Multiplication of Literals 

The process of multiplying literals is identical to the operation of multiplying integers. Multiplication was learned in arithmetic as repeated addition.

For instance, 4 + 4 + 4 + 4 is referred to as 4 times 4 and is written as 4 x 5.

Similarly, if an is a literal, p + p + p + p equals 4p and is denoted by the symbol 4p.

Occasionally, the multiplication symbol is mistaken with the letter x. To prevent such misunderstanding, we remove the sign of multiplication when a number is multiplied by a literal or when two literals are multiplied by a number.

Thus, if there is no symbol between a literal and the sum of two literals, it is understood that the two have been multiplied.

Therefore, a + a + a + a + a = 5 x a = 5a

Likewise, the product of the literals a and b is denoted by ab.

It is worth noting that the type y 4 product is not written as y4. Traditionally, it is spelled as 4y.

# Examples of Literal Multiplication

1. Write the following sentences using numbers, literals, and addition, subtraction, and multiplication operations:

1. 5 times a

Ans: 5a

2. a times b

Ans: ab

3. x times 10

Ans: 10x

4. The product of x and y.

Ans: xy

5. 7 times a added to b.

Ans: 7a + b

6. a times b added to 4.

Answer: ab + 4

7. 10 times the sum of x and y.

Ans: 10(x + y )

8. 10 times a is subtract from a

Ans: b – 10a.

9. p times q is subtract from 10

Ans: 10 – pq.

10. 200 more than twice a number y.

Ans: 200+2y

11. Thrice a number 

Ans. y = 3y.

12. A number is 10 more than thrice a number 

Ans. y = 3y + 10

13. 10 times x added to y .

Ans: 10x + y

14. p times q added to 5 .

Ans: pq + 5

15. 10 times the sum of a and b.

Ans: 10(a + b )

16. a times the sum of 15 and b.

Ans: a(15 + b)

17. 15 times p is subtract from q

Ans: q – 15p.

18. p times q is subtract from 20

Ans: 20 – pq.

Commutative, Associative, and identity properties

The characteristics of literal multiplication are given below.

1. Commutative property:

Commutativity states that for any two literals a and b, ab = ba.

Thus, literal multiplication is commutative.

2. Associativity property:

Consider any three literals a, b, or c, we have,

(a x b )  x c  = a x (b x c)

Thus, literal multiplication is associative.

3. Identity: Consider a literal P

 P x 1 = 1 x P

In this case, '1' is referred to as the multiplication identity.

4. Distributive carried out on multiplication and addition: Consider any three literals p,q, and r.

p x (q + r) = pq + pr