Addition of Literals

Addition of literals obey all properties of addition of numbers. Suppose we are asked to find the sum of two numbers, say 3 and 5. The sum of 3 and 5 is denoted by 3 + 5. Exactly in the same way, the sum of the literal y and a number 7 is denoted by y + 7 and is read as ‘y plus 7’. y + 7 can also be read as ‘7 more than y or increase y by 7’.

Similarly, y more than a literal x is written as x + y. We can also read x + y as the sum of x and y. (x + y) + z means that the sum of literals x and y is added to the literal z whereas x + (y + z) means that the literal x is added to the sum of literals y and z.

Let us consider an algebraic entity ‘m’ and we want to add 25 to it. We write this operation as m + 25, just as we do for arithmetical quantities. We may also add one quantity m to another quantity n and this process is represented by m + n. The sum of m and 25 is written as m + 25.

Sum of two literal numbers m and n is written as m + n.

The sum of m and m is written as m + m = 2m.

Sum of m, n and 5 is written as = m + n + 5.

Properties of Addition of Literals:

Since literals are used to represent numbers. Here, we list the properties of addition of literals.

Commutativity: For any two literals a and b, we have

a + b = b + a

2 + x = x + 2

Associativity: For any three literals a, b and c, we have

(a + b) + c = a + (b + c)

(3 + x) + y = 3 + (x + y)

Identity: For any literals a, we have

a + 0 = a = 0 + a

5 + 0 = 5 = 0 + 5

Here ‘0’ is known as the additive identity.

Problems on Addition of Literals

Write each of the following phrases using numbers, literals and the basic operation of addition :

(i) The sum of x and 3.

Answer: x + 3

(ii) The sum of 10 and z.

Answer: 10 + z

(iii) The sum of x and y.

Answer: x + y

(iv) 3 more than a number x.

Answer: x + 3

(v) 100 more than a number p.

Answer: p + 100

(vi) x added to 9.

Answer: x + 9

(vii) m added to 50.

Answer: m + 50

(viii) Increase x by 4.

Answer: x + 4

(ix) Increase z by 10.

Answer: z + 10

(x) The sum of x and 5 added to y.

Answer: (x + 5) + y

(xi) The sum of m and 25 added to n.

Answer: (m + 25) + n

(xii) The sum of x and y added to z.

Answer: (x + y) + z

(xiii) The sum of a and b added to 5.

Answer: (a + b) + 5

(xiv) x added to the sum of y and 4.

Answer: x + (y + 4)

(xv) 5 added to the sum of a and b.

Answer: 5 + (a + b)

(xvi) a added to the sum of y and z.

Answer: a + (y + z)