Addition of Literals

The Properties of Literal Addition:

Due to the fact that literals are utilized to represent integers, adding variables follows all of the same rules as the addition of integers. The addition of Literals (variables) follows all of the characteristics of number addition.

Consider the situation in which we are requested to determine the sum of two integers, say 4 and 4. The total of four and four is represented as 4 + 4. Similarly, the sum of the literal x and a number 5 is represented as x + 5, which can alternatively be interpreted as 'x plus 5' or 'increase x by 5'.

Similarly, y that is more than a literal x is denoted as x + y. Additionally, we may interpret x + y as the total of x and y.

(x + y) + z denotes the addition of the literals x and y to the literal z, while x + ( y + z) denotes the addition of the literal x to the total of the literals y and z.

The next section discusses the characteristics of variable addition.

Commutativity: 

We have commutativity for any two literals u and v.

u + v = v + u

2 + A = A + 2.

Associativity:

We have associativity for any three literals a, b, and c.

E.g 1. (a + b) + c = (b + c) + (a)

E.g.2. (5+ x) + y = 5 + (x + y).

Identity:

We have an identity for any literals a.

E.g. 1. A + 0 equates to 0 + A

2 + 0 = 

0 + 2.

In this case, '0' is referred to as the additive identity.

Problems related to Addition of Literals

Each of the following sentences should be written using numbers, literals, and the fundamental addition operation:

1. The sum of x and 5.

Ans. x + 5

2. The sum of y and 5.

Ans. y + 5

3. The sum of x and y.

Ans. x + y

4. Four more than x.

Ans. x + 4

5. 10 more than a certain number q.

Ans. q + 10

6. x added to 20.

Ans. x + 20

7. Increase z by a factor of ten.

Ans. z + 10 

8. The sum of n and 20 added to x.

Ans: (n + 20) + x

9. The sum of a and b added to c.

Ans: (a + b) + c

10. The sum of x and y is added to 4.

Ans: (x + y) + 4

An overview of literal subtraction 

Literals and their composition with numbers are subtracted according to the same principles as numbers.

When required to subtract four from nine, we write 9 – 4.

Similarly, when required to subtract a number from a literal h, such as 2, we write h – 2, which is interpreted as 'h minus 2'.