I am an undergraduate secondary math education major. In 2 weeks I have to give a Number Talk (https://www.mathmammoth.com/lessons/number_talks.php) in my math ed class on the problem "3.9 times 7.5". I need to come up with as many different solution methods as possible. (I was unsure of which tag was appropriate for this post.)
Here is what I have come up with so far:
The most common way: multiply the two numbers "vertically", ignoring the decimal, to get 2925. Since there are two numbers to the right of the decimal, place the decimal after the 9 to get the answer 29.25
Write both numbers as improper fractions (or mixed numbers): 3.9=39/10 and 7.5=75/10. Then multiply 39/10*75/10 to get 2925/100, which simplifies to 29.25
Use lattice multiplication. This is a very uncommon method that I doubt the students will use, and I need to review it myself before I consider it.
Since 3.9 is very close to 4, we could instead do 47.5=30 and then subtract 0.17.5=.75 to get 30-.75=29.25
Similarly, since 7.5 rounds up to 8, we can do 3.98=31.2 and then subtract .53.9=1.96 to get 31.2-1.95=29.25
Are there any other possible methods the students might use? (Note: they are junior college math ed students.) Thanks!