OPERATIONS INVOLVING NATURAL NUMBERS

Addition

Addition is ...

... bringing two or more numbers (or things) together to make a new total.
Here 1 ball is added
to 1 ball
to make 2 balls:

external image add.jpg
Using Numbers it is:

1 + 1 = 2



And in words it is:

"One plus one equals two"

Larger Numbers: Addition in Columns

To add larger numbers, you can use Column Addition :
Column Addition
Column Addition

Names

Other names for Addition are Sum, Plus, Increase, Total

And the numbers to be added together are called the "Addends":
external image addition.gif

Subtraction

Subtraction is ...

... taking one number away from another.
external image subtraction.gif
If you have 5 apples
and you subtract 2,
you will be left with 3.
This would be written:
5 - 2 = 3

Names

Other names used in subtraction are Minus, Less, Difference, Decrease, Take Away, Deduct.
The names of the numbers in a subtraction fact are:
Minuend - Subtrahend = Difference
Minuend - Subtrahend = Difference


Minuend - Subtrahend = Difference

Minuend: The number that is to be subtracted from.
Subtrahend: The number that is to be subtracted.
Difference: The result of subtracting one number from another.

Long Multiplication

Long Multiplication is a special method for multiplying larger numbers.
It is a way to multiply numbers larger than 10 that only needs your knowledge of the ten times Multiplication Table.
Let us say we want to multiply
612 × 24
  • First we multiply 612 × 4 (=2,448),
  • then we multiply 612 × 20 (=12,240),
  • and last we add them together (2,448+12,240=14,688).
But we can do better!
When we multiply 612 × 20 we only need to multiply 612 × 2 and place the result one column over(so it is the same as multiplying by 20).
long multiply
long multiply

Division

Division is splitting into equal parts or groups.

It is the result of "fair sharing".


Symbols

÷ /
We use the ÷ symbol, or sometimes the / symbol to mean divide:
12 ÷ 3 = 4

12 / 3 = 4

I will use both symbols here so you get used to it.

Names

There are special names for each number in a division:
dividend ÷ divisor = quotient


But Sometimes It Does Not Work Perfectly!

Sometimes you cannot divide things up evenly ... there may be something left over.

Example: There are 7 cookies, and 2 people want to share them equally.

But 7 cookies cannot be divided exactly into 2 groups,

each person gets 3 cookies,

but there will be 1 left over:
remainder-7-2
remainder-7-2

We call that the Remainder.