# 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**

• Addition of Literals

• Subtraction of Literals

• Multiplication of Literals

• Division of Literals

• Constants and Variables

• Coefficient

• Addition of Literals

• Subtraction of Literals

• Multiplication of Literals

• Division of Literals

• Constants and Variables

• Coefficient