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.

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

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

Solution: r + 7

Solution: p + 9

Introduction to Algebra