# MSC #3 – Number Splitting

Number splitting or number decomposition involves partitioning a number into
two or more components. Many arithmetic calculations can be simplified by
number splitting but it also has applications in higher math.
The division 653,978 ÷ 13, for example can be simplified by splitting the
dividend to 65| 39 | 78. We can then mentally divide 65, 39 and 78 separately
to give an answer of 05| 03 | 06 or 50, 306.
We can also express 997 as (1000 – 3) so that 997 x 7 can be easily computed
as 7000 – 21 or 6,979.
In our example, we want to find out what 17.5% of 840 is. We can avoid
decimal multiplication by splitting 17.5% into 10% + 5% + 2.5% and get the
equivalent percentages easily:
10% of 840 is 84
5% is half of 10% or 42
2.5% is half of 5% or 21.
So, 17.5 % of 840 is 84 + 42+ 21 = 147
Let us take another example: What is 47% of 74?
We can express 47% as (50% – 3%)
50% of 74 = half of 74 = 37
1% of 74 = 0.74
2% of 74 = 1.48
3% of 74 is 0.74 + 1.48 = 2.22
47% of 74 = 37 – 2.22 = 34.78