1. Halley calculates 45% of 280 in the following way: Half of 280 is 140. I know 10% is 28, so 5% is half of that, which is 14. So

I get 140 minus 14, which is 126. (a) Explain briefly why it makes sense for Halley to solve the problem the way she does. What is the idea behind her strategy? (b) Write a string of equations that incorporate Halley's ideas. Which properties of arithmetic did Halley use(knowingly or not) and where? Be thorough and be specific.