The document discusses dividing a decimal number by another decimal number. It explains that regular division does not work comfortably with decimal divisors. Instead, it is better to multiply the dividend and divisor by powers of 10 to clear the decimals, then perform long division. This allows dividing decimal numbers using the standard procedure. It provides an example of dividing 37.5 by 1.25 by first multiplying both numbers by powers of 10 to obtain integers that can be divided using long division.

1. Dividing by a
Decimal Number
The strange story of:
37.5 ÷ 1.25

2. FIRST…
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.

3. 37.5 ÷ 1.25
125 375
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 ?

4. 37.5 ÷ 1.25
will give the same answer as 375 ÷ 12.5
...since we multiplied BOTH Dividend and Divisor by 10.
125 375
…and we can do this multiplication by moving the
decimal point one place to the right !

5. and 375 ÷ 12.5
will give the same answer as 3750 ÷ 125
…since we multiplied BOTH Dividend and Divisor by 10 again.
125 3750
…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.

6. and 3750 ÷ 125
we can solve in the usual way
30
125 3750
-375
0

7. and 3750 ÷ 125
we can solve in the usual way
30
125 3750
-375
0