The first step in the strategy is to break a number down into its components: ones, tens, hundreds, etc. For example, the number 1234 would become:
1000+200+30+4; and 789 would become:
700+80+9.
The next part of the strategy is to use the associative property to change the order of the components:
30+1000+4+200, or 9+700+80, for example.
But here’s where the trick is: the order isn’t random. The order is arranged so as to make manipulation of two numbers easier, if we need to add, subtract, multiply or even divide two numbers. These operations can then be broken down into a set of easier sums, in many cases using mental arithmetic. The associative property can also be used to rearrange the arithmetic:
Example: Suppose we want to subtract 789 from 1234.
Here’s how you could do it using place value strategy.
1234=1000+200+30+4, and we keep this order as it is.
Now we look at 789=700+80+9. We keep this order, too, but we rearrange the arithmetic when we do the subtraction:
1000-700+200-80+30-9+4. The arithmetic is now simplified because we can reduce this to some simple sums by grouping the operations:
1000-700=300+
200-80=120+
30-9=21+
4.
The final sum is:
300+
120+
21+
4=
445.
This is the result of calculating 1234-789.