Trick No. 5 – Multiplying and Dividing with Decimal Points

This trick actually incorporates a few other tricks. Some we’ve already learned. One in particular is brand new, and another isn’t so much a trick as a sensible approach…

Step 1: Disregard any decimal points and ending zeros
For example, 2.4 x 1.50 should be viewed as 24 x 15

Step 2: Do your multiplication or division
24 x 15
= (4 x 6) x (3 x 5) (this is a new trick in its own right, but  handy)
= 4 x 5 x 3 x 6
= 20 x 18 – apply Trick No. 1 to get 2 x 18 = 36, and add a zero to get 360, although we don’t really need this, as we’ll see in a minute.

Step 3: Apply a Test of Reasonableness (ToR)
The original problem was 2.4 x 1.5. That’s about 2 and a half times 1 and a half: More than 2, but less than 4.
This tells us where to put the decimal point:

3.6 is our final answer (not 360 or 36 or 0.36…)

Example 1: 1.2 x 1.2
Step 1: Convert to 12 x 12
Step 2: Multiply to get 144
Step 3: ToR for decimal place; answer: 1.44
(The original problem was close to 1 x 1)

Example 2: 48 ÷ 2.4
Step 1: Convert to 48 ÷ 24
Step 2: Divide to get 2
Step 3: ToR for decimal place; answer: 20
(The original problem was close to 50 ÷ 2)

Example 3: 930 ÷ 3.1
Step 1: Conver to 93 ÷ 3 (remember dropping zeros?)
Step 2: Divide to get 31
Step 3: ToR for decimal place; answer: 310
(The original problem was close to 900 ÷3)