The strange story of: 37.5  1.25 Dividing by a Decimal Number

FIRST … QUICK ESTIMATE Come up with a QUICK ESTIMATE … 37.5  1.25 looks like it will be close to 37  1, which would equal just 37. SO… we will be looking for an answer around 37 and REJECT an answer of 300-something or 3-something.

 37.5  To solve this problem using the “paper and pencil” procedure we would set it up like THIS. BUT… the regular division procedure does not work comfortably with decimal divisors… what can we do ?

37.5  will give the same answer as 375  since we multiplied BOTH Dividend and Divisor by 10. …and we can do this multiplication by moving the decimal point one place to the right !

 and 375  will give the same answer as 3750  125 …since we multiplied BOTH Dividend and Divisor by 10 again. …and we can do this multiplication by moving the decimal point one more place to the right ! and annexing a zero in the ones place.

and 3750  125 we can solve in the usual way