Question

Find the difference: $13007 - 9999$

Answer 1

Hint: We can write 9999 as the difference from the closest power of 10. We can rewrite the expression and do the subtraction place by place. Then we can simplify the other operations to get the required difference.

Complete step-by-step answer:
We need to find the value of $13007 - 9999$.
We can write 9999 as the difference of a simple number that is easier for subtraction.
 $ \Rightarrow 9999 = 10000 - 1$
On substituting this on the given expression, we get,
  $13007 - 9999 = 13007 - \left( {10000 - 1} \right)$
On opening the bracket and applying the negative signs, we get,
  $ \Rightarrow 13007 - 9999 = 13007 - 10000 + 1$
Now we can do the addition.
  $ \Rightarrow 13007 - 9999 = 13008 - 10000$
Now we can subtract the numbers. For that we can write the numbers one below the other and subtract the numbers belonging to each place from the number above it.
So, we can write,
 $
  \,\,\,\,\,\,\,\,13008 \\
  \left( - \right)\,\underline {10000} \\
  \,\,\,\,\,\,\,\,03008 \\
 $
Now we can write the given expression as,
  $ \Rightarrow 13007 - 9999 = 3008$
Therefore, the required difference is 3008.

Note: An alternate method to solve this problem is given by,
We need to find $13007 - 9999$ .
We can write 13007 as the sum of 10000 and remaining numbers.
So, we can write, $13007 = 10000 + 3007$
So the expression will become,
 $ \Rightarrow 13007 - 9999 = 10000 + 3007 - 9999$
On rearranging, we get,
 $ \Rightarrow 13007 - 9999 = 10000 - 9999 + 3007$
On doing the subtraction, we get,
 $ \Rightarrow 13007 - 9999 = 1 + 3007$
On further addition of the terms, we get,
 $ \Rightarrow 13007 - 9999 = 3008$
Therefore, the required difference is 3008.