Literal numbers are the letters which are used to represent a number.
The literal numbers are also known as literals. Literal numbers obey all the rules of addition, subtraction, multiplication and division of numbers. Thus,
a + b means b is added to a
a - b means b is subtracted from a
a × b means a is multiplied by b
a ÷ b means a is divided by b
In multiplication, sometimes dot ‘.’ is used instead of ‘×’. The sign ‘.’ or ‘×’ is generally omitted between a digit and a letter or between two or more letters.
(i) 5 × a or 5∙a can be written as 5a.
(ii) 10 × p can be written as 10∙p or 10p.
(iii) a × b can be written as a∙b or ab.
(iv) 2 × a × b can be written as 2∙a∙b or 2ab.
(v) a × b × c can be written as a∙b∙c or abc.
(vi) x × y × z can be written as x∙y∙z or xyz.
(vii) 5 × l × m × n can be written as 5∙l∙m.n or 5lmn.
(viii) a × x × y × z can be written as a∙x∙y.z or axyz.
(xi) 10 × j × k × l × m can be written as 10.j.k.l.m or 10jklm.
(x) 1000 × x can be written as 1000.x or 1000x.
But ‘.’ or ‘×’ must never be omitted between the digits.
Thus, 3× 5 can be written as 3∙5, but 3×5 or 3∙5 can never be written as 35.
Now, let us consider the perimeter of a square. We know that the perimeter is equal to the sum of all sides of a square.
Perimeter of a square of side 5 units =(5 + 5 + 5 + 5) units
= 4 × 5 units
= 20 units
Similarly, perimeter of a square of side 10 units = (10 + 10 + 10 + 10) units
= 4 × 10 units
= 40 units
Perimeter of a square of side 20 units = (20 + 20 + 20 + 20) units
= 4 × 20 units
= 80 units and so on.
Thus, we observe that in each case the perimeter is four times the length of its sides. That is,
Perimeter = 4 ×(Length of the side)
If we represent perimeter by P, length of the sides by s, the above statement can be briefly written as
P= 4 × S
The result (or rule) is true for all the system of units and for all possible value of the lengths of the side of the square.
So, from the above discussion that the use of the letters to represent numbers helps us to build formula such as
P = 4 × s, i.e., Perimeter of a square = 4 × length of the side
x × 0 = 0
and, 1 × a = a
Here, P, s, x and a represent numbers.
Also, the use of letters to represent numbers helps to think in more general terms. These letters are generally known as literals.
From now onwards unless, otherwise stated, instead of the saying ‘x represents a number’ we shall simply say ‘x is a number’.
Similarly, for ‘y represents a number’ we shall simply say ’y is a number’, and so on.
Properties of Multiplication of Literals
6th Grade Page
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