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Inclusive Counting

The concept of inclusive counting is crucial for accurately solving problems where both endpoints are included in the count. This method adjusts for the common oversight in ordinary subtraction, which automatically excludes the lower endpoint.
  • Inclusive counting is used when both the starting and ending values are part of what we are counting.
  • To perform inclusive counting, subtract the lower value from the higher value and then add one to include the starting value.
  • This method is essential for accurately determining the length of events or the quantity of items within a specified range.
  • Examples provided include calculating the number of days in a workshop, the duration of contract negotiations, and the count of multiples of a number within a range.
Understanding Inclusive Counting
Applying Inclusive Counting to Real-World Problems
Inclusive Counting in Contract Negotiations
Counting Multiples with Inclusive Counting

FAQ: I can’t remember how many days are in each month of the year. Will I need to know this for the test?

A: It’s highly unlikely that you’d have to know this. If there’s a question on the test where you need to know how many days are in a certain month, the information would probably be given as part of the problem.

However, if you want to be hyper-prepared for the test, and you want to be ready for any situation that might come up on the test (however unlikely), then you could learn how many days are in each month (here’s a poem that will help). Otherwise, don’t worry about this – it’s VERY unlikely that you’ll need to know it!

FAQ: For the last example (multiples of 8 between 200 - 640 inclusive), I subtracted 200 from 640, divided by 8 and then added one. Is this a valid strategy?

A: Yes, this method works!

You need to be careful, though: how did you know to add 1? That’s the correct thing to do here, but make sure you're not off by 1 in your final answer. One way to double check is to use small numbers/intervals that you can count directly as well to verify. For example:

How many multiples of 5 are there between 20 and 10 inclusive?

Just by counting, we know there are 3: 10, 15, 20

20 - 10 = 10

Divide by 5 = 2

2 + 1 = 3 

OK, so we confirmed that adding 1 should give us the correct result. So you add 1 to 55 in this case.

It’s always a good idea to check with smaller numbers if you're using a method like this!