# Multiplication of Literals

In this section we will discuss about multiplication of literals In arithmetic, we have studied multiplication as the repeated addition. For example, 2 + 2 + 2 + 2 is called 4 times 2 and is written as 4 x 3. Similarly, if a is literal, then a + a + a + a is 4 times a and is written 4 x a , this is Multiplication - Literals.

Sometimes, the sign of multiplication is confused with letter x. To avoid such confusion, we omit the sign of multiplication between a number and a literal or between two literals. Thus, when there is no sign between a literal and a number or between two literals, it is understood that the two are multiplied.
Thus, a + a + a + a = 4 x a = 4a

Similarly, the product of literals x and y is written as xy.

It should be noted that the product of the type a x 4 is not written as
a4 . Conventionally, we write it as 4a .

Properties of Multiplication of Literals :

As mentioned earlier that literals are used to represent numbers. Therefore, multiplications of variables obey all properties of multiplication of tables. Here, we list the properties of multiplication of variables.

Commutativity : For any two literals a and b, we have , ab = ba i.e. , the multiplication of variables is commutative.

Associativity : For any three literals a, b and c, we have, (ab)c = a (bc) i.e. the multiplication of variables is associative.

Identity: For any literal a, we have, b x 1 = b = 1 x b. Here ‘1’ is known as the multiplication identity.

Distributive of multiplication over addition: For any three literals a, b and c, we have (i) a (b + c) = ab + ac (ii) (b + c)a = ba + ca

Examples :

Write each of the following phrases using numbers, literals and the basic operations of addition, subtraction and multiplication:
(i) 4 times x
solution : 4x

(ii) The product of 4 and y
solution : 4y

(iii) Multiply x by 7
solution : 7x

(iv) a times c
solution : ac

(v) 3 times y added to z
solution : 3y + z

(vi) 4 times the sum of a and b
solution : 4( a + b)

(vii) 5 times x is subtracted from z
solution : z - 5x

(viii) 8 times d
solution : 8d

(ix) a times c added to 3
solution : ac + 3

(x) 5 times t subtracted from s
solution : s - 5t

Introduction to Algebra