Addition

Addition involves combining two numbers to form their sum. For example, the sum of 5 and 8 is given by
            5 + 8 = 13
and the sum of 11 and 5 is given by
            11 + 5 = 16

Multiplication

Multiplication is simply repeated addition. The number obtained as the result of multiplication is called a product. For example, the product of 4 and 5 is given by 
            4 × 5 = 5 + 5 + 5 + 5 = 20  
and the product of 7 and 4 is given by
            7 × 4 = 4 + 4 + 4 + 4 + 4 + 4 + 4 = 28

Does the Order Matter?

Addition and multiplication are "commutative" operations. This means that when we add or multiply numbers together, the order in which we do it does not matter. For example,
            5 + 8 = 8 + 5
            7 × 4 = 4 × 7 
Addition and multiplication are also "associative" operations. This means that, for example, 
            (5 + 5) + 3 = 5 + (5 + 3)
            (2 × 2) × 5 = 2× (2 × 5)
where the parts in brackets are always carried out first. Again, the order in which the numbers are added or multiplied does not matter. Subtraction and division are two of the four basic operations of arithmetic. The other two are addition and multiplication.

Subtraction

Subtraction is the inverse operation of addition. Subtraction involves taking one number away from another to find the difference between the two numbers. For example, subtracting 2 from 9 gives
            9 - 2 = 7
and subtracting 3 from 5 gives
            5 - 3 = 2

Division

Division is the inverse operation of multiplication, and is a process of sharing. For example, sharing 12 sweets among 4 people is the same as dividing the 12 sweets by 4. The result of dividing one number by another is a quotient. For example, dividing 12 by 4 gives a quotient of 3. That is,
            12 ÷ 4 = 3
Dividing 8 by 2 gives a quotient of 4. That is,
            8 ÷ 2 = 4

Go to top

Does the Order Matter?

Subtraction and division are not "commutative" operations. This means that, when we subtract or divide numbers, the order in which we do it matters. For example, 9 - 2 ¹ 2 - 9
            12 ÷ 4 ¹ 4 ÷ 12
The symbol ¹ means "is not equal to". Neither subtraction nor division are "associative" operations. For example,
            (9 - 2) - 3 = 7 - 3 = 4
but
            9 - (2 - 3) = 9 - (-1) = 10
Therefore,
            (9 - 2) - 3 ¹ 9 - (2 - 3)
Similarly,
            (16 ÷ 8) ÷ 2 = 2 ÷ 2 = 1
but
            16 ÷ (8 ÷ 2) = 16 ÷ 4 = 4
Therefore,
            (16 ÷ 8) ÷ 2 ¹ 16 ÷ (8 ÷ 2)
Again, the order is which the numbers are subtracted or divided is important.