odd number
Grade 4 students learn about odd numbers in Saxon Math Intermediate 4 Chapter 1, defined as whole numbers that cannot be split into two equal groups—there is always one left over. Odd numbers end in 1, 3, 5, 7, or 9 regardless of how many other digits the number contains. The number 578 is even (last digit 8), even though it contains odd digits 5 and 7. Students also practice identifying even numbers (ending in 0, 2, 4, 6, 8) and understanding that 8,465 is odd because its last digit is 5, so it cannot be divided into groups of 2 with nothing left over.
Key Concepts
Property If a whole number is not an even number, then it is an odd number ($1, 3, 5, 7, \ldots$). If you try to separate an odd number of objects into two equal groups, there will be one extra object.
$463$ is odd because its last digit is $3$. $99$ is odd because it ends in $9$. Trying to split $5$ dots into two groups leaves one dot leftover, proving $5$ is odd.
Odd numbers are the quirky individualists of the number world! When you try to divide them into two equal groups, there’s always one item left out, like the odd one out. A number is odd if its very last digit is a 1, 3, 5, 7, or 9. That's the only clue you need!
Common Questions
What is an odd number?
An odd number is a whole number that cannot be divided evenly into two equal groups—there is always one item left over. Odd numbers end in 1, 3, 5, 7, or 9.
How do you determine if a large number like 8,465 is odd or even?
Look only at the last digit. The last digit of 8,465 is 5. Since 5 is an odd digit (in the list 1, 3, 5, 7, 9), the number 8,465 is odd.
Is 578 an odd number?
No. Even though 578 contains the odd digits 5 and 7, only the last digit matters. The last digit is 8, which is even. Therefore 578 is an even number.
What digits make a number odd?
A number is odd if and only if its last digit is 1, 3, 5, 7, or 9. The other digits in the number do not matter at all for determining odd or even.
Why does only the last digit determine if a number is odd or even?
Because any multiple of 10 (hundreds, thousands, etc.) is always even—only the ones column can contribute an odd amount. So the entire number's odd-or-even status depends solely on the ones digit.
Can a farmer equally fill cartons of 2 with 8,465 eggs?
No. 8,465 is an odd number (last digit 5), so it cannot be divided into groups of 2 with nothing left over. One egg would always remain outside the cartons.