Quandaries and Queries


Hello - I am a grad student in elementary education and have some math questions:
  1. Without performing the division, explain why 5 divided by 1/7 is a number greater than 5 divided by 2/3.
  2. Is the least common multiple of two prime numbers always their product? Why or why not?
Thank you!



I can answer your first question about 5 divided by 1/7 being greater than 5 divided by 2/3. The division question is really this one:

How many times does 1/7 go into 5 and how many times does 2/3 go into 5? Since 1/7 is smaller than 2/3 it would go into 5 more times, and hence the first question would have the larger answer. Students can understand this when the question is formulated this way. They can really see and understand when you use manipulatives such as pattern blocks and fraction blocks. If you're not sure what these blocks are, write again.




The answer to your second question is yes if the two primes are different.


Go to Math Central