Multiply by Four
Multiplying by four is almost the same as multiplying by nine except that now we only add "half" the neighbor. Remember too that when adding "half" the neighbor we also add 5 if the number is odd.

The Rules For Multiplying By Four

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

An Example - Multiplying 3524 By 4


We will look at 3524 x 4 as our example. As for multiplying by nine we will put the nines and ten above the multiplicand that we need to subtract from. Remember this is just for illustration you don't write these down you just remember them.
Multiplying by Four Example 1 Setup

Step 1
Starting on the right we subtract the 4 from 10 giving us 6, there is no neighbor so we write this down.
Multiplying by Four Example 1 Step 1

Step 2
Moving left one place we now subtract 2 from 9 giving us 7. We now add "half" the 4 which is 2 to give a total of 9. We write down the 9.
Multiplying by Four Example 1 Step 2

Step 3
Moving left again we now subtract 5 from 9, which is 4. The 5 is odd so we need to add 5 to the 4 giving us 9. Half of 2 is 1, adding this to the 9 gives us 10.
Multiplying by Four Example 1 Step 3
We write the 0 down and carry the one. We put a dot above the 0 to show the carry.

Step 4

For the next digit we subtract 3 from 9 to get 6. The 3 is odd so we add another 5 to get 11. We add the carry from the previous step to get 12.  Adding "half" of 5, which is 2, we end up with 14.
Multiplying by Four Example 1 Step 4
We write the 4 down and carry the 1, indicated by a dot.

Last Step
We are now at the last step where we take "half" of 3, the neighbor, which is 1 but we have to subtract 1 from this giving us 0. Adding the carry from the previous step we end up with 1.
Multiplying by Four Example 1 Last Step
We write the 1 down giving us our answer of 14096.

These rules will work for all numbers, however when multiplying a single digit number by 4 you would simply omit rule 2 and only use rules 1 and 3.

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