## Algebra

## Related Lessons

- Adding and Subtracting Scientific Notation
- Adding Fractions
- Algebra Calculators
- Arithmetic Sequence
- Average Rate of Change
- Change of Base Formula
- Cm to M
- Commutative Property of Addition
- Completing the Square
- Cross Product Calculator
- Determinant Calculator
- Determinant of a Matrix
- Difference of Squares
- Discriminant
- Divisibility Rule for 7
- Dot Product Calculator
- Eigenvalue Calculator
- Eigenvector Calculator
- Equation of a Circle
- Even Numbers
- Exponent Rules
- Factorial Calculator
- Fractional Exponents
- How to Find the Median
- Interval Notation
- Matrix Addition
- Matrix Subtraction
- Midpoint Formula
- Multiplying Negative Numbers
- Negative Exponents
- Odd Numbers
- One to One Function
- Partial Fraction Decomposition Calculator
- Point Slope Form
- Properties of Multiplication
- Rationalize the Denominator
- Rectangular to Polar Calculator
- Reflexive Property
- Round to the Nearest Tenth
- RREF Calculator
- Slope Calculator
- Slope Intercept Form
- Standard Form
- Summation Calculator
- Vertex Form

### Tutors/teachers:

Nikkolas

Tutor and Aerospace Engineer

# Odd Numbers

## The Definition of an Odd Number

**An odd number is an integer not divisible by 2 without having a remainder. Odd numbers end in 1, 3, 5, 7, and 9. **In other words, an integer is considered an odd number if dividing it by 2 does not result in an integer.

An integer is a whole number. Examples of integers are 0, 5013, and -44. Examples of non-integers are 3/5, 1.3, and -√11. Non-integers are not considered odd or even. They do not follow the requirements of either category.

Some odd numbers shown with green background.

### How to Prove Odd Numbers are Odd

Here’s a look at the single digit odd numbers being divided by two. Remember, these are integers that result in a non-integer when dividing by two.^{1}⁄_{2} = 0.5^{3}⁄_{2} = 1.5^{5}⁄_{2} = 2.5^{7}⁄_{2} = 3.5^{9}⁄_{2} = 4.5

We can keep going up and up the list of odd numbers and the result of dividing by two will always be 0.5 ± some integer.

### Example Problems

**Problem 1:**

Is 24 an odd number?

Solution:

24 is an integer. To see if it is an odd number, let’s check with both methods. The last digit is 4, so it must not be an odd number. Dividing it by 2, we get 24/2 = 12, which has no remainder/is an integer result.**No, 24 is not an odd number.**

**Problem 2:**

Is 37 an odd number?

Solution:

37 is an integer. To see if it is an odd number, let’s check with both methods.

The last digit is a 7 so we know it must be an odd number. Dividing it by 2, we get 37/2 = 18.5, which has a remainder/is a non-integer result.**Yes, 37 is an odd number.**

### Result :

### Worksheet 1

Download.pdf

### Cheat sheet

Download.pdf