# Addition of Literals

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Suppose we are asked to find the sum of two numbers, say 3 and 4. The sum of 3 and 4 is denoted by 3 + 4. Exactly in the same way, the sum of the literal x and a number 8 is denoted by x + 8 and is read ‘x plus 8’, which can also be read as ‘8 more than x,’ or ‘increase x by 8’.

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.

**properties of Addition of Literals**

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

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

a + b = b + a

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

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

**Identity**: For any literal a, we have

a + 0 = a = 0 + a, where 0 is known as additive identity

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

(i) The sum of y and 2.

**Solution:**y + 2

(ii) 4 more than a number y.

**Solution:**y +4

(iii) x added to 8.

**Solution:**x + 8

(iv) Increase x by 5

**Solution:**x + 5

(v) The sum of x and 6 added to z

**Solution:**(x + 6) + z

(vi) y added to the sum of z and 4

**Solution:**y + (z + 4)

(vii) The sum of a and b

**Solution:**a + b

(viii) The sum of c and 4

**Solution:**c + 4

(ix) r added to 7

**Solution:**r + 7

(x) Increase p added 9

**Solution:**p + 9

**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

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