**Elementary School Number Sense Lesson 18: Finding How Many Odd or Even Numbers are between Two Numbers**

This concept appeared

**8 times**this year on elementary tests (once per test), always at

**question # 18**.

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There are a few versions of this problem:

- How many
**whole numbers**are between X and Y? - How many
**odd**(or**even**) numbers are between X and Y? - How many numbers between X and Y are
**divisible by Z**?

Please do not give in to the temptation to

**count**the relevant numbers. A simple calculation will give you the answer.

**Whole Numbers:**

- Subtract the endpoints.
- Subtract 1.
*Since we are finding the numbers***between**, we can’t include either endpoint.

**Odds:**

- Subtract the endpoints.
- Divide by 2.
- If the endpoints were both even, leave the answer as is.
- If one endpoint was odd and one was even, round down to the whole number.
- If both endpoints were odd, subtract 1.

**Evens:**

- Subtract the endpoints.
- Divide by 2.
- If the endpoints were both odd, leave the answer as is.
- If one endpoint was odd and one was even, round down to the whole number.
- If both endpoints were even, subtract 1.

**Divisible by Z:**

- Divide the larger endpoint by Z, and disregard any remainder.
- Divide the smaller endpoint by Z, and disregard any remainder.
- Find the positive difference between the quotients.

**Example 1: How many whole numbers are between 17 and 34? ___**

- Subtract: 34 – 17 =
**17** - Subtract 1 to get
**16**

**Example 2: How many odd numbers are between 14 and 40? ___**

- Subtract: 40 – 14 =
**26** - Divide by 2 to get
**13**. Both endpoints are even, so leave the answer as is.

**Example 3: How many even numbers are between 18 and 24? ___**

- Subtract: 24 – 18 =
**6** - Divide by 2 to get
**3**. Both endpoints were even, so subtract 1 to get**2**. (They are 20 and 22).

**Example 4: How many odd numbers are between 11 and 48? ___**

- Subtract: 48 – 11 =
**37** - Divide by 2 to get
**18**R 1. The endpoints were odd and even, so round down to**18**.

**Example 5: How many numbers between 11 and 82 are divisible by 6? ___**

- Divide 82 by 6 to get
**13**R 4. Disregard the remainder. - Divide 11 by 6 to get
**1**R 5. Disregard the remainder. - Subtract: 13 – 1 =
**12**.

**Here's a free worksheet to help you practice OddEven:**

oddeven.pdf |

**Up Next for Elementary School: Mult75**