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.

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.

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

(i) The sum of x and 3.

(ii) The sum of 10 and z.

(iii) The sum of x and y.

(iv) 3 more than a number x.

(v) 100 more than a number p.

(viii) Increase x by 4.

(ix) Increase z by 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)

Subtraction of Literals

Multiplication of Literals

Properties of Multiplication of Literals

Division of Literals

Powers of Literal Numbers

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles 1. ### Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

Dec 01, 23 01:16 AM

There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

2. ### Days of the Week | 7 Days of the Week | What are the Seven Days?

Nov 30, 23 10:59 PM

We know that, seven days of a week are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. A day has 24 hours. There are 52 weeks in a year. Fill in the missing dates and answer the questi…

3. ### Types of Lines |Straight Lines|Curved Lines|Horizontal Lines| Vertical

Nov 30, 23 01:08 PM

What are the different types of lines? There are two different kinds of lines. (i) Straight line and (ii) Curved line. There are three different types of straight lines. (i) Horizontal lines, (ii) Ver…