To find the number of integers between two given integers, subtract the smaller integer from the larger integer and then subtract 1.
Let's break this down:
-
Find the Difference: Subtract the smaller integer from the larger one. This gives you the total number of integers including both the starting and ending integers.
-
Subtract 1: Because we want the integers between the two given integers (and not including them), we subtract 1 from the difference.
Example:
Let's say you want to find the number of integers between 3 and 7.
- Find the Difference: 7 - 3 = 4
- Subtract 1: 4 - 1 = 3
Therefore, there are 3 integers between 3 and 7 (which are 4, 5, and 6).
Formula:
If a and b are integers, where b > a, then the number of integers between a and b is:
( b - a ) - 1
Why does this work?
The initial subtraction (b - a) gives you the total number of integers from a to b, inclusive. Since we only want the numbers between a and b, we exclude both a and b by subtracting 1.
