100$ is $\frac{70}{100}$, or $\frac{7}{10}$, which is 0.7.
  • $70 \div 100$ is equivalent to $70 \boldcdot \frac{1}{100}$, which is $\frac{70}{100}$ or 0.70, or 0.7.
• 0.35. Sample reasoning:
  • $35 \boldcdot \frac{1}{100}$ is 35 groups of one-hundredth, which is 35-hundredths.
  • $35 \boldcdot \frac{1}{100}$ is the same as $35 \div 100$, which is 0.35.
  • $70 \div 100$ or $70 \boldcdot \frac{1}{100}$ is 0.7.  Because 35 is half of 70, and $35 \boldcdot \frac{1}{100}$ is half of 0.7, which is 0.35.
• 35. Sample reasoning:
  • $35 \div 100$ is 0.35, so $(0.35) \boldcdot 100$ is 35.
  • $(0.35) \boldcdot 10$ is 3.5, so $(0.35) \boldcdot 100$ is 10 times 3.5 or 35. 
  • 0.35 is $\frac{35}{100}$, and $\frac{35}{100} \boldcdot 100 = \frac{3,500}{100}$, which is 35.
• 1.05 (or equivalent). Sample reasoning:
  • $\frac{100}{100}$ is 1 and $\frac {5}{100}$ is 0.05, so $\frac{105}{100}$ is 1.05.
  • $\frac{105}{100}$ is $105 \div 100$, which is 1.05.
  • $(1.05) \boldcdot 100$ is 105.

To involve more students in the conversation, consider asking:

• “Who can restate $\underline{\hspace{.5in}}$’s reasoning in a different way?”
• “Did anyone use the same strategy but would explain it differently?”
• “Did anyone solve the problem in a different way?”
• “Does anyone want to add on to $\underline{\hspace{.5in}}$’s strategy?”
• “Do you agree or disagree? Why?”
• “What connections to previous problems do you see?”

Highlight two points: that dividing a number by 100 gives the same result as multiplying the number by $\frac{1}{100}$, and that a fraction can be interpreted as division ($\frac{105}{100}$ can be understood as $105 \div 100$).