Multiply by ThreeOur rules for multiplying by three are similar to those we used when multiplying by eight but we only add "half" the neighbor this time. When adding half the neighbor we also add 5 if the number is odd. The other difference is we only take "half" of the left-hand digit and reduce it by two.

The Rules For Multiplying By Three

  1. First Step: Subtract from 10 and double, and add 5 if the number is odd.
  2. Middle Steps: Subtract from 9, double and add 5 if the number is odd, and add “half” the neighbor.
  3. Last Step: Take “half” the left-hand digit of multiplicand and reduce by 2.

An Example - Multiplying 2583 By 3

Lets look at 2583 x 3 as our example. We prepare the sum as we did before.Multiplying by Three Example 1 Setup

Step 1
Starting on the right we subtract 3 from 10 to give us 7, doubled it is 14, adding 5 because 7 is odd gives us 19.Multiplying by Three Example 1 Step 1We write down the 9 and put a dot above it to show we are carrying the 1.

Step 2
Moving left we now subtract 8 from 9 giving us 1, doubled is 2, we add the 1 from the carry so we have 3. Adding "half" of 3, the neighbor, which is 1 for a total of 4.Multiplying by Three Example 1 Step 2We write the 4 down.

Step 3
Moving left again we subtract 5 from 9 which is 4, doubled is 8. We add 5 more, as 5 is odd, for a total of 13, adding 4 from "half" of the 8 gives us 17.Multiplying by Three Example 1 Step 3We write down the 7 and carry the 1, indicated by a dot above the 7.


Step 4
Going left again we now subtract 2 from 9, which is 7, doubled is 14. "Half" of 5 is 2, plus the carry gives us 17.Multiplying by Three Example 1 Step 4We write down the 7 and carry the 1. Another dot indicates the carry.

Last Step
On the last step we take "half" of the 2 which is 1. We add the carry giving us 2 then we subtract 2 for a total of zero. We do not need  to write the zero and we have our answer of 7749.TS_M3_E1_LastStep

These rules will work for all numbers, however when multiplying a single digit number by 3 you would simply omit rule 2 and only use rules 1 and 3.

If you have any questions or comments please leave them below.