Natural Numbers - Basics

An even number is a number that is divisible by $2$ with no remainder. It can also be described as a number that can be divided into $2$ equal groups.

An odd number is a number that when divided by $2$ has a remainder. It can also be described as a number that cannot be divided into $2$ equal groups.

Reminder - What is a remainder?
A remainder is the part left over after dividing by $2$. It's exactly the part that doesn't allow us to divide into $2$ equal groups.

A trick to check if a number is even or odd -
Check the ones digit of the number (the last digit of the number. When there is only one digit in the number, it is its ones digit)
If the ones digit of the number is $0$ or $2$ or $4$ or $6$ or $8$ - the number is even!
If not, the number is odd.

Let's practice:
Is the number $345$ even?
Solution: No. The ones digit is $5$ therefore the number is odd.
Is the number $230$ even?
Solution: Yes. The ones digit is $0$ therefore the number is even.

Want to learn more about even and odd numbers? Click here!

The decimal structure of a number classifies the number according to positions and sorts each digit into its corresponding group based on its position:
ones, tens, hundreds, thousands, and ten thousands.
For example, in the number $87,234$ there are
$4$ ones, $3$ tens, $2$ hundreds, $7$ thousands, and $8$ ten thousands

When we are asked about the value of each digit, we need to multiply the digit by its associated place value as follows:
The value of the digit $4$ is $4\cdot1=4$
We multiplied by $1$ because $4$ is in the ones place and $1$ represents ones.
The value of the digit $3$ is $3\cdot10=30$
We multiplied by $10$ because $3$ is in the tens place and $10$ represents tens.
The value of the digit $2$ is $2\cdot100=200$
We multiplied by $100$ because $2$ is in the hundreds place and $100$ represents hundreds.
The value of the digit $7$ is $7\cdot1000=7000$
We multiplied by $1000$ because $7$ is in the thousands place - $1000$ represents thousands.
The value of the digit $8$ is $8\cdot10000=80000$
We multiplied by $10000$ because $8$ is in the ten thousands place and $10000$ represents ten thousands.

Click here if you want to learn more about the decimal system.

Addition is marked with $+$
An operation that combines two numbers together.
In addition problems, the commutative property applies. We can switch the positions of the numbers and still obtain the same result.
Subtraction is marked with $–$
An operation that subtracts one number from the first number.
Here we cannot use the commutative property.
Multiplication is marked with $×$ or with $\cdot$
An operation that multiplies one number by another. It's very important that you learn the multiplication table!
The commutative property applies and we can switch the positions of the numbers without obtaining a different result.
Division is marked with $:$
An operation that divides a number into equal parts.
For example:
$10:2=5$
Here the commutative property does not apply.

Want to learn about basic operations? Click here!

Rounding numbers allows us to represent a number using a "round" number that is close to it, meaning a number whose ones digit is $0$.
For example, the number $48$ can be rounded to $50$.
Rounding numbers is a method that is not used in specific calculations, but rather when we want to perform general and simplified calculations,
such as when we need to do mental math for instance.

If we were asked to round to tens:
We check the ones digit -
If the ones digit is $5$ or higher, we round up to the nearest tens place. For example, $289$ rounds to $290$.
If the ones digit is less than $5$, we round down to the nearest tens place.
For example, $23$ rounds to $20$.

If we were asked to round to hundreds:
If the tens digit is $5$ or higher, we round up at the hundreds level to the nearest larger round number.
If the tens digit is less than $5$, we round down at the hundreds level to the nearest smaller round number.

Click here if you want to learn about rounding numbers!